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Investigations of semiconductor laser modulation dynamics and field fluctuations
Citation
Newkirk, Michael Avery
(1991)
Investigations of semiconductor laser modulation dynamics and field fluctuations.
Dissertation (Ph.D.), California Institute of Technology.
doi:10.7907/98ma-fx75.
Abstract
Active-layer photomixing is an optical modulation technique to probe the fundamental modulation response of a semiconductor laser. By heterodyning two laser sources with a tunable frequency difference in the device's active region, the gain, and hence the optical output, is modulated at the beat frequency of the sources. Using an equivalent circuit model for the laser diode, the optical modulation is shown to be decoupled from the electrical parasitics of the laser structure. The fundamental modulation response of the laser can thereby be studied independently of the parasitic response, which would otherwise mask the fundamental response. The photomixing technique is used on GaAs/GaAlAs lasers at room temperature, liquid nitrogen and liquid helium temperature, and it is verified that the modulation response appears ideal to millimeter-wave frequencies.
Application of the active-layer photomixing technique led to the discovery and explanation of a new effect called the "gain lever." It enhances the modulation efficiency of a semiconductor laser with a quantum well active layer. By inhomogeneously pumping the device, regions with unequal differential gain are created. If the laser is above threshold, then the overall modal gain is clamped, and by modulating the section with larger differential gain, the output power can be modulated with greater than unity quantum efficiency.
The fundamental coupling between intensity noise and phase noise in semiconductor laser light is investigated. This coupling, described by the [alpha] parameter, causes the well-known linewidth enhancement, but also implies the fluctuations are correlated. By the technique of "amplitude-phase decorrelation," the intensity noise can be passively reduced by the ratio 1/(1 + [alpha](2)). Using a Michelson interferometer as a frequency discriminator, intensity noise from a DFB laser is reduced below its intrinsic level up to a factor of 28.
A balanced homodyne detection scheme is used to study the noise reduction in relation to the photon shot noise floor. The decorrelated intensity noise can be reduced to within a dB of the shot noise level. Reduction below shot noise may be inhibited by uncorrelated phase noise in the lasing mode.
Item Type:
Thesis (Dissertation (Ph.D.))
Degree Grantor:
California Institute of Technology
Division:
Engineering and Applied Science
Major Option:
Applied Physics
Thesis Availability:
Public (worldwide access)
Research Advisor(s):
Vahala, Kerry J.
Thesis Committee:
Unknown, Unknown
Defense Date:
21 May 1991
Record Number:
CaltechETD:etd-07102007-112900
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DOI:
10.7907/98ma-fx75
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Investigations of Semiconductor Laser
Modulation Dynamics and

Field Fluctuations

Thesis by

Michael Avery Newkirk

In Partial Fulfillment of the Requirements
for the Degree of

Doctor of Philosophy

California Institute of Technology
Pasadena, California
1991

(Defended May 21, 1991)

Michael Avery Newkirk

ill

to Lily

Acknowledgments

I wish to express deep thanks to my parents (who may read at least this far into
the dissertation). Now they can stop wondering if I’m ever going to finish school.
I especially thank my advisor, Kerry Vahala. I have thoroughly enjoyed working
with him and learning from him. He has shared with me many seminal ideas and
a beautiful laboratory in which to do research. I know I will always look back with
pride on what we accomplished.

Of course, everyone in the Vahala group who has helped make the pursuit of
a Ph. D. more interesting deserves to have their name in print: Michael Hoenk,
Pete Sercel, John Lebens, Charles Tsai, Jay Dawson, Namkyoo Park, and Winston
Saunders. Good luck to all of you. Others who have helped out in dire times include
Bill Bridges, Steve Sanders, Lars Eng, Hal Zarem, Ed Croke, Ed Yu, and especially
Carl (Chiick) Krill. Also, the assistance of Vicky Arriola, Rosalie Rowe, and Larry
Begay is much appreciated.

Many of the experiments in this thesis were performed with lasers and detectors
supplied by Ortel Corporation. Those from Ortel who have donated their time and
expertise are Joel Paslaski, T. R. Chen, Kam Lau, Hank Blauvelt, Nadav Bar-Chaim,
Norman Kwong, and Amnon Yariv. I also thank Tom Koch of AT&T Bell Labs for
his cooperation.

Regarding my financial support, I gratefully acknowledge fellowships from IBM
Corporation and Rockwell International. I also appreciate the opportunity I had to

moonlight as a T.A. for APh 50 for three years. In addition, the National Science

Foundation and the Caltech Program in Advanced Technologies provided funding for
much of the research in this thesis.

Special thanks go to my grandfather, who first exposed me to the amazing world
of Caltech and JPL. I also thank Prof. David Park of Williams College with whom I
spent a valuable year of independent study in physics.

Finally, my deepest thanks go to my wife, Lily. Your understanding and love

during these past five years have been the greatest.

Abstract

Active-layer photomixing is an optical modulation technique to probe the fun-
damental modulation response of a semiconductor laser. By heterodyning two laser
sources with a tunable frequency difference in the device’s active region, the gain, and
hence the optical output, is modulated at the beat frequency of the sources. Using
an equivalent circuit model for the laser diode, the optical modulation is shown to
be decoupled from the electrical parasitics of the laser structure. The fundamental
modulation response of the laser can thereby be studied independently of the parasitic
response, which would otherwise mask the fundamental response. The photomixing
technique is used on GaAs/GaAlAs lasers at room temperature, liquid nitrogen and
liquid helium temperature, and it is verified that the modulation response appears
ideal to millimeter-wave frequencies.

Application of the active-layer photomixing technique led to the discovery and
explanation of a new effect called the “gain lever.” It enhances the modulation effi-
ciency of a semiconductor laser with a quantum well active layer. By inhomogeneously
pumping the device, regions with unequal differential gain are created. If the laser
is above threshold, then the overall modal gain is clamped, and by modulating the
section with larger differential gain, the output power can be modulated with greater
than unity quantum efficiency.

The fundamental coupling between intensity noise and phase noise in semiconduc-
tor laser light is investigated. This coupling, described by the a parameter, causes

the well-known linewidth enhancement, but also implies the fluctuations are corre-

vil

lated. By the technique of “amplitude-phase decorrelation,” the intensity noise can
be passively reduced by the ratio 1/(1 + a”). Using a Michelson interferometer as a
frequency discriminator, intensity noise from a DFB laser is reduced below its intrinsic
level up to a factor of 28.

A balanced homodyne detection scheme is used to study the noise reduction in
relation to the photon shot noise floor. The decorrelated intensity noise can be reduced
to within a dB of the shot noise level. Reduction below shot noise may be inhibited

by uncorrelated phase noise in the lasing mode.

vill

Contents

1 Introduction 1
1.1 Semiconductor lasers ..........-. 00 ee eee eee eae 1
1.2 Outline ofthe thesis ........20...020..2.2.0 000000 bene 4

2 Active-layer photomixing: Parasitic-free modulation of a semicon-

ductor laser 11
2.1 Introduction... 2... 11
2.2 The physical principles of active-layer photomixing .......... 14
2.2.1 Photomixing in a semiconductor... ...........000.4 14
2.2.2 What is active-layer photomixing?. ............... 18
2.2.3 Relationship to heterodyne detection .............. 18
2.3 The fundamental modulation response of a semiconductor laser ... 19

2.4 Active-layer photomixing vs. conventional current modulation: Equiv-
alent circuit model .. 2... 2... ee 28
2.4.1 Equivalent circuit for conventional current modulation .... 29

2.4.2 Intrinsic impedance of the laser diode. ............. 30

2.4.3 Equivalent circuit for active-layer photomixing ........ 34
2.5 Experimental implementation of active-layer photomixing ...... 35
2.6 Fundamental modulation response of a TJS laser diode ........ Al
2.7 Low-temperature modulation response of a TJS laser diode. ..... 47
2.7.1. Experimental details ..............2..02.-208. AT
2.7.2 The effects of low temperature on a laser diode ........ 48
2.7.3 Experimental results... 0... ee ee 51
2.8 Active-layer photomixing to millimeter-wave frequencies ....... 58

2.8.1 Detection of high-frequency modulation with a Fabry-Perot in-

terferometer . . 6... ee 59

2.8.2 Modulation sidebands in the field spectrum .......... 63
2.8.3 Experimental details .................0.2-0-, 65
2.8.4 Experimental results ..............-02.22.200, 66
2.8.5 Sideband detection to higher frequencies ............ 68

2.9 Conclusion. . 2... 2. 72

The gain lever: Enhancing the modulation efficiency of quantum

well lasers 79
3.1 Introduction... 2... 2... 2 ee 79
3.2 Intuitive model of the gain lever. ........-.........04.-. 80
3.3 Rate equation formulation of the gain lever... ............ 84
3.4 The gain-lever limit and saturable absorption ............. 86

3.5 Implementation of the gain lever. ............-.....08. 89

3.6 Experimental results 2.2... . 0.0.0... 0... .0 0-00-0000. 93
3.7 Improvements and future applications. ................. 101
3.8 Conclusion. 2... eee 103

Amplitude-phase decorrelation: Reduction of semiconductor laser

intensity noise 107
4.1 Introduction... 0.0. 107
4.2 Semiconductor laser noise ... 2... ee ee a 109

4.3 Intensity noise reduction with a passive, external transmission function 114

4.3.1 Transformation of field fluctuations ............... 115
4.3.2 Spectral density of transformed fluctuations .......... 119
4.3.3 Correlation properties ..........0 0-000. eee ees 124
4.3.4 Effect of a power-independent linewidth ............ 129
4.4 Intensity noise reduction with a dispersive, intracavity loss element . 132
4.5 Experimental results 2.2... . 0... 2 eee ee ee ees 135
4.6 Conclusion. 2... 2 ee eee 147

Semiconductor laser intensity noise reduction and the photon shot
noise floor 153
5.1 Introduction... 0... ee 153
5.2 Laser intensity noise measurement with a balanced homodyne detector 154
5.2.1 Balanced homodyne detection ...............24. 155
5.2.2 Experimental details ........0..0.0 0.00. ce ee eee 159

5.2.3 Experimental results 2... 0.0.0... ee ee 160

5.3

5.4

Amplitude-phase decorrelation in relation to the photon shot noise floor 164

5.3.1 Experimental results .................020000, 166
5.3.2 Amplitude-phase decorrelation at the quantum level... .. . 172
Conclusion. . 1... 2. ee 173

List of Figures

2.1 Optical absorption in a direct-gap semiconductor ........... 16
2.2 Similarity between active-layer photomixing and optical heterodyne
detection 2... 2... 20

2.3 Fundamental modulation response of a GaAs/GaAlAs TJS laser diode 26

2.4 Equivalent circuit model for conventional current modulation... . . 31
2.5 Intrinsic impedance of the laser diode vs. frequency .......... 33
2.6 Equivalent circuit model for active-layer photomixing ......... 36

2.7 Loading of active-layer photomixing modulation by the depletion layer
capacitance . 2... 37

2.8 Schematic diagram of the experimental setup for active-layer pho-

tomixing 2... ee 39
2.9 Measured modulation response of a TJS laser ............. 44
2.10 Resonance frequency squared vs. bias current ............. 45
2.11 Damping rate vs. resonance frequency squared ............. 46
2.12 L-I characteristic at three temperatures. ..............., 50

2.13 Lasing spectrum of the TJS at three operating temperatures ..... 52

2.14

2.15

2.16

2.17

2.18

2.19

2.20

2.21

2.22

3.1

3.2

3.3

3.4

3.5

3.6

3.7

xii

I-V characteristics of the TJS at three operating temperatures ... .

Active-layer photomixing modulation response data at three tempera-

Square of resonance frequency vs. output power per facet... ....
Damping rate vs. square of resonance frequency ............
Graphical evaluation of modulation sideband detection ........
Laser field spectrum and modulation sidebands ............
Schematic diagram of millimeter-wave photomixing experiment... .

Modulation response of the GaAs/GaAlAs laser to millimeter-wave

frequencies 2...

Fiber/grating bandpass filter... ............. Lee

Modal gain vs. carrier density fora 100 A quantum well .......

Differential modal gain vs. carrier density for a 100 A GaAs quantum

Schematic picture of a quantum well laser divided into control and
slave sections 2...
Schematic diagram of the experimental setup. .............

Scanning electron micrograph of the top surface of the quantum well

Schematic cross section of the GaAs/GaAlAs laser with a single 100 A
quantum well embedded ina GRINSCH .................

Output power modulation amplitude vs. absorbed input power... .

4.1

4.2

4.3

4.4

4.5

4.6

4.7

4.8

4.9

4.10

4.11

4.12

4.13

4.14

4.15

4.16

5.1

5.2

5.3

0.4

XIV

Laser and a passive, external transmission function T(w) ....... 115
The transmission function as a frequency discriminator ........ 117
Low-frequency intensity noise level vs. slope .............. 121
Noise reduction spectrum... 1... 0. ee 123
Maximum noise reduction and optimum slope vs. frequency ..... 125
Cross-spectral density of the field fluctuations ............. 127
Rotation of the correlation ellipse by T(w) ......5........ 130
Laser with a frequency-dependent intracavity loss y(w) ........ 133
Schematic diagram of the experimental arrangement including a Michel-

son interferometer .. 2... 2. ee 137
Measured DFB laser linewidth vs. inverse power. ........... 138
Scanning the Michelson interferometer by one fringe. ......... 140
Experimental noise loops... 2... 2... ee ee ee 142
Theoretical noise loops... 1... 143
Cross-section of noise loops ....... 0... 00. eee eee 144
Measured spectrum of noise reduction... ............20-0. 146
Experimental noise loops for a DFB laser with jaJ~5 ........ 148

Schematic diagram of the intensity noise measurement setup including

the balanced homodyne detector. ..........0...0 000000084 158
DBR laser intensity noise and the shot noise level vs. output power . 161
Confirmation of shot noise level measurement ............. 163

RIN of the DBR lasing mode and the SNL vs. incident optical power 165

5.0

5.6

5.7

5.8

Noise loops in relation to the shot noise level at low bias ....... 167
Noise loops in relation to the shot noise level at high bias... .... 168
Intrinsic RIN and reduced RIN in relation to the shot noise level... 169

8 parameter vs. incident laser power .............0000.% 171

Chapter 1

Introduction

1.1 Semiconductor lasers

Since the first reports of lasing emission from a semiconductor p-n junction device
in 1962 [1]-[4], semiconductor lasers have developed at a remarkable pace [5], [6].
Initially, the high injection current densities needed to reach lasing threshold caused
severe heating problems. Lasing action could only be generated continuously at low
temperature or in pulsed operation at room temperature. Device lifetimes were short.
Since that time, fabrication technology and device design have progressed to the
point where lasers with extrapolated room temperature lifetimes of a century are
commonplace. Because of their low cost, reliability, low power consumption, and
capability for high-speed modulation, among other features, semiconductor lasers
are attractive sources of coherent light for a variety of applications. Most notably,
semiconductor lasers are beginning to play a major role in the expanding lightwave

communications industry.

The semiconductor material systems for laser fabrication are generally of two main
types, the GaAs/GaAlAs system and InP/InGaAsP system. In a conventional buried
heterostructure design, the laser’s active region (where the lasing occurs) is composed
of a lower bandgap material, such as GaAs, which is surrounded by higher bandgap
material, such as GaAlAs, in order to confine the injected carriers (the source of
the optical gain) and to guide the optical mode. GaAs/GaAlAs devices typically
have lasing wavelengths in the range 0.7-0.9 wm while InP/InGaAsP devices can
be made to operate at longer wavelengths within the 1.1-1.6 wm range. There are
many applications which dictate the choice of lasing wavelength. For instance, longer
wavelength lasers are required for long-distance terrestrial optical communication
because the wavelength region of minimum loss for silica fiber occurs near 1.55 ym.
In an optical disk memory, where information is read or written by a focused laser
beam, a shorter wavelength laser is advantageous because the light may be focused
to a smaller spot, increasing the storage density.

Specialized laser structures are currently fabricated to optimize specific features
of their performance. A few important examples are listed here. Lasers designed
for high-speed intensity modulation can have direct modulation bandwidths of over
10 GHz, allowing information to be conveyed on an optical carrier at very high
rates [7], [8]. In contrast to the more conventional Fabry-Perot laser cavity formed
by the cleaved semiconductor crystal facets, single-frequency lasing (side-mode sup-
pression > 30 dB) is achieved in distributed feedback and distributed Bragg reflector

cavity configurations [9]. Improved single-frequency sources which have a narrow "

linewidth [10] and tunability [11], [12] are also being developed. These types of
devices will be necessary components of future coherent lightwave communication
systems. Lasers with a quantum-well (i.e., quasi-two-dimensional) active region have
been fabricated which have sub-mA threshold current [13], and proposed lasers with
lower-dimensional quantum-confined active regions (i.e., quantum wires and quantum
dots) promise enhanced modulation performance and even lower thresholds {14], [15].
Arrays of low-threshold lasers are envisioned in a future optically-interconnected com-
puter. Furthermore, semiconductor lasers designed for mode locking can emit a con-
tinuous stream of short optical pulses at a very high repetition rate, up to 100’s of
GHz [16], [17]. Optical pulse trains will be useful for high-speed timing in synchronous
systems, such as an optical computer or a phased-array radar.

Apart from their many applications, semiconductor lasers are intrinsically interest-
ing from a physicist’s point of view. For example, a semiconductor laser can be used as
a miniature laboratory to investigate fundamental dynamics of the intra-cavity pho-
ton and carrier populations by modulating the gain and observing the lasing output.
The modulated laser light can thus provide a window into the interactions taking
place within the active region. The interplay between the carriers and photons in
the active region is also responsible for a variety of peculiar phenomena. An exam-
ple of this is the fluctuations, or noise in the laser output arising from spontaneous
emission. Noise is an important practical concern because it degrades the fidelity of
information encoded on the beam of light. Nevertheless, in a semiconductor laser the

amplitude and phase components of the field fluctuations are strongly coupled, in

contrast to the more typical case where spontaneous emission perturbs the amplitude
and phase of the lasing field independently. This coupling enhances the fundamental
laser linewidth by a large factor, as is well known, but the full implications of the

amplitude-phase coupling remain to be explored.

1.2 Outline of the thesis

In this thesis, experiments and accompanying theory are presented to investigate
fundamental aspects of semiconductor laser modulation and noise.

Chapter 2 covers “active-layer photomixing,” an experimental technique to probe
the fundamental modulation response of a semiconductor laser [18]-[24]. The fun-
damental response is important because it depends on only a handful of basic laser
parameters, such as the carrier spontaneous lifetime and the differential gain, and
therefore yields insight into these parameters and the physics of lasing in semicon-
ductors. Ordinarily, the fundamental response is not directly accessible to measure-
ment because electrical parasitics in the device structure can dominate the measured
response, especially at high frequencies. By active-layer photomixing, the fundamen-
tal modulation response of the laser can be studied independently of the parasitic
response. In the technique, two laser sources with a tunable frequency difference are
heterodyned in the semiconductor laser’s active region. This modulates the gain,
and hence the optical output, at the beat frequency of the sources. Using an equiv-
alent circuit model for the laser diode, the optical modulation is shown to be decou-

pled from the parasitic circuit. The active-layer photomixing technique is used on

a GaAs/GaAlAs transverse junction stripe laser at room temperature, liquid nitro-
gen and liquid helium temperature, and it is verified that the modulation response
appears ideal to millimeter-wave frequencies (> 30 GHz).

In chapter 3 we discuss the “gain lever,” an effect which enhances the modulation
efficiency of quantum well semiconductor lasers [25], [26]. The gain lever arises in a
quantum well because of the special behavior of the optical gain as a function of carrier
concentration. By inhomogeneously pumping the active layer, regions with unequal
differential gain are created, and by modulating the region with larger differential
gain the output power can be modulated with greater than unity quantum efficiency,
i.e., one injected carrier can generate more than one additional lasing photon. Experi-
ments with a GaAs/GaAlAs quantum well laser show enhanced modulation efficiency
in accordance with the gain lever mechanism.

In chapter 4 the subject switches from laser modulation to laser noise with a dis-
cussion of “amplitude-phase decorrelation” [27]-[29]. Implications of the fundamental
coupling between intensity noise and phase noise in semiconductor laser light are in-
vestigated. The amplitude-phase coupling causes the well-known enhancement of the
fundamental laser linewidth by a factor 1+a*, where a is the linewidth enhancement
parameter, but it is shown theoretically that this inherent coupling can be exploited
to reduce intensity noise below its intrinsic level by a factor of 1/(1 +a). When this
occurs, the amplitude and phase fluctuations of the field are decorrelated. Exper-
imentally, the decorrelation technique is applied to passively reduce intensity noise

from an InGaAsP distributed feedback laser below its intrinsic level up to a factor of

28.

Because amplitude-phase decorrelation can potentially reduce intensity noise by
such a large factor, it is important to determine where the reduced noise stands in
relation to the fundamental shot noise floor. In chapter 5 we use a balanced homodyne
detection scheme to simultaneously measure laser intensity noise and the photon shot
noise level. Although the decorrelated intensity noise can be reduced to within a dB
of the shot noise level, reduction below the shot noise level appears to be inhibited
by uncorrelated phase noise in the instantaneous frequency fluctuation spectrum.

Work presented here is contained in the following published articles and conference

proceedings [18]~[30].

Bibliography

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S. Sanders, L. Eng, J. Paslaski, and A. Yariv, “108 GHz passive mode locking
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M. A. Newkirk and K. J. Vahala, “Parasitic-free measurement of the fundamental
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K. J. Vahala and M. A. Newkirk, “Measurement of the intrinsic direct modulation
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[20]

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M. A. Newkirk and K. J. Vahala, “Low temperature measurement of the fun-
damental frequency response of a semiconductor laser by active-layer photomix-
ing,” presented at 11th Int. Semiconductor Laser Conf., Aug. 29 - Sept. 1, 1988,
Boston, MA, postdeadline paper PD14.

M. A. Newkirk and K. J. Vahala, “Low-temperature measurement of the funda-
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Appl. Phys. Lett., vol. 54, pp. 600-602, 1989.

K. J. Vahala and M. A. Newkirk, “Parasitic-free modulation of semiconductor
lasers,” IEEE J. Quantum Electron. vol. QE-25, pp. 1393-1398, 1989.

M. A. Newkirk and K. J. Vahala, “Measurement of the fundamental modulation
response of a semiconductor laser to millimeter wave frequencies by active-layer
photomixing,” Appl. Phys. Lett., vol. 55, pp. 939-941, 1989.

M. A. Newkirk, K. J. Vahala, T. R. Chen, and A. Yariv, “A novel gain mechanism
in an optically modulated single quantum well semiconductor laser,” presented
at Conf. on Lasers and Electro-Optics, April 24-28, 1989, Baltimore, MD, paper
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K. J. Vahala, M. A. Newkirk, and T. R. Chen, “The optical gain lever: A novel
gain mechanism in the direct modulation of quantum well semiconductor lasers,”
Appl. Phys. Lett., vol. 54, pp. 2506-2508, 1989.

M. A. Newkirk and K. J. Vahala, “Amplitude-phase decorrelation: A method for
reducing intensity noise in semiconductor lasers,” IEEE J. Quantum Electron.,
vol. QE-27, pp. 13-22, 1991.

K. J. Vahala and M. A. Newkirk, “Intensity noise reduction in semiconductor
lasers by amplitude-phase decorrelation,” presented at XVII Int. Quantum Elec-
tron. Conf., May 21-25, 1990, Anaheim, CA, postdeadline paper QPDP29.

K. J. Vahala and M. A. Newkirk, “Intensity noise reduction in semiconductor
lasers by amplitude-phase decorrelation,” Appl. Phys. Lett., vol. 57, pp. 974-976,
1990.

[30] M. A. Newkirk and K. J. Vahala, “Investigation of the intensity noise level of a 1.3
pm InGaAsP DFB laser by measurement with a balanced homodyne detector,”
presented at Opt. Fiber Comm. Conf., Feb. 18-22, 1991, San Diego, CA, paper
WG3.

Chapter 2

Active-layer photomixing:
Parasitic-free modulation of a

semiconductor laser

2.1 Introduction

The modulation properties of semiconductor lasers are of great interest due to their
importance in optical communication systems. Simply by modulating the laser’s bias
current, information may be written directly onto the light beam at GHz rates. The
light may then be conveyed by optical fiber for tens of kilometers with very little
loss. Because optical fiber has such an enormous bandwidth, on the order of THz,
the capacity of the laser/fiber system is not constrained by the fiber’s transmission
bandwidth. For this reason, it is desirable to push the modulation bandwidth of

_ the laser to its theoretical limit. This requires a full understanding of the physics of

high-speed modulation in semiconductor lasers.

Active-layer photomixing is an experimental technique, developed in our labora-
tory, to study the modulation properties of a semiconductor laser. The name “active-
layer photomixing” describes the interaction of two coherent optical fields which are
absorbed in the laser’s active layer. The beating between the fields produces a pop-
ulation of electrons and holes which oscillate at the beat frequency and subsequently
modulate the output power from the device. The advantage of this technique is that
it allows one to probe the fundamental, or intrinsic modulation response of the laser,
virtually free of device parasitics. Injection current modulation of the laser, on the
other hand, is governed by a superposition of the intrinsic response and the parasitic
response. At high frequencies, the modulation behavior is dominated by the electrical
parasitics, masking the laser’s intrinsic response.

Observation of the laser’s intrinsic response function, uncontaminated by parasitic
effects, provides insight into the physics of lasing in semiconductors. Agreement
between the measured response and the theoretically predicted response may also
justify the validity of the rate equations from which the theoretical response function
is derived. We note that the modulation data in this chapter represent the first direct
measurements of the fundamental modulation response of a semiconductor laser.

In this chapter, the physical principles of the active-layer photomixing technique
as well as experimental results are discussed. For completeness, the fundamental
modulation response of a semiconductor laser is derived from a set of rate equations

for the photon and carrier populations. The parasitic-free nature of the photomixing ©

technique is also justified in terms of an equivalent circuit model for photomixing
which may be compared to an equivalent circuit for conventional current modulation.

Three sets of experiments are described. First, the active-layer photomixing tech-
nique is used to modulate a transverse-junction stripe (TJS) laser at room tempera-
ture. Several tests of ideality are applied to the measured response, and no parasitic
effects are observed. Second, the technique is used in a low-temperature experiment.
A TJS laser is cooled to temperatures as low as 4.2 K and modulated by photomixing
at rates up to 15 GHz. The laser is cooled for two reasons. One, semiconductor
laser dynamics change in dramatic ways at low temperature. Two, the parasitic-
free nature of active-layer photomixing is further demonstrated because the device
parasitics become especially severe at low temperature. Finally, the response of a
buried-heterostructure laser is measured to millimeter-wave frequencies (> 30 GHz).
For this experiment, not only is the modulation generated optically but detected
optically with a Fabry-Perot interferometer.

The semiconductor lasers used in the active-layer photomixing experiments in
this chapter are GaAs/GaAlAs devices with lasing wavelengths near 0.8 um [1]-[7].
Since the introduction of the active-layer photomixing technique, however, others
have applied a related parasitic-free optical modulation technique to the study of

longer wavelength InP/InGaAsP lasers [8]-[12].

2.2 The physical principles of active-layer photomixing

In this section we provide a simple picture of the physical principles of the active-
layer photomixing technique. We also indicate the relationship between active-layer
photomixing and ordinary optical heterodyne detection. First, the physics of pho-

tomixing must be reduced to its essentials.

2.2.1 Photomixing in a semiconductor

Consider two plane-polarized plane waves of frequencies w; and we, with w, & we,
normally incident on a semiconductor slab. The incident electric field vector is given
by

E(t) = E, cosw,t + Ey, cos wot (2.2.1)

where for simplicity the spatial dependence is ignored and the waves are in phase at
the time origin. Let the photon energies of the waves, hw; and hw2, be greater than
the bandgap energy of the material, assumed to be a direct gap semiconductor such as
GaAs, so that the light is strongly absorbed. Because the dipole matrix element for the
| absorptive transition is isotropic, the absorption rate does not depend on the absolute
orientation of the E-field vector. By Fermi’s Golden Rule, the absorption rate per
unit volume is a function of the square of the electric field amplitude. Electron-hole
pairs are created at a rate proportional to |E(t)|?, and the carrier generation rate,
m(t), has a steady-state and a time-dependent part resulting from the beating of the

two fields.

m(t) x |E(t)/? = |E, cosuyt + E, cos wet?

= 5 (IEA? + |E2|*) + Ey - Ez cos(w, — wa)t. (2.2.2)

Components of m(t) which oscillate at the optical frequencies w,, w2 and w, +w» have
been temporally averaged. As shown above, the carrier generation rate is modulated
at the difference frequency of the incident fields, and the strength of this modulation
depends on the relative polarization of E, and Ep.

A simple two-band diagram in Fig. 2.1 shows what happens to an electron-hole pair
after absorption of an input photon. Because the k quantum number of the electron
is approximately conserved, and the transition energy is greater than the bandgap,
the electron is sent high into the conduction band above the band-edge energy. The
carriers are quite hot in comparison to the thermal energy of the system. They quickly
cool to their respective band edges where they remain until they recombine.

This picture of the carrier dynamics is based on the important fact that intraband
transitions occur on a much faster timescale than spontaneous interband transitions.
Although these issues comprise an active area of study, for a semiconductor such
as GaAs it is generally understood that intraband relaxation times are near 107)” s
while band-to-band spontaneous transition lifetimes are on the order of 10-° s. Re-
cent pump-probe experiments with ultrashort laser pulses in GaAs have measured
separate relaxation times for hot electrons as they cool to the electron temperature
(0.3 x 107!? s) and to the lattice temperature (1.5 x 107!? s) [13]. In comparison to
timescales relevant to this thesis, these intraband relaxation processes are practically
instantaneous. Consequently, the carrier pool within each band maintains thermal

equilibrium even though the electron and hole populations may not be in thermal

CONDUCTION
BAND
Ros Annan
ho, nr ane
kK

ens

H.H. VALENCE
BAND

Figure 2.1: Sequence of events in a direct-gap semiconductor when a photon is absorbed.
An electron is excited high into the conduction band and rapidly decays to the band edge.
The hole similarly relaxes to the valence band edge. When two fields at frequencies w, and

wa are incident, the carrier transition rate is modulated at the beat frequency w; — we.

equilibrium with each other. This is the conventional justification for a description
of the carrier populations based on quasi-Fermi levels.
In equilibrium, the occupancy of states in a given band is governed by the Fermi

distribution. The electron concentration is given by
+00
N= / p(E — E.)f.(E) dE (2.2.3)

where p.(£) is the density of states in the conduction band, E, is the energy of the

band edge, and f, is the Fermi factor, defined as

F(E) ~~ ¢ (E-F.)/kaT +17

(2.2.4)

Here, F, is the quasi-Fermi level for the conduction band, kg is Boltzmann’s constant,
and T is the temperature of the crystal lattice. We see that, for T constant, if N
changes by optical pumping or some other means, then the quasi-Fermi level must
also change.

Returning to (2.2.2) and Fig. 2.1, it is clear that the carrier population is coherent
with the generation rate a(t), since the photo-excited carriers tumble down the band
and rapidly equilibrate with the carrier pool. Equivalently, the quasi-Fermi level
F, in (2.2.4) is coherent with x(t). Of course, we must assume that the inverse
beat frequency of the mixing fields, 1/(w, — w2), is much less than the intraband
relaxation time. From the above discussion, this condition may be satisfied for beat
frequencies approaching 100 GHz. Thus, by photomixing two coherent fields in a
semiconductor, it is possible to drive the carrier populations at ultra-high frequencies

while maintaining thermal equilibrium within each carrier pool.

2.2.2 What is active-layer photomixing?

Active-layer photomixing is a clean, optical technique to probe the fundamental lasing
dynamics of a semiconductor laser. In active-layer photomixing, the coherent input
fields described above are selectively mixed in a semiconductor laser’s active region.
Because optical gain in a semiconductor is a function of the carrier population, the
technique provides a means to high-frequency modulate the gain by driving the car-
riers at the beat frequency. This allows one to study the fundamental dynamics of
the interaction between the gain and the lasing mode of the semiconductor laser.
Clearly, the benefits of optical modulation are (1) the modulation may be gener-
ated at arbitrarily high frequency by tuning the beat frequency of the mixing sources,
and (2) the carriers are produced directly in the active region where they immediately
influence the optical gain. In addition, by bringing the mixing beams to a point focus
it becomes possible to locally modulate the carrier density over a small portion of
the laser’s active region. In fact, by point modulating a semiconductor laser with a
quantum-well active layer, a new gain mechanism was discovered—the “gain lever” —
which is the topic of chapter 3. Active-layer photomixing is therefore a unique tool

with which to study semiconductor laser dynamics.

2.2.3 Relationship to heterodyne detection

Active-layer photomixing may be viewed as a relative of ordinary optical heterodyne
detection. Both methods involve the mixing of two coherent optical fields to generate

a response at the difference frequency. In a typical heterodyne detection scheme, the

two fields are absorbed in the intrinsic region of a p-i-n photodiode. The oscillating
carrier population is swept from the generation volume with a static electric field,
and the beating between the input fields modulates the photocurrent at the difference
frequency. This is illustrated in Fig. 2.2, where the photocurrent spectrum is given
by a peak at w, —w. The essential feature is that the mixing of the light creates
carriers which are coupled out of the detector as a modulated current. In active-layer
photomixing, by constrast, the two fields are mixed in a laser diode’s active region
where, because the intrinsic impedance of the active region is very small (see section
2.4), the photocarriers remain to modulate the optical gain. So far the modulation
has not been recovered. But because the semiconductor laser is above threshold, the
oscillating gain remodulates the semiconductor laser output at the beat frequency
Ww, — Ww 2. Assuming that the device is lasing at a single frequency wz, the result is
that sidebands are generated at wz + (w — w2) (see Fig. 2.2). In this sense the beat
frequency of the input fields has been detected through the appearance of sidebands

on the optical carrier.

2.3 The fundamental modulation response of a semiconduc-

tor laser

The starting point for treatment of the modulation response of a laser diode is the
pair of single-mode spatially-averaged rate equations for photon density in the lasing

mode, P, and carrier density in the active region, N. For above-threshold operation,

6)
aD

OPTICAL HETERODYNE DETECTION

ACTIVE-LAYER PHOTOMIXING

Figure 2.2: Similarity between active-layer photomixing and optical heterodyne detection.
Heterodyning two fields on a detector modulates the photocurrent at the beat frequency,

while active-layer photomixing generates sidebands on the lasing frequency.

the rate equations may be written as [14]

d P

a? = TG(N,P)P-— +0 (2.3.1)
< N = —G(N,P)P —R(N)+1 (2.3.2)

where G is the optical gain, [is the mode confinement factor, 7, is the photon lifetime,
© is the spontaneous emission rate into the lasing mode per unit volume, R is the
carrier spontaneous recombination rate per unit volume, and II is the pumping rate
in units of carrier density per second.

Some of these terms need to be clarified. The gain, G, is not only a func-
tion of the inversion, NV, but of photon density as well. This accounts for power-
dependent mechanisms which tend to reduce the gain as mode power increases (non-
linear gain) [15], [16]. Because the active region is usually smaller than the lasing
mode volume, the confinement factor, [ (< 1), is needed to account for the incomplete

spatial overlap. The photon lifetime, 7,, is defined as

= = (a; + in(-)) (2.3.3)

T m4
where c is the speed of light, m; is the refractive index of the active layer, L is the
cavity length, and r is the facet reflectivity. +, measures the damping of the photon
population due to (useful) facet loss and internal loss, a;, such as waveguide scattering
and free-carrier absorption.

The rate equations are linearized by first decomposing the dynamic variables N(t),

P(t), and II(t) into a steady-state part and a small, time-varying part

P(t) = P,+>p(t) where p(t)/P, <1, etc. (2.3.4)

22
N(t) = N,+n(t) (2.3.5)

M(t) = I, +7(t). (2.3.6)

Then, the gain and spontaneous recombination rate are Taylor expanded to first order

about the operating point (P,, N,).

G(MO),PO) = GNP) +nOgTG(N,P.)| + Pg EOWa PI],
= Go+n(t)gn + p(t)gp (2.3.7)
RIM) = RUN) +n()ERWN)|
- p+ rl) (2.3.8)

Tsp
Here, g,, is the differential gain, g, is the non-linear gain, and 7,, is the carrier spon-
taneous lifetime. Substituting these expansions into the rate equations, and neglect-

ing products of small-signal quantities, the following time-independent equations are

found
P,
[G.P, -—+90 = 0 (2.3.9)
Tp
—G,P, -—R,+, = 0. (2.3.10)

Equation (2.3.9) shows the familiar gain clamping condition whereby the steady-
state modal gain TG, equals the loss plus a contribution from spontaneous emission.
Often the spontaneous term may be neglected. Equation (2.3.10) shows that the laser
power above threshold varies linearly with pumping rate. Continuing, we also find

the small-signal rate equations

jy = T(GotopP.)p t+ TonPon — © (2.3.11)
dt Tp

a, > —g,P.n _ (G, + IpPo)p ~ — +7 (2.3.12)
dt Tsp

which may be Fourier transformed with respect to frequency 2 to yield the small-
signal modulation response. In matrix form, the transformed equations are
(TG, + Tg,P. - a +i) l'9,P, p(Q) 0
(Cot gpPo) — -(gnPo + + -i9) } | a) ~#(9)
Inverting the 2 x 2 matrix gives

p(2) D gn Pe it(Q)
D(Q)

n(Q) (TG, +P 9pPo — 7 + i)
where the resonant denominator, D((), is a lengthy expression.

. 1 ] nPo 1 1
D(Q) = 2? —iX(g,P, + — —TG, —TopP, + —)+ Gn"? _ (TG, 41 9,P, - —).
p Pp

sp Tp Tsp
(2.3.13)
D(Q) may be simplified using the gain clamping condition (2.3.9) and the fact that the
(T9,P.)/Tsp term may be neglected in comparison to the (g,P,)/T» term (for a laser

with a typical 300 um cavity length, the carrier spontaneous lifetime is 2-3 orders of

magnitude greater than the photon lifetime, whereas g, ~ I'g,). As a result,

. 1 QO, gnP,
D(Q) = — —i0(9,P, + — —To,P, + —) +4

Tsp P, Tp

(2.3.14)

The small-signal modulation response functions for the photon density and carrier

density may then be written compactly in their final form.

. lgnP, .
p(Q) = oh? yn) m(Q) (2.3.15)

. —(U9pPo — B+ i)
Q) = 2 i 3.
n(Q) oA 7 (2) (2.3.16)

where wr, the relaxation oscillation resonance frequency, and ¥, the relaxation oscil-

lation damping rate, are defined as

wr = [Ste (2.3.17)
Tp
= 142469, -Ty)P (2.3.18)
7 7 Tsp P, In 9p °" a

The response functions (2.3.15) and (2.3.16) are fundamental in the sense that they
stem from the basic laser dynamics as modeled by the rate equations. These functions
therefore yield insight into the physics of lasing in semiconductors. Because the cavity
photon density is directly proportional to the laser output power, #(9) governs the
fundamental modulation properties of the laser output. Equation (2.3.15) shows
that p(Q) is equivalent to the response of a damped harmonic oscillator. Important
features of (2.3.15) are: The response is flat at low frequencies, there is a resonance at
the natural frequency of the coupled photon/carrier system (the relaxation resonance,
wr [23]), the width of the resonance is governed by the damping, 7, and the response
decays as 1/?, or 20 dB/dec, beyond the resonance.

The response function for the carrier density (2.3.16) is similar to #(Q), as they
share the same resonant denominator. The low-frequency behavior is quite different,
however, because of the 7. term in the numerator. If not for the g, term, at high
output power the carrier density would be perfectly clamped near de (i.e., % — 0).
At high frequencies beyond the resonance, the carrier and photon populations are in
quadrature. Equation (2.3.16) will be used later for evaluating the intrinsic impedance
of the laser diode.

In the laboratory, modulated semiconductor laser light is detected with a photo-

diode, and the ac photocurrent power from the detector is measured as a function
of frequency with an electronic microwave spectrum analyzer. Consequently, what is
measured is proportional to |p(Q)|*?. From (2.3.15), the measured intensity modula-

tion response of the laser is given by

o (T9nP.)*
(wR — 07)? + 70?"

ae) (2.3.19)

(Q)

Figure 2.3 shows a calculated response function for a GaAs/GaAlAs semiconductor
laser (the transverse junction stripe laser discussed in the following sections) at two
different bias levels. The response is normalized by its low-frequency value. As
output power increases, the resonance frequency moves out to higher frequencies, in
accordance with (2.3.17). One important feature of the fundamental response |p(2)|?
is that it eventually rolls off as 1/*, or 40 dB/dec at high frequencies beyond the
resonance.

From an optical communications standpoint, wr serves as the definition of the
practical modulation bandwidth of a semiconductor laser. It is therefore desirable
to increase wR as much as possible. From (2.3.17), we see that wr depends on three
parameters, differential gain, photon density, and photon lifetime. Much progress
has been made in extending vp ( = wp/(27)) beyond 10 GHz by the use of multiple
quantum well active layers to increase g,, [17], [18], window structures or tight optical
confinement to increase P, [19], [20], and short cavity lengths to reduce 7, [21], [22].

The overall shape of the fundamental response |f({)|* is characterized by just two
parameters, the relaxation resonance frequency, wr, and the damping rate, y. Both

of these parameters may easily be determined from the resonance peak of the ideal

ro)

mo
ro

oo
ro)

RELATIVE MODULATION (dB)

aan
>)

0.1

0.2

0.5

MODULATION FREQUENCY (GHz)

Figure 2.3: Calculated fundamental modulation response |p|? for a GaAs/GaAlAs TJS laser

at two different bias levels (1.17 J, and 1.54 Ij,, where Jy, is the threshold current). The

Tesonance moves out to higher frequencies as a function of laser bias. The response decays

at 40 dB/dec beyond the resonance.

response function. If the resonance reaches its maximum value at the frequency Omer
with relative height |f(Qmax)/p(0)|?, then

wp = Roe (2.3.20)

a0) |’
to aes

and the damping rate is found from

4? = 2(w2 —?,,,). (2.3.21)

By extracting wr and y from a series of response curves at different laser bias levels,
the dependence of these parameters on output power can be compared with theory.

From (2.3.17) and (2.3.18), wa and y can be reexpressed as

w, = gnke (2.3.22)
Tp
1 0 Tgp
Y= i + B + Trwp(1 + a? (2.3.23)
= Yo + Tpwh(1 + Pigol,) (2.3.24)

where y. is a power-independent contribution to the damping (the O/P, term is
negligible except for operation very near threshold). It can be seen that w}, is a linear
function of laser output power, whereas ¥ is expressible as a linear function of w.
In addition to spontaneous and stimulated recombination, the carrier density in
the active region may be damped by diffusion and other effects [24]. Although such
mechanisms were not explicitly included in the original set of rate equations(2.3.1)
and (2.3.2), additional independent damping rates may easily be incorporated in
the power-independent spontaneous damping term, y,, to account for all sources of -

damping to the carrier population.

In summary, the rate equations predict that the fundamental modulation response
of the laser diode (2.3.19) is flat at low frequencies, has a damped resonance near the
relaxation oscillation frequency, wr, and eventually rolls off at 40 dB/dec beyond the
resonance. In addition, w}, is a linear function of laser power, and the damping rate,
+ is a linear function of w}. All of these features can be used to test the ideality

of the measured response function when the laser is modulated by the active-layer

photomixing technique.

2.4 Active-layer photomixing vs. conventional current mod-

ulation: Equivalent circuit model

When directly modulating the current to the laser diode, electrical parasitics in the
device packaging and the laser structure will divert modulation current from the
active region. The response of the laser to conventional current modulation is thus a
superposition of the fundamental response, given above, and the parasitic response.
The fundamental modulation response is therefore obscured by the parasitic loading,
especially at high frequencies.

In this section we show that, unlike conventional current modulation, active-layer
photomixing is a parasitic-free modulation technique. By modeling the laser diode
in terms of an equivalent electrical circuit [3], including an equivalent impedance for
the active region, it will be seen that the modulation generated by the photomixing

is effectively decoupled from the parasitic circuit at all frequencies.

29
2.4.1 Equivalent circuit for conventional current modulation

The fundamental response p()/7#(Q) (2.3.15) is the reponse of the photon density
to modulation of the carrier density in the active-region. The conventional means for
applying the modulation is through modulation of the laser’s bias current. However,
electrical parasitics will influence the degree to which the injection current modulation
translates into carrier density modulation. In other words, the pumping rate II(t)
in (2.3.2) is a function of the bias current I(t) flowing to the device which must
additionally drive an external parasitic circuit not accounted for in the rate equations.

In the frequency domain, the small-signal quantities are related by
#(Q) = Hrc(2)i(2) (2.4.1)

where Hprc(Q) is the parasitic response function. The response function for con-
ventional current modulation, p(Q)/%(Q), is thus a superposition of the fundamental

response and the parasitic response. That is,

l9nP,
we — 2? — 17D

(2.4.2)

The fundamental response is thus obscured by the parasitics, especially at high fre-
quencies. For an example of how parasitics may dominate the measured response
function, see [25].

The parasitic circuit is a combination of many things. Among them are the induc-
tance of the bond wire, series resistance and capacitance of the contact layer, and the
capacitance of the p-n junction’s depletion region. Some of these impedances may be

reduced by careful design of the laser and mount. However, they can only be reduced

so far. For instance, the depletion layer capacitance is unavoidable because the p-n
junction is integral to the structure of a laser diode.

An equivalent circuit for conventional current modulation of the laser diode is
shown in Fig. 2.4. The current source i({) is coupled into the circuit through the
bond wire. The laser’s active region is represented by an equivalent impedance,
Z(Q), discussed below. It can be seen that there are parasitic paths through the
depletion capacitance C'p and contact-layer capactance C which divert current around
the active layer. Typical values for the parasitic impedances are R = 10 2, C =
10 pF, Cp = 10 pF, and L = 1 nH. Because |Z({)| is extremely small (see below),
by inspection of the figure the parasitic response is primarily governed by the parallel
combination of the contact layer capacitance, C, and resistance, R. The corner
frequency of this RC circuit is about 1.6 GHz for the values given above. Reductions
in C’, and improvements in the parasitic corner frequency, have been obtained for
devices on semi-insulating substrates [26]. Nevertheless, even for optimal tailoring
of the parasitics, there will always be some high-frequency cut-off beyond which the

parasitic response dominates the modulation response of the laser.

2.4.2 Intrinsic impedance of the laser diode

In order to model the semiconductor laser by an equivalent circuit, it is useful to
describe the laser diode by an effective impedance [27]. This impedance is given by
Z(Q) = 6(Q)/i,(Q) where @ is the small-signal voltage amplitude across the junction,
i.e., the quasi-Fermi level separation, and iz is the small signal injection current

amplitude into the active region. The voltage is related to the carrier density #(()

Convential Current Modulation
Equivalent Circuit Model

—_—_——

SL
R —™
_”
=—=c
cL Z(Q) tL
“TC D LASER
°@

Figure 2.4: Equivalent circuit model for conventional current modulation of a laser diode.

The active region is represented by an effective impedance Z(Q).

(2.3.16) by the following expression [28]

_ MkgT A(Q)

7 ON (2.4.3)

5(2)

where kg is Boltzmann’s constant, T is the lattice temperature, g is the electron

charge, N, is the average carrier density, and M is given by

N 1 1
were Me (Ag), 244
2+ 7 Aly tN, 244)

Here, N, and N, are the effective density of states for the valence and conduction
band, respectively.

Using i, (2) = gV7(Q), where V is the active region volume, the intrinsic impedance
is

MkpT $- —V9pP. — i
G@VN, wh —2? — iV

Z(Q) = (2.4.5)

Using values for g,, wp, and -y measured for a GaAs transverse junction stripe laser dis-
cussed below, |Z((2)| is plotted in Fig. 2.5 for several photon densities corresponding
to output powers from 0.5 mW to 10 mW. |Z()| peaks at the relaxation resonance
frequency, but overall the impedance is rather small. At low frequencies, |Z()| is on
the order of 10’s of milli-Ohms. Intuitively, the intrinsic impedance is small because
the gain saturation impels the carrier density to clamp to its threshold value. The
junction voltage is therefore clamped, giving rise to a small impedance. The finite
impedance at low frequency in Fig. 2.5 results primarily from the nonlinear gain term
Gp- If this term were absent, then the low-frequency impedance at high output power

would approach zero.

VA
10-1 YW N
ZO

10-2 XN

|Z(Q)| (Ohms)

0 0.1 1 10 100

MODULATION FREQUENCY (GHz)

Figure 2.5: Intrinsic impedance of the laser diouc vs. frequency. Characteristics correspond,

from left to right, to output powers of 0.5, 1.0, 5.0 and 10 mW per facet.

34
2.4.3 Equivalent circuit for active-layer photomixing

As shown below, the advantage of active-layer photomixing is that the laser can be
modulated nearly independently of the parasitics. Initially, this may appear obvious
because the carriers are optically generated directly in the active region instead of
being injected from the outside world. No matter how the carrier population is being
modulated, however, an oscillating carrier density implies that the separation between
the quasi-Fermi levels, and hence the junction voltage, is also oscillating (see (2.2.4)).
We must therefore evaluate how this voltage interacts with the parasitic circuit before
we may claim that the active-layer photomixing technique is parasitic-free.

An equivalent circuit model for active-layer photomixing is shown in Fig. 2.6. The
parasitic circuit is identical to Fig. 2.4, but for photomixing the optical modulation
within the active region is equivalent to a current source 2((2) across the intrinsic
impedance Z(]). Parasitic current paths through the contact-layer resistance and
depletion capacitance are shown in the figure. Because |Z(Q)| < R, the only potential
source of any significant parasitic loading is through Cp. The impact of this loading
can be measured by the following transfer function,

in 1

% 1+iNCpZ(Q)’ 246)

Figure 2.7 shows |%;,/2| for two laser power levels and several values of Cp. The impact
of parasitics on the active-layer photomixing modulation is evident near the relaxation
resonance frequency, but only for large Cp is any capacitive loading apparent. At
higher modulation frequencies beyond the resonance the small amount of parasitic

loading is actually diminished, in contrast to conventional current modulation where

the parasitics only become worse at higher modulation frequencies. For the laser
diode discussed below, Cp is estimated to be less than 10 pF. From the figure, we see
that for Cp < 10 pF, the optical modulation generated by active-layer photomixing

is effectively decoupled from the parasitic circuit at all frequencies.

2.5 Experimental implementation of active-layer photomix-

ing

In order to perform active-layer photomixing in a semiconductor laser, there are some
basic experimental requirements which must be met. First of all, two single-frequency
lasers are needed for the photomixing sources, and at least one of them must be
tunable. Returning to Fig. 2.1, it is apparent that the optical frequency of the mixing
beams is not critical so long as the photon energy exceeds the band gap energy
of the semiconductor material in the active layer. However, it is often preferable
to photomix through the top surface of the laser diode. This is possible because
in a conventional buried heterostructure semiconductor laser, the active region is
surrounded by higher bandgap material in order to confine the carriers and to guide
the optical mode. For surface pumping, the mixing light is thus constrained to a range
of photon energies where the active region is absorbing but the overlying material is
transparent. Alternatively, the active region may be optically modulated through one
of the facets. Because the mixing light is strongly absorbed, however, this approach
accelerates facet degradation which may lead to premature failure of the device under

study.

Photomix Induced Modulation
Equivalent Circuit Model

Cc
; aa Z(Q)
4 7 Cp LASER

Figure 2.6: Equivalent circuit model for modulation of a laser diode by active-layer pho-

tomixing .

1.0 OS i ae c==—
he ‘ tee y" saeaaasd
. \ aosoerne” plates
\ i, ‘ \. i .
4 Ms 4
0.9 oo
—— Cp = 1 pF bho
--- Cp = 10 pF
esene Cp = 50 pF
0.6

0.1 1 10 100
MODULATION FREQUENCY (GHz)

Figure 2.7: Loading of active-layer photomixing modulation by the depletion layer capaci-

tance for several values of Cp. Characteristics are shown for laser output powers of 1 mW

(low-frequency dip) and 10 mW (higher-frequency dip).

A typical experimental setup for active-layer photomixing is shown in Fig. 2.8.
The photomixing sources are provided by a Kr ion laser and a tunable dye laser.
Either the Kr line at 752.5 nm or 676.4 nm was used at different times for surface
pumping a GaAs/GaAlAs laser diode. These two Kr wavelengths satisfy the need
for absorption in the GaAs active layer and transmission through the surrounding
GaAlAs. The dye laser, pumped by an Ar ion laser, operates at these wavelengths
by running either Pyridine 2 or DCM laser dye, respectively.

Both lasers are single frequency. The Kr laser is forced to run single frequency
by an intra-cavity etalon, while the dye laser has multiple intra-cavity etalons and a
tunable birefringent filter. The free-running Kr laser maintains an effective linewidth
of about 20 MHz, which is caused by mechanical vibrations in the resonator, primarily
from cooling water flow. The dye laser, on the other hand, is electronically locked
to an external cavity, maintaining an rms linewidth of 500 kHz. Since the two lasers
are independent of each other, the beatnote spectrum is dominated by the jitter in
the Kr lasing frequency, giving a beatnote linewidth of about 20 MHz. The dye
laser frequency may be electronically scanned continously over 30 GHz without mode
hopping.

The two laser outputs are focused into single-mode optical fibers. A 50/50 fiber
coupler is then used to combine the mixing beams into the same fiber. Initial overlap
of the two frequencies is accomplished by first directing the output from one arm of the
fiber coupler into a 0.75 m grating spectrometer. The dye laser is mode jumped until

the two laser frequencies fall within 10 GHz, the resolution of the spectrometer. We

M LL
} ———73 > SPECTRUM

ANALYZER
FIBER

COLLIMATING
LENS

CYLINDRICAL
LENS f..

BEAM
SPLITTER

NAT NS ——S[S===

TV MONITOR

FOCUSING
LENS

DETECTOR
LASER DIODE

COLD STAGE #

Figure 2.8: Schematic diagram of the experimental arrangement for modulation of a semi-

conductor laser by active-layer photomixing.

then illuminate a photodiode with the mixed light and scan the dye laser frequency
until the beat frequency falls within the bandwidth of the photodiode. A beatnote
in the photocurrent then appears on an electronic spectrum analyzer. The dye laser
scan offset is then adjusted until the beat frequency can be continuously scanned
from 0 to 30 GHz. Of course, higher beat frequencies are obtained simply by mode
jumping the dye laser.

So that the maximum power is available for optical modulation (see (2.2.2)), the
polarizations of the mixing beams need to be aligned at the output of the fiber coupler.
In our experiment, the relative polarization is controlled by squeezing one of the input
fibers between two metal plates using a PZT. The polarization can be rotated in this
way because a single mode fiber becomes birefringent when stressed [29].

A p-i-n photodiode is used to detect the intensity modulation of the semiconductor
laser. Of course, the measured response of the laser diode will be superposed with
the frequency response of the detector. However, a side benefit of the active-layer
photomixing technique is that the mixing beams may first be used to accurately
calibrate the response of the detector by heterodyning the beams on the detector and
scanning the beat frequency [30], [31]. The detector response may then be factored
out of the measured laser diode response.

Efficient coupling of the mixing light into the narrow (~ 3 ym) active region
of a laser diode proved to be experimentally challenging. A video camera with an
infrared-sensitive vidicon is used to image the top surface of the laser diode on a

CRT. The camera, in conjunction with a microscope objective lens, serves as a video

microscope. First, the laser is slightly forward biased so that the luminescent stripe
from the active region is visible. Because of the beam splitter, the back reflected
mixing light is also visible, and this enables rough alignment of the pump light into
the active region. Then, the bias voltage to the laser is turned off, and the pump
focus is adjusted to maximize the dc photocurrent in the biasing circuit induced by
the pump light. By using the laser diode in this way as a photodetector, the coupling
into the active-region can be brought reasonably close to the optimum. Next, the
laser is biased above threshold and the photomix-induced beatnote is monitored on
a microwave spectrum analyzer while making final adjustments to the pump focus.
Finally, the fiber squeezer is tweaked to maximize the modulation power by bringing

the polarizations of the mixing beams into alignment.

2.6 Fundamental modulation response of a TJS laser diode

In this section, the active-layer photomixing technique is used to measure the funda-
mental frequency response of a GaAs/GaAlAs semiconductor laser to 12 GHz [1], [2].
Well beyond the relaxation resonance, the theoretically predicted 40 dB/dec rolloff in
the response is observed. Other features of the measured response function are also
observed to be the theoretical ideal.

The device used in this experiment is a Mitsubishi GaAs transverse junction stripe
(TJS) laser diode with a 16.2 mA lasing threshold and lasing wavelength of 838 nm.
This particular device has a transparent contact to facilitate the photomixing process.

It was mounted in a low-frequency hermetically-sealed capsule which was disassembled

for the experiment. As shown in Fig. 2.8, the mixed pump light is focused by a
cylindrical lens and microscope objective to a stripe coincident with the active region.
In this way we can couple uniformly into the active region over the entire length of
the device. The modulation signal is detected with a p-i-n photodiode (Ortel PD050-
OM). An optical isolator with 35 dB isolation (not shown) suppresses feedback to the
laser diode and rejects any scattered pump light going to the detector. The detected
microwave photocurrent is measured with an HP 8565A spectrum analyzer combined
with an HP 8349B amplifier. We calibrated the detection system—p-i-n photodiode,
amplifier and cables—to 20 GHz by photomixing directly on the detector, as discussed
above. A storage normalizer is then used to subtract the detector response from the
measured modulation characteristics. The cold stage was not used in this room
temperature experiment.

The beat frequency power incident on the active region of the semiconductor laser
is approximately 7 mW, which takes into account a 30% Fresnel reflection from the
contact layer. The intensity modulation index of the semiconductor laser output
may be found from the ratio of the amplitude of the ac photocurrent to the dc
photocurrent induced in the detector. The modulation index is 5.6% and 10.3% well
below the resonance for a 28 mA and 22 mA bias, respectively.

Plots of the observed modulation response (normalized by their low-frequency
value) at different bias currents appear in Fig. 2.9. Data points are only given on two
curves for clarity. The data for the 25 mA characteristic extend as far 12 GHz (the

high-frequency cut-off in the data is caused by the noise floor in the detection system,

which rises as a function of frequency). We note the resonances are clearly defined.
For each characteristic we also observe the ideal 40 dB/dec rolloff well beyond the
resonance. This is most easily seen on the 17, 19, and 22 mA characteristics where the
data extend to several multiples of the resonance frequency. By use of (2.3.20) and
(2.3.21) we can extract from these characteristics wp and + for each bias level. A plot
of v3, where vp = wp/(27), versus laser bias current, proportional to output power,
appears in Fig. 2.10. These data exhibit the theoretical linear behavior predicted by
(2.3.22).

The damping rate, 7, can be expressed as
Y= + Kw (2.6.1)

where 7. includes the power independent sources of damping and K = 7,(1 + Feel) (see
(2.3.24)). The theoretical linear relationship between 7 and w?, is verified in Fig 2.11.
The slope and intercept of the fitted line yield estimates for y, and K of 0.84 GHz
(corresponding to a carrier spontaneous lifetime of 1.2 ns) and 6.2 ps, respectively.
Based on a photon lifetime for this device of 3 ps, differential gain parameter of
2.5 x 10~§ cm® sec™!, and mode confinement factor of 0.4, then |g,| is determined to
be 6.9 x 10~-® cm? sec™!.

In conclusion, we have measured the intrinsic modulation response of a
GaAs/GaAlAs TJS laser diode by the active-layer photomixing technique. The mea-
sured response characteristics appear to be ideal, and there is no indication of any
parasitic effects. Well beyond the resonance, the theoretically predicted 40 dB/dec

rolloff is observed. The dependence of the resonance frequency and damping rate on

0.1 0.2 0.5 1 2 5 10 15
10 10
o~
wa! ¥ ad oe wt \
Z \
Oo
= -10 -10
a -40 dB /DECADE \ \ WW 28
Oo mA
= N
lu 25mA
= -20 \ . ——|-20
- 22
Si 19maA [mA
or
~30 \ 17mA “30
0.1 0.2 0.5 1 2 5 10. 15

MODULATION FREQUENCY (GHz)

Figure 2.9: Measured modulation response at different bias levels. The resonance peaks and
40 dB/dec rolloff at high frequency are clearly visible, indicating the abscence of parasitic

effects.

20/ -
Lo)
PS
10+ 4
(@)
fe)
i ; {
15 20 25 30

I (mA)

Figure 2.10: Square of the resonance frequency vs. bias current. The ideal linear relationship

is predicted by the rate equations.

oO
i @ ie
oO
= o£
4-
2 Il i i j it i 1 !
0 2 4 6 8 10

@ p?(1x 10” rad?/sec?)

Figure 2.11: Damping rate y vs. w}. The ideal linear relationship is predicted by the rate

equations.

laser output power are also observed to be the theoretical ideal.

2.7 Low-temperature modulation response of a TJS laser

diode

In this section, we use the active-layer photomixing technique to directly modulate
the output of a GaAs/GaAlAs TJS laser operating at cryogenic temperatures [4]-
[6]. Our objective in these low-temperature experiments is twofold. First, the laser
dynamics change in dramatic ways at low temperature [32]. From the measured re-
sponse functions, the relaxation resonance frequency and the damping rate can be
extracted. The temperature dependence of these parameters can then be compared
with theory. Second, the parasitic-free nature of the photomixing technique can be
further verified because the device parasitics become especially severe at low temper-
ature. For instance, at 4.2 K, the parasitic RC’ corner frequency is estimated to be
410 MHz, yet the response of the TJS laser measured by active-layer photomixing

appears ideal out to 15 GHz.

2.7.1 Experimental details

The experimental arrangement for the low-temperature measurements is similar to
the layout shown schematically in Fig. 2.8, the main difference being that the laser
is mounted on a copper heat sink in a low-temperature cryostat under vacuum con-
ditions (5 x 10~® Torr). The cryostat may be operated with either liquid nitrogen or

liquid helium. It is also equipped with a resistive heater and temperature controller to

maintain the heat sink within a degree of the desired temperature. Because efficient
optical coupling into the laser diode’s active region requires sub-micron mechanical
stability, however, it proved necessary to allow sufficient time (= 1 hr.) for thermal
stresses in the mount and supporting column to equilibrate. For this reason, the
heater was turned off, and the measurements were performed only at room tempera-
ture, liquid nitrogen temperature (77 K), and liquid helium temperature (4.2 K).

For the TJS laser, the photomixing light at the 752.5 nm wavelength used in the
room-temperature measurement of the previous section is less efficiently absorbed
in the active region at low temperature. Because the band gap increases as the
semiconductor crystal is cooled (see below), the GaAs becomes less absorbing at this
wavelength. We therefore switched to a shorter pump wavelength, using the 676.4 nm
Kr line and converting the dye laser to run DCM dye. The GaAs is more strongly
absorbing at this shorter wavelength from room temperature down to 4.2 K, while
the GaAlAs cladding layer remains transparent. This wavelength was then used for
all subsequent photomixing experiments.

A pair of quartz windows positioned at right angles on the vacuum chamber pro-
vides access to the top surface and front facet of the TJS laser. Because the working
distance from the chamber window to the laser is about 5 cm, high-quality lenses

were required to provide the best possible diffraction-limited focus.

2.7.2 The effects of low temperature on a laser diode

When a semiconductor laser is cooled, many things happen. Among them: the thresh-

old current decreases, the lasing wavelength shifts to shorter wavelengths, the differ-

ential gain increases, and the series resistance of the contact layer increases. Many of
these effects stem from the temperature dependence of the Fermi distribution func-
tion, which becomes more step-like as temperature goes down (see (2.2.4)). However,
each of these effects will be dicussed in turn.

A sharper Fermi factor at low temperature causes the gain spectrum to narrow
considerably [33]. Consequently, the carrier density required to reach threshold is
correspondingly reduced [34]. In Fig. 2.12, light output power from the TJS laser
versus bias current (L-I characteristic) is shown at three temperatures. Threshold
current decreases from 14.3 mA at room temperature to 0.63 mA at liquid helium
temperature. There appear to be no ill effects from cooling on the laser, because the
L-I characteristics are highly linear at all three temperatures.

A narrower gain spectrum also enhances the differential gain [35]. This has a direct
effect on the fundamental modulation response, because the relaxation resonance is
pushed out to higher frequencies for a given output power. This will become evident
when the low-temperature modulation data are presented below.

The band gap of the semiconductor is also dependent on temperature [36]. Upon
cooling, the thermal contraction of the crystal lattice increases the width of the direct
gap. Therefore, as the temperature is lowered the lasing wavelength moves to shorter
wavelengths. Figure 2.13 shows the lasing spectrum at three temperatures. The
wavelength shifts from 823 nm at room temperature, to 787 nm at liquid nitrogen
temperature, and to 782 nm at liquid helium temperature. Interestingly, the TJS is

seen to be fairly single-mode at 293 K and 77 K, but becomes multimode at 4.2 K.

| | J | | | i i }
25/ :
S oL |
z 2
= 15} 4
QO
}—
_)
Ou
o 4k
mm)
re)
0.54 4
{ | | nga } j {
0 12 3 4 5S%10 15 20 25
BIAS CURRENT (mA)

Figure 2.12: Lasing output power versus injection current (L-I characteristic) at three

temperatures. The threshold current is 14.3 mA at room temperature and falls to 0.63 mA

at liquid helium temperature.

The reason for this is not known.

A further low-temperature effect on the TJS is that the resistance of the contact
layer increases owing to the freezing-out of excess carriers. The parasitic response is
thus degraded, because the RC corner frequency of the parasitic circuit (see Fig. 2.4)
decreases as R increases. Current-voltage characteristics for the laser diode at forward
bias are shown in Fig. 2.14. The differential resistance dV/dI increases from 7 2 at
room temperature to 39 2 at liquid helium temperature, over a factor of five increase.
Assuming a typical 10 pF contact layer capacitance for this device, the parasitic RC
corner frequency is only 410 MHz at 4.2 K. Conventional current modulation of the

laser at microwave frequencies thus becomes very inefficient at low temperature.

2.7.3 Experimental results

Typical response curves at each temperature for optical modulation of the TJS are
shown in Fig. 2.15. The bias levels are adjusted so that each curve corresponds to an
output power of approximately 2 mW per facet. We see that the resonances are clearly
defined, and that the relaxation resonance frequency increases considerably as the
temperature is lowered. In addition, the room temperature response curve eventually
rolls off at the theoretical 40 dB/dec rate. The high-frequency cut-off in the data
results from the limited photodetector bandwidth and noise floor of the microwave
spectrum analyzer. As mentioned above, the parasitic RC corner frequency is about
410 MHz at 4.2 K, yet there is no effect on the measured response curve, with the
data appearing to be ideal out to 15 GHz.

Modulation response functions for many different output power levels were mea-

T { i t i ii

6r _
Q T=42K T=77K T=293K
= |
S55
} a
@ gt -
YQ) 3b 4
za .
tu
zm = 4

1 = —

WAU WL. - L wi _ rw fp | ASA,
781 783 785 787 789 821 823 825

WAVELENGTH (nm)

Figure 2.13: Lasing spectrum at three operating temperatures. The lasing wavelength shifts

from 825 nm at room temperature to 782 nm at liquid helium temperature.

F _ dV/dl = 392

a dV/dl = 17

E _

dV/dI = 7Q

——- =

_———
——
-_——
oe oe ee ome

VOLTAGE (V)
an

esseseseuen ~ 42K
-~—— 77K
r 293°K
1 L L L i LL. | L
0 5 10 15 20
CURRENT (mA)

Figure 2.14: The differential resistance of the TJS laser increases from 7 Q at room tem-
perature to 39 Q at liquid helium temperature. The two low-temperature characteristics
have sharp knees at turn-on and are indistinguishable from the asymptotes. Also note the
turn-on voltage increases as temperature is lowered, another manifestation of the increasing

band gap energy and concomitant increase in quasi-Fermi level separation at threshold.

10 7 207K 77

oot

-40 dB/DECAD

RELATIVE MODULATION (dB)

23mA

0.5 1 Q 5 10 15 20
MODULATION FREQUENCY (GHz)

Figure 2.15: Active-layer photomixing modulation response data at three temperatures.

For each characteristic the output power is 2 mW per facet.

sured at each temperature. From these, the resonance frequency and damping rate
were extracted, in accordance with (2.3.20) and (2.3.21).

A plot of the square of the relaxation resonance frequency (vp = wp/(27)) versus
output power appears in Fig. 2.16. The theoretical linear behavior given by (2.3.22)
is seen at all three temperatures. The slope of the line increases by a factor of 7.0
and 13.6 at 77 K and 4.2 K, respectively, over the room temperature slope. Assuming
that the photon lifetime and modal volume of the lasing mode are not significantly
affected by temperature, then the increase in slope results primarily from a large
increase in g, caused by the narrower gain spectrum at low temperature.

In Fig. 2.17 the damping rate + is plotted as function of w2. For each temperature
the linear relationship predicted by (2.3.24) is observed. The slope of the fitted
line decreases from 9.3 ps at 293 K to 5.6 ps at 77 K and 4.2 K. This decrease
in slope, from room temperature to liquid nitrogen temperature, is consistent with
the theoretical expression which incorporates the nonlinear gain (2.3.24) and the
measured increase in the differential gain at 77 K. The apparent saturation in the
slope as the temperature is lowered from 77 K to 4.2 K has two possible explanations.
One is that the increased differential gain causes the I'|gp|/g, term to become much
less than unity, so that the slope is equal to the photon lifetime, t,. However, a 5.6 ps
photon lifetime is too long for a 250 um long laser with uncoated facets (see (2.3.3)).
We estimate that for this device, r, is approximately 3 ps. The remaining explanation
for the apparent saturation in the slope is that in going from 77 K to 4.2 K, the

measured increase in g, is compensated for by an increase in |g,|. Although we do

200
180L oO T=293K
Oo T=77K
iol «=| A OT#=42K
140} A
em (120 /
Ae 0
%S* 400h /
80 }-
60+
40\—
20/- /
o——O
Oo
ro L N { i
QO 5 1 15 2 25 3

OUTPUT POWER (mW)

Figure 2.16: Square of resonance frequency vs. output power per facet.

r /
/ °
[e)
st
5 fe)
“e
x EF
= a © 293K
sb
4 JL i i 1 rt | i 1 L 1
Q 1 2 3 4 5
8 (1 x 10° rad@/sec?)
60 --
% OL A a
@ 40
o ia
SF ger
x as O 77K
— 20F oa . ;
= A42«K
| ao .
0 20 40 60 80
wo (1x 107 rad*/sec?)

Figure 2.17: Damping rate vs. square of resonance frequency.

not speculate here on the many proposed origins of the nonlinear gain (e.g., spectral
hole burning [37], dynamic carrier heating [13], standing wave dielectric grating [38],
etc.) further low-temperature modulation experiments could help discriminate among
possible mechanisms.

In summary, we have used the active-layer photomixing technique to directly mod-
ulate the output of a semiconductor laser operating at cryogenic temperatures. The
technique produces parasitic-free modulation, enabling a measurement of the laser
diode’s intrinsic modulation response. Even at 4.2 K, where the parasitic corner fre-
quency is estimated to be 410 MHz, the modulation response appears ideal out to
15 GHz. From the measured response curves we find values for the relaxation reso-
nance frequency and the damping rate. Their low-temperature behavior agrees with

the simple theory incorporating the nonlinear gain.

2.8 Active-layer photomixing to millimeter-wave frequen-
cies

In this section the active-layer photomixing technique is used to measure the room
temperature modulation response of a GaAs/GaAlAs laser diode to the millimeter
wave frequency of 37 GHz [7]. The modulation sidebands in the field spectrum are
detected with an ultra-high-finesse (~ 40,000) Fabry-Perot interferometer, and the
measured response agrees with the theoretical response function. Although wide-band
millimeter wave modulation (to 38 GHz) has been reported for a cooled InGaAsP

laser with a 31 GHz corner frequency [39], in this measurement the laser diode’s

resonance frequency is only 6.5 GHz. As will be seen, with a moderately faster device
(i.e., resonance frequency ~ 10 GHz), it should be possible to directly measure the

modulation response beyond 100 GHz.

2.8.1 Detection of high-frequency modulation with a Fabry-Perot inter-

ferometer

To measure the laser diode’s modulation response, the modulated light is usually
detected with a fast p-i-n photodiode connected to an electronic microwave spectrum
analyzer, as in sections 2.5 — 2.7. The detection bandwidth of commercially available
near-infrared photodetectors, however, is limited ‘to about 20.GHz. In addition, the
photocurrent signal must compete with a noise floor in the spectrum analyzer which
typically starts at -110 dBm near de (for a 10 kHz integration bandwidth) and climbs
at a rate of 1.7 dB/GHz [40]. A much larger detection bandwidth can be obtained
by measuring the modulation signal with an optical spectrum analyzer, a scanning
Fabry-Perot interferometer (FPI). The-medulation then appears as sidebands in the
laser field spectrum. However, the ability to observe-modulation sidebands at high
frequencies depends critically on the finesse of the FPI, which should be as high as
possible. For this experiment, the FPI (Newport SR-240) has a finesse of 40,000, a
free spectral range of 8 THz, and an instrumental resolution of 200 MHz for 800 nm
light.

As shown below, beyond the resonance frequency the modulation sidebands in the
field spectrum asymptotically approach a 40 dB/dec rolloff. Clearly there exists some

high-frequency limit beyond which the sideband signal is not measurable. However,

in contrast to the electronic spectrum analyzer, the background, or noise floor, arising
from the FPI is a decreasing function of frequency. This background results from the
presence of the lasing mode ({i.e., the optical carrier) which appears as a Lorentzian
with the linewidth of the FPI, assuming the FPI linewidth is much greater than the
lasing mode linewidth, as is the case here. The tails of this Lorentzian roll off at
20 dB/dec, eventually obscuring the sideband signals. As Fig. 2.18 shows, however,
this point of intersection can be at ultrahigh frequencies, far into the millimeter wave
regime (> 30 GHz). The figure shows, in a log-log plot, a typical modulation response
function (|p|?) of a laser diode with a 10 GHz resonance frequency and relative side-
band amplitude, at the resonance, of 10%. Also shown is the background from the
optical carrier, assuming a corner frequency of 100 MHz, corresponding to a 200 MHz
linewidth for the Lorentzian. At frequencies where the modulation response function
lies above the Lorentzian, the modulation sidebands are, in principle, detectable. For
this example the high frequency detection limit can be over 150 GHz. In practice,
the background level may be raised somewhat by spontaneous emission from the laser
diode, but this did not affect our measurement.

In general, the frequency of intersection in Fig. 2.18 is given by

mu,

Q, = (2.8.1)

Qrp
where m is the modulation index, wp is the relaxation resonance frequency of the
laser, and Qyp is the 3 dB frequency of the Fabry-Perot Lorentzian. If the exper-
imental goal is to observe the modulation response of the laser diode to as high a

' frequency as possible, then (2.8.1) shows that a Fabry-Perot with a narrow linewidth

ro)

rh
‘s)

on
Oo

MODULATION RESPONSE (dB)
oO

Q, ‘\
>. ~— 150 GHz —
2r .
~70F- 4
! i i
0.1 1 10 100

MODULATION FREQUENCY (GHz)

Figure 2.18: Graphical evaluation of modulation sideband detection using a Fabry-Perot
interferometer. At frequencies where the modulation response function lies above the back-

ground Lorentzian (dashed curve), the modulation sidebands are observable.

is required, and that mw? should be maximized. To increase the modulation index
m, the photomixing power can be increased, but for facet pumping, as in this ex-
periment, the mixing power must be kept relatively low so as not to damage the
laser facet. Although it may seem possible to increase 0, by running the laser diode
at high bias, thereby pushing wr to higher frequencies, 0, is actually independent
of laser power, because m has inverse power dependence (m « p/P, whereas w?, =
GnFo/Tp). An ideal laser diode for this experiment is thus intrinsically fast, i.e., gn/Tp
is maximized, and also single mode, so that the modulation energy is not partitioned
into numerous sidebands on each lasing frequency.

The FPI used in this experiment has a 20 ym cavity and 30 cm radius of cur-
vature mirrors. In this near-planar resonator, higher-order transverse modes spaced
27.6 GHz apart may be excited by a single-frequency optical input [41]. These modes
may potentially interfere with the detection of the modulation sidebands whenever
the modulation frequency is near a multiple of 27.6 GHz. However, the higher-order
transverse modes appear only on the high-frequency side of the fundamental, whereas
the modulation sidebands appear symmetrically on both sides of the fundamental.
The low-frequency sideband can thus be tracked more readily as a function of modula-
tion frequency. Careful matching of the optical input to the fundamental transverse
mode is still required, however, because weakly excited longitudinal modes of the
semiconductor laser, spaced 140 GHz apart, may excite their own set of higher-order
transverse modes in the FPI. In our experiment, optimum mode-matching into the

FPI suppresses the higher-order transverse modes by at least 26 dB compared with

the fundamental.

2.8.2 Modulation sidebands in the field spectrum

We now examine how the intrinsic response function p() relates to the laser field
spectrum, which is what is observed at the output of a FPI. Direct modulation of
a semiconductor laser, by active-layer photomixing or injection current modulation,
affects the amplitude and also the phase of the laser field due to the dependence of

refractive index on carrier density. The time-dependent field may then be taken as
E(t) = (E, + E(Q) cos Mt) exp [i (wet + 4(M) cos Mt)| (2.8.2)

where wz, is the cw oscillation frequency and E(Q) is the small-signal field amplitude,

given by
EQ) _ 12(0)

i 73° P. (2.8.3)

i.e., the field amplitude is proportional to the photon density amplitude when they
are small-signal quantities. In (2.8.2), ¢(Q) is the response function of the phase

deviation, given by [42]

$a) = 50 (2.8.4)
where a@ is the linewidth enhancement factor. Although #(Q), E(Q), and ¢() are,
in general, complex functions, we treat them as real for our purposes since their
relative phases become zero at high frequencies beyond the relaxation resonance [16].
The field spectrum resulting from (2.8.2) consists of the center line at wz, and AM

and FM induced sidebands at wz +n, where n is an integer. For modulation

frequencies greater than the relaxation oscillation frequency, only the n = 1 sidebands

7 O +7 +28 GHz

25 GHz

Figure 2.19: Laser field spectrum observed with a scanning Fabry-Perot interferometer.
The upper photo shows the lasing line with modulation sidebands at + 7 GHz. The peak
at 27.6 GHz is a higher order Fabry-Perot mode as discussed in the text. The lower photo

shows a close-up of a modulation sideband when the laser is modulated at 25 GHz. The

decaying tail of the background Lorentzian is clearly visible.

are observable. The amplitude of these first sidebands is equal to

Alor £9) = (Boh(3())” + [58() (Jo(4(2)) — 4(4(2)))] (2.8.5)

where J,, is the Bessel function of order n. For small-signal modulation we may use

the approximation

n(x) % Sar? tand so obtain
Alwr +9) = 7 (E24(0)? + B()?) x (HM)? (2.8.7)

where (2.8.3) and (2.8.4) were used to get the final proportionality relation. The
amplitude of the first order modulation sidebands, as a function of 2, is therefore

directly proportional to the square of the intrinsic response function p(2).

2.8.3. Experimental details

The experimental arrangement appears in Fig. 2.20. The laser under study is an
Ortel GaAs/GaAlAs buried heterostructure device with a 23 mA threshold current
and lasing wavelength of 786 nm. The laser, at room temperature, is biased above
threshold by a dc injection current and the output is small-signal modulated by the
active-layer photomixing technique. For the photomixing sources we use the Kr laser
operating at 676.4 nm and the dye laser running DCM dye at the same wavelength.
These sources are collimated from the output of a 50/50 fiber coupler and focused
onto the rear facet of the laser diode, which is mounted on a narrow (300 ym) stub so

' that both facets may be accessed. A short-wavelength pass filter prevents feedback

to the rear facet from semiconductor laser light reflecting from the fiber end. The
incident photomixing power is about 2.5 mW.

The emission from the modulated semiconductor laser is focused into a 50 m long
single-mode optical fiber. An optical isolator with 40 dB isolation suppresses feedback
to the front facet, and a narrow bandpass filter prevents any scattered pumping light
from reaching the FPI. Coupling into the fiber serves the dual purpose of spatially
filtering the lasing mode and rejecting a significant amount of spontaneous emission.
Approximately 5 cm of the fiber jacket is removed at the input end and the exposed
cladding is immersed in glycerine to strip the cladding modes propagating in the
fiber. This was found to improve the mode-matching into the FPI. The output from
the fiber is coupled into the FPI cavity through a 10 cm focusing lens, and the light
transmitted through the FPI is conveyed to a photomultiplier tube (PMT) by a fiber
bundle. The PMT photocurrent is converted to a voltage signal which is amplified
and displayed on an oscilloscope whose sweep is synchronized with the FPI. The
PMT gain is then set to a high value and the input light intensity is adjusted with

calibrated neutral density filters.

2.8.4 Experimental results

Figure 2.21 shows the full modulation response of the laser diode running at a bias
current of 40.5 mA. The high-frequency data (12 GHz < 2/2 < 37 GHz) were ob-
tained by measuring the modulation sideband relative amplitude, as discussed above.
At the resonance, the relative amplitude (sideband/carrier) is 2%. For complete-

ness, the low-frequency response (2/2 < 12 GHz) is also shown. These data were

SHORT WAVE PASS pray LASER
FIBER FILTER = gpitreR DIODE
COUPLER r \

OPTICAL
ISOLATOR

VIDEO CAMERA
NEUTRAL

SPECTRUM DENSITY ny
ANALYZER FILTERS

SINGLE-MODE
FIBER 50m

OSCILLOSCOPE
ULTRA - HIGH-FINESSE

SCANNING
FABRY-PEROT
INTERFEROMETER

Figure 2.20: Schematic diagram of the experimental arrangement. The high-frequency
modulation is generated in the laser diode by active-layer photomixing, and detected with

an ultra-high-finesse Fabry-Perot interferometer.

recorded with a photodiode and microwave spectrum analyzer, because at low mod-
ulation frequencies, higher order sidebands complicate the spectrum observed on the
FPI [44], [45]. From the low-frequency data we can determine the resonance frequency
(6.5 GHz) and damping rate (4.7 GHz). A theoretical response curve based on these
parameters also appears in the figure. The high-frequency data agree reasonably well
with the theoretical curve to the highest measured frequency of 37 GHz. Again, no
device parasitic effects are observable. Notice that the modulation sideband signal
is lost approximately where the response curve and background Lorentzian inter-
sect. We mention that a slightly faster laser (wr/2m ~ 7.5 GHz for the same output
power) was modulated to 44 GHz before the sideband signal was lost in the back-
ground. Unfortunately, it catastrophically failed before a complete response curve

could be mapped out.

2.8.5 Sideband detection to higher frequencies

Equation (2.8.1) shows how the fundamental laser and Fabry-Perot parameters de-
termine the high-frequency detection limit of the modulation sidebands. For a given
laser and FPI, the response function and background Lorentzian cross at a fixed fre-
quency, 2,. However, it is possible to boost the detection bandwidth by selectively
filtering out the lasing mode carrier frequency before coupling into the FPI. This has
the effect of pushing down the background Lorentzian in Fig. 2.18, thereby increasing
Q,. We tested this idea by modifying part of the experiment as shown in Fig. 2.22.
The modulated semiconductor laser light reflects from a diffraction grating before

coupling into the optical fiber going to the FPI. Otherwise the experimental setup is

ae
oO

nN
oO

& 3

MODULATION RESPONSE (dB)
nn
(o>)

i i \ 1 1
0.1 0.3 1 3 10 30 100

MODULATION FREQUENCY (GHz)

Figure 2.21: Modulation response of the GaAs/GaAlAs laser to millimeter-wave frequencies.
The high-frequency data (+) were measured with a Fabry-Perot, and the low-frequency data
(©) were recorded with a p-i-n photodiode. The background Lorenztian (dashed curve) is

also shown.

identical to Fig. 2.20.

The idea is to use the diffraction grating in conjunction with the single-mode fiber
as a narrow bandpass filter. The grating fans the light into its spectral components,
and because the coupling efficiency into the fiber is highly sensitive to the position
of the beam focus, only those frequency components which are propagating along
the fiber/lens axis are efficiently launched into the fiber. By rotating the grating the
filter becomes tunable. Quite simply, the fiber/grating system is like a conventional
grating spectrometer where the fiber waveguide plays the role of the exit slit.

Measurements on the luminescence from the laser diode below threshold showed
that this technique, while somewhat crude, provided a narrow-band filter with a
FWHM of approximately 80 GHz. The grating (American Holographic,
2200 grooves/mm) had 85% diffraction efficiency into the first order. Thus by tuning
the filter to track one of the modulation sidebands as the modulation frequency is
increasing, the carrier could be attenuated without sacrificing much of the sideband
power.

Using this filtering technique, we observed one of the modulation sidebands out as
far as 77 GHz. However, it was difficult to make a quantitative measurement of the
sideband amplitude, as the signal was extremely weak. At these low signal levels, the
sideband did not have a definite peak, as in Fig. 2.19, but rather appeared as a fuzzy
packet which was barely distinguishable from the background noise. We were thus
unable to generate meaningful data points to fit a response function at these high

frequencies. Nevertheless, it was important to verify that generation and detection

DIFFRACTION GRATING

LASER DIODE

FOCUSING
LENS

SINGLE-MODE
FIBER

TO FABRY-PEROT
INTERFEROMETER

Figure 2.22: Fiber/grating bandpass filter. The field from the modulated laser diode is
reflected from a diffraction grating and coupled into the optical fiber. One sideband is

efficiently launched into the fiber while the carrier frequency is attenuated.

of semiconductor laser modulation was still possible even at 77 GHz. Further active-
layer photomixing experiments with an optimized laser diode and a more sophisticated

detection scheme should enable sideband detection well beyond 100 GHz.

2.9 Conclusion

Active-layer photomixing is an optical modulation technique to probe the funda-
mental modulation response of a semiconductor laser. By heterodyning two laser
sources with a tunable frequency difference in the semiconductor laser’s active re-
gion, the gain, and hence the optical output, is modulated at the beat frequency
of the sources. Using an equivalent circuit model for the laser diode, the optical
modulation was shown to be decoupled from the electrical parasitics of the laser
structure. The fundamental modulation response of the laser can thereby be studied
independently of the parasitic response. Under conventional current modulation, on
the other hand, the fundamental response would be overwhelmed by the parasitic
loading, especially at high frequencies.

The active-layer photomixing technique was used to modulate a GaAs/GaAlAs
TJS laser at room temperature, liquid nitrogen and liquid helium temperature. In all
cases there was no indication of parasitic effects and the measured response functions
appeared to be ideal. The high-frequency decay and dependence of the resonance
frequency and damping rate on laser output power agreed with the theoretical pre-
dictions. Further photomixing experiments on a GaAs/GaAlAs buried heterostruc-

ture laser showed that the modulation response appeared ideal to millimeter-wave

frequencies.

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Chapter 3

The gain lever: Enhancing the
modulation efficiency of quantum

well lasers

3.1 Introduction

When the active-layer photomixing technique was used to locally modulate a semi-
conductor laser with a quantum well active region, it was found that the modulation
efficiency was enhanced compared to what was normally observed for a semiconductor
laser with a bulk active region, such as the TJS laser discussed in the previous chap-
ter. In some instances, the quantum well laser could be optically modulated with

greater than unity quantum efficiency, i.e., one input photon could generate more

than one additional lasing photon. This enhancement in the modulation efficiency ©

indicated the presence of a new effect — the gain lever [1], [2].

The gain lever arises in a quantum well because of the special behavior of the
optical gain as a function of carrier density. Whereas, in a bulk active layer the
optical gain (at the peak of the gain spectrum) is very nearly a linear function of
the carrier concentration [3], in a quantum well the gain characteristic is highly sub-
linear because of the step-like density of states of a quasi-two-dimensional electron
gas [4]. A typical gain function for a 100 A GaAs quantum well is shown in Fig. 3.1.
This curve was calculated using a technique discussed in [5], where a confinement
factor T = 1/30 was assumed. The important feature of the gain function is that
it saturates at high carrier concentration. As a result, the slope, or differential gain
is greater for low carrier density and tends to decrease at higher carrier densities.
Therefore, by inhomogeneously pumping a quantum well laser it is possible to create
regions in the active layer with unequal differential gain. This is the basis of the
gain-lever mechanism. To explore the implications of a sub-linear gain characteristic,
an intuitive model is first developed followed by a more rigorous description based
on the small-signal rate equations. Finally, experimental results for a two-section
GaAs/GaAlAs single quantum well laser show enhanced modulation efficiency and

saturation behavior described by the gain-lever mechanism.

3.2 Intuitive model of the gain lever

Assume that we have a quantum well laser divided into two independent sections
which comprise a single laser cavity. The two sections are referred to as the control

and slave, where the choice of names will become clear presently. The rate equation

100 1 T ] T T T T

ra)

-1)

pb
Oo

rs)

CONTROL

MODAL GAIN g (c

do
rs)

| i | | | | l
0 1 2 3 4 5

CARRIER DENSITY n (1018 cm’)

-100

Figure 3.1: Modal gain vs. carrier concentration calculated for a 100 A GaAs quantum
well. This shows the origin of the gain-lever mechanism. When the control and slave
regions operate at different excitation levels, a displacement along the gain characteristic in

the control causes an enhanced change in the slave.

describing the laser photon dynamics is given by

“ =TIG.(N,)P +T0G(Ns)P — ~ (3.2.1)
Pp

where the subscript c or s denotes the control or slave section, respectively. In (3.2.1),
P is the cavity photon density, G, (G,) is the material gain of the control (slave), and
I’ is the transverse confinement factor of the optical mode. I’, (I',) is the longitudinal
confinement factor of the optical mode in the control (slave), accounting for the
relative fraction of the total cavity length occupied by each section, so that T, + T,
= 1. N, (N,) is the carrier density in the control (slave), and 7, is the photon lifetime.
In the final analysis, we will require that the control region occupy a much smaller
volume than the slave region, i.e., [, < I,. When the control region is relatively
small, it is reasonable to treat the photon density as uniform throughout the entire
cavity, as in (3.2.1), even though the gain of the two regions may be very different
(e.g., the control can be absorbing). Spontaneous emission is also neglected in (3.2.1)
to simplify the analysis.
For steady-state conditions (i.e., 4 — 0), we have from (3.2.1)

P.PG.(N.) +2,0G,(N,) —~ =0. (3.2.2)

Tp
In terms of the modal gain of the control and slave, g, and g,, where g, = TG, and
gs =TG,, (3.2.2) becomes

Pege( Ne) + l',9s(Ns) a 7 = 0 (3.2.3)

which expresses the gain clamping condition for the two-section device. Because the

cavity losses are fixed, the overall modal gain, given by the sum of the modal gain

in each region, is clamped to its threshold value. Thus any change in modal gain in
the control region must be offset by a complementary change in slave modal gain, or
I.Ag, = —I’,Ag;. By linearizing the modal gain in each region about the operating

point, we have the equivalent constraint
P.gAn, = —T,g,Ans (3.2.4)

where g/ is the differential modal gain and An; is a small-signal change in carrier
density.

Returning to Fig. 3.1, we may intuitively illustrate the gain-lever effect in a two-
section quantum well device. To make the figure readable, we assume that the two
sections occupy the same volume, so that [, = I, for the time being. In addition,
the laser is above threshold, but is inhomogeneously pumped so that the control
and slave regions operate at different excitation levels, shown by operating point 1
(OP1) in the figure. If the carrier density in the control region is now raised by an
amount An,, then the modal gain increases by Ag, = gi An,, and the control region
operating point moves to OP2. Because of the clamping constraint given by (3.2.4),
the slave modal gain must drop by an equal amount. As the slave moves from OP1
to OP2, however, there is an enhanced decrease in carrier density in this region due
to the smaller differential gain. But because the carrier injection rate into the slave
region is fixed, a decrease in carrier density in this region implies that there must be
an increase in the stimulated emission rate into the lasing mode, and corresponding
increase in optical output power. This is the basic physical mechanism responsible for

the gain lever. Because of the larger differential gain in the control region, a change

in the control carrier density can lever a larger change in the slave region than would
otherwise be possible.
3.3 Rate equation formulation of the gain lever

To describe the gain lever in a quantitative way, we write down the coupled rate

equations for the photon density and carrier density in the control and slave regions,

given by
dP = PIG.A(N.)P+0,0G,(N,)P - © (3.3.1)
dt Tp
a © = _G(N,)\P — R.(N-) +1 (3.3.2)
< = —G,(N,)P — R,(N,) +1, (3.3.3)

where R, (R;) is the spontaneous recombination rate per unit volume in the control
(slave), IT, ( II,) is the carrier injection rate into the control (slave) in units of carrier
density per second, and the other terms are defined after (3.2.1). These equations are

solved by first making the following small-signal expansions,

P(t) = P,+p(t) (3.3.4)
Ni(t) = N? +ni(t) (3.3.5)
Gi(N;) = G?+gin; (3.3.6)
RAN; = e+e (3.3.7)
II.(t) = 2? +7.(t), (3.3.8)

where 7; is the small-signal spontaneous lifetime and the subscript 2 signifies c or s ©

to denote the control or slave region, respectively. A small-signal expansion for II,

is not needed because the pumping to the slave region is constant. Substituting the

above expansions into (3.3.1)-(3.3.3), the following small-signal equations result

2 = IIgiPone+TTgiPons (3.3.9)
dn. ° ; Ne
Te GP ~ GePome — = + Me (3.3.10)
dn, ° ; Ns
Go GSP ~ 9sPos — — (3.3.11)

where we view 7, as the driving term and p as the response. For steady-state condi-
tions (2 — 0 and ani —+ 0), the slave region carrier density can be eliminated from
the above equations using the clamping constraint ['.gin, = —I',gin,. The resulting

coupled equations for p and n, can be written in matrix form as

l’.g/,
G. -(L+9 Po) | [ p 0
3J' = (3.3.12)
Go (3, + 9 Po) Me Te
The 2 x 2 matrix can then be inverted to yield the response function
Pr.
= Te 3.3.13
P Carag me

PGE + PGs (Z + 94 Po)g
which describes the small-signal change in the cavity photon density resulting from a
change in the control pumping rate.
The analysis is more revealing if (3.3.13) is expressed in terms of the control differ-
ential quantum efficiency 7,, i.e., the number of additional output photons produced
for every additional carrier injected into the control. When cavity losses are domi-

nated by facet loss (this is true for GaAs quantum well lasers, where internal losses

< 2 cm”! are possible [6]), the number of additional output photons (per second) is

pV/(T't) = p(PsG +1.G2)V, where V is the total volume of the active region and
V/T is the volume of the lasing mode. Because the number of additional input carri-
ers to the control (per second) is [.V7,, then y., the differential quantum efficiency,

is given by
..G?

_ D',G3
PeGe (++ 9,P.)g95°
P.Go (+9, Po)g9%

(3.3.14)

Equivalently,
l.G?

_ P,G3
T.G2 (1+ per) Po

TG?” (+ fe) Ps

Ne (3.3.15)

where the saturation photon density, P’** = 1/(gi7;). The saturation photon den-
sity is a useful quantity because it defines the photon density for which the carrier
stimulated lifetime (1/(g/P,)) equals the spontaneous lifetime (7;).

The gain lever in its most general form, apart from the effects of saturable ab-
sorption (see next section), is contained in (3.3.15). Enhancement in modulation
efficiency is possible when the control and slave regions operate at unequal saturation
photon densities. In particular, we see from (3.3.15) that if P** < Ps, then n, can

be greater than unity. Conversely, if the control and slave regions operate at equal

saturation photon densities, then 7, = 1, and no enhancement occurs.

3.4 The gain-lever limit and saturable absorption

Although the gain lever can occur in any two-section laser with P3 < P2**, we have

not made any definite assumptions about the relative size of the two sections. If

the gain of the two regions is comparable, where |[.G?| ~ |[,G2|, then saturable
absorption effects may occur in conjunction with the gain lever. In fact, saturable
absorption may completely dominate the modulation behavior of the laser, especially
near threshold. However, the gain lever is distinct from conventional saturable ab-
sorption. We show that in the gain-lever limit, where |[[.G?| < |I',G@|, saturable
absorption effects vanish, but the gain-lever mechanism persists.

To illustrate the effects of saturable absorption, assume that the control and slave
regions are the same size (T, = I',), the control region is unpumped and absorbing
(G2 < 0), the slave region is pumped above transparency (G? > 0), but the laser
is slightly below threshold. From (3.3.15), the differential quantum efficiency for

modulation of the control is given by

-IGel

+1
Gs
Ne ~ —|G?| pst ° (3.4.1)
Ge Pt

If the control region saturates differently from the slave, or P3** #4 P25, then n, will
become singular as the slave region is pumped harder and ial => Fa Roughly
speaking, this describes a discontinuous jump in the laser output power as the gain
contributed by slave section bleaches the absorption of the control section [7]. Such
a laser may be bistable, exhibiting hystersis in output power as a function of pump-
ing to the slave section [8], [9]. It is true that 7, was derived assuming a uniform
photon density throughout the cavity, and for the conditions stated above the pho-

ton density is certainly not uniform. Nevertheless, this example shows qualitatively

how conventional saturable absorption effects may turn the laser into a device with a

highly non-linear transfer characteristic, akin to an optical flip-flop. The important
point is that saturable absorption behavior may be predominant when the impact of
the control region gain on the lasing mode is comparable to the impact of the slave
gain.

In order to avoid effects due to conventional saturable absorption, we must require
that any saturable loss from the control be insignificant compared to the nonsaturable
losses in the cavity. This can be ensured by limiting the control region to a small
fraction of the total cavity volume, so that , the control region gain on the lasing is completely negligible. Thus in the gain-lever
limit, where T.G2/T,G3 — 0, we have from (3.3.15)

_ NO + ye) 3.4.2
= pa Pay (3.4.2)

Ne
Equation (3.4.2) reveals the gain lever without the complications of conventional
saturable absorption. There are three important features of this result. First, the
modulation enhancement is seen to be independent of the actual size of the control
and slave regions, so long as the condition [,G?/T,G° — 0 is satisfied. Second, at
low power, where P, < P3*', the modulation enhancement is governed by the ratio

of the saturation photon densities in the two regions. The maximum enhancement is

thus given by
Pet giTe

mar —
; .
937s

Ne = Psat (3.4.3)

Although the the intuitive model (see Fig. 3.1) indicated that the amount of leverage
depends on the ratio of differential gains in the two regions, (3.4.3) shows that the

ratio of the saturation photon densities is the controlling variable. Third, at high

output power, where P, >> P5*‘, the gain lever becomes less effective. Ultimately, the
differential quantum efficiency approaches unity, describing a one-for-one conversion
of input carriers to the control to output lasing photons. This negation of the gain
lever at large intracavity photon densities is merely a lifetime effect. Quite simply,
as P, — oo, the control carrier lifetime is dominated by its stimulated component
(1/(gP,)) which tends to saturate the inversion. It thus becomes more difficult
to affect the control region carrier concentration, and hence the control gain, by

modulating the pumping to this section.

3.5 Implementation of the gain lever

As stated above, the gain lever in its most general form (3.3.15) occurs in any two-
section laser where P** < P3**, However, a quantum well laser provides an ideal
structure in which to implement the effect. In a quantum well, the two components
of saturation photon density, carrier spontaneous lifetime and differential gain, are
dependent on carrier concentration (more so for differential gain). It is thus a simple
matter to force P3** < P%* by inhomogeneously pumping the quantum well active
layer.

Differential modal gain as a function of carrier concentration for a typical 100 A
GaAs quantum well appears in Fig. 3.2. This is the derivative of the gain characteristic
in Fig. 3.1. As the carrier density is reduced, the differential gain rises considerably.

By pumping the control region to low excitation compared to the slave, the ratio of

differential gains in the two regions can be made rather large.

ee i —

ro)

tc {[. —

Zz toh 4

Oo LL _

Zoo _

a _

wm LF _

A ol 1 tt 1 fy ft
6] 1 2 3 4 5

CARRIER DENSITY n (10'8 cm*%)

Figure 3.2: Differential modal gain as a function of carrier density for a 100 A GaAs quantum

well. This is the derivative of the gain function in Fig. 3.1.

However, the spontaneous carrier lifetime is also dependent on the carrier density,
so this will affect the ratio of the saturation photon densities as well. The spontaneous

recombination rate can be expressed as a power series in N,
R(N) = AN + BN? +CN® (3.5.1)

where A, B, and C are the non-radiative, radiative, and Auger recombination co-
efficients for the semiconductor material, respectively. In terms of the small-signal
spontaneous lifetime in the control and slave regions,

i 1

— _ (2) o\2
NRO) ene == = A+ 2BN? +3C(N?), (3.5.2)

so that the spontaneous lifetime is generally a decreasing function of carrier density.
Experimentally, it is found that 7; for an undoped GaAs quantum well at room tem-
perature is dominated by band-to-band radiative recombination [10], so z is nearly
a linear function of N?. 2B was determined to be 5 x 107° cm? sec™! for a 100 A
well over a wide range of carrier densities (1016 cm~? — 10'8 cm73).

Thus, in a quantum well, both differential gain and spontaneous lifetime decrease
as carrier density increases. Therefore, to ensure P*** < Pt, the control should be
pumped to a lower level of excitation than the slave. In addition, the control section
should be small so that saturable absorption effects do not occur. Figure 3.3 shows
such a two-section laser with the small control section adjacent to one facet. The
slave region is pumped by a dc injection current and the control region is separately
modulated either optically or electrically.

In order to relate the theoretical gain-levered modulation enhancement to exper-

iment, (3.4.2) can be expressed in terms of output power from the laser. Non-ideal

mod

Rut YS

> 5 um fe————_ 250 um —___»

CONTROL SLAVE

Rute SS

CONTROL SLAVE

Figure 3.3: The laser is composed of two separate regions, the control and the slave, where
the control is only a small fraction of the total cavity volume. A dc current J, applied to

the slave region biases the laser above threshold. The control region is modulated optically

or electrically.

coupling should also be accounted for, because not all of the input modulation en-
ergy to the control will reach the active layer. For electrical modulation, the ratio of

output power modulation to input current modulation is given by

AP, he ihe Ps**(1 + pear)
Al, = "TY gq = "TY oq PstI + fae

(3.5.3)

where «, is the coupling efficiency for current into the control, h, c, and q are Planck’s
constant, the speed of light, and the electron charge, respectively. A, is the laser
wavelength, and 7, is the differential quantum efficiency defined in (3.4.2). For optical
modulation of the control, the ratio of output power modulation to input power

modulation is
AP, di A; Pot(1 + gte)
= Kp—Ne = KP
AP, “PX, ~ “PX, Pot + Fe)

(3.5.4)

where /; is the input wavelength and «p is the coupling efficiency for the input light.
Thus, for optical modulation, xp carriers are created through optical absorption for
every input photon to the control. Also, the power gain ae is decreased by the ratio
di, where \; < A, in order that the input photons are above the bandgap of the active

layer material and therefore absorbed.

3.6 Experimental results

To demonstrate the gain-lever effect, we study a GaAs/GaAlAs laser with a 100 A
single quantum well (SQW). The experimental setup is shown in Fig. 3.4. The laser
is biased above threshold by a dc injection current applied through a metal contact

over nearly the full cavity length. This defines the slave region. A small opening in

the metal contact adjacent to one of the facets defines the control region which is un-
pumped by the bias current. This opening permits the control region to be optically
modulated. Figure 3.5 shows the top surface of the laser diode. For this laser, the
control region is 5 um long compared to a slave region 250 um in length. The control
thus forms 2% of the cavity volume—a very small slice—so we are definitely operating
in the: gain-lever limit where saturable absorption is not a factor (see (3.4.2)). For
argument’s sake, even if the control region has an absorption coefficient of approxi-
mately 50 cm7', as depicted in Fig. 3.1, then the impact of 50 cm™! absorption over
a 5 um length is miniscule.

For optical pumping of the control we use a cw Kr laser operating at 676 nm.
Although the gain-lever effect was initially discovered while photomixing two lasers
in the control section (modulation enhancement was observed out to several GHz),
for the experiment discussed here only one laser is used to provide the control input.
This allows the gain lever to be characterized in the steady-state regime (4* — 0)
simply by varying the incident Kr power. The output power from one (or both) of
the SQW laser facets is then monitored with a p-i-n detector.

A cross section of the SQW laser is shown in Fig. 3.6. The quantum well active
layer is embedded in a graded index separate confinement heterostructure (GRIN-
SCH). Although the GRINSCH is a standard component of a high-performance quan-
tum well laser [11], the presence of the GRINSCH is important for efficient optical
modulation of the control. Even though the input light at 676 nm is well above the

bandgap of GaAs, very little (~ 1%) of the input is directly absorbed by the active —

PUMP
LASER

BEAMSPLITTER
VIDEO CAMERA
——
MICROSCOPE |
OBJECTIVE |
WZ
\/
DETECTOR

LASER DIODE

Figure 3.4: Schematic diagram of the experimental setup. The quantum well laser diode is
biased above threshold by a dc injection current, while a small region of the active layer is

optically pumped by a Kr laser. The change in ouput power is monitored by a photodetector.

Figure 3.5: Scanning electron micrograph of the top surface of the quantum well laser. A
5 ym opening in the metal contact adjacent to the facet defines the control region which

may be optically modulated.

region since it has a thickness of only 100 A. Fortunately, most of the input absorp-
tion occurs in the GRINSCH, and the photocarriers are then quickly swept into the
well by the built-in electric field arising from the GRINSCH’s graded bandgap. In
fact, the carrier capture time (GRINSCH — quantum well) is on the order of ps, as
recent photoluminescence studies have shown [12]. Based on a 30% Fresnel reflection
from the top surface, and an estimated 30% absorption by the GRINSCH and SQW,
approximately 20% of the incident Kr photons are converted into control carriers.
Figure 3.7 shows data from the modulation experiment, where the change in total
output power (both facets) from the SQW laser is plotted as a function of the absorbed
input power in the control (AP, vs. «pAP; from (3.5.4)). The SQW laser had a
threshold current of 27 mA and lasing wavelength of 850 nm. Characteristics are
shown for slave bias currents (J,) from 28 mA up to 45 mA, where the output power
from the SQW with no control input (P,) ranges from 1.4 mW to 14.5 mW. At low
laser bias, the ratio of output power modulation to input Kr power is as high as four.
As the bias level increases the modulation enhancement decreases, but for J, > 45 mA
the characteristics were no different from the J, = 45 mA characteristic. However,
this form of saturation is predicted by (3.4.2). At high slave bias current, the large P,
limit of (3.4.2) is approached, where the gain lever is negated by the lifetime-related
saturation of the control population. There is no power gain, merely a one-for-one
conversion of absorbed input photons to output photons. In the high-power limit,

3.5.4) predicts -4£2, = +1, The measured slope of the characteristic at high bias is
P RPOP; ~ Xo &

in satisfactory agreement with this value, with 3 = eeun = 0.79.

SINGLE QUANTUM WELL LASER

n - AlGaAs

n’- GaAs

GRIN-SCH

- A
1.5 um p Ga, Al. Ss

GY 0.2 um GaAlAs -> Ga, Al, As
100 A GaAs SQW

Y); 0.2 um Ga Al .As -> Ga ,Al, As

1.5 umn-Ga_Al_As
5.5

Figure 3.6: Schematic cross section of the GaAs/GaAlAs laser with a single 100 A quantum
well. The active layer is surrounded by a graded index separate confinement heterostructure

(GRINSCH), wherein most of the absorption of input light occurs.

4.0
Fe
= le
Soak Po/ Pi=4.0 e 'b=28MA, Pp=14mW
< ” /
Ee 0.6 -- /
aS / ° lb =35 MA, Ph =7.1 mW
Q = »Pp=7.1m
= 04 é bd 9 b= 40 mA, Pp = 10.7 mW
tu a @ lp=45 MA, Py =14.5mW
ou 0.2 -— ee
be /e bd
/ e
a / Lx
= / 3
> 0062 | | |
O , 0.05 0.1 0.2 0.3 0.4

ABSORBED INPUT POWER (mW)

Figure 3.7: Change in the output power (both facets) from the laser diode vs. absorbed

optical input power for different slave region bias levels.

100

The measured factor of four enhancement in modulation efficiency is reasonable
in view of the following argument. Because the control region is unbiased, the control
junction voltage, and hence the control carrier density N?, is floating. The control
is thus easily bleached by the lasing mode, pushing this region close to transparency.
The transparency point in Fig. 3.1 corresponds to a control carrier density of about
1.3 x 1018 cm-3. The location of OP1 for the slave is most likely near 50 cm7!, which
is a reasonable threshold gain for a 255 ym long GaAs SQW laser with uncoated facets
(threshold gain = ;In(+) insofar as internal loss is negligible, where L is the cavity
length and r is the facet reflectivity, ~ 30% for GaAs). The slave carrier density N?
thus lies near 3.0 x 10! cm73. As a result, from Fig. 3.2, the ratio of the differential
gains in the control and slave is about 2.5, while the ratio of the spontaneous lifetimes
in the two regions is about 2.3, assuming the lifetime is inversely proportional to the
carrier density (see (3.5.2)). This gives Ps / Pst = 5.8 for the maximum modulation
enhancement, not far from the measured factor of 4.0. It is also true that the control
was not electrically isolated from the slave. Consequently, there may have been some
leakage of slave carriers into the control which would further diminish the amount of
modulation enhancement that could be obtained.

In addition to the photon density related saturation discussed above, another form
of saturation is apparent in the data in Fig. 3.7. A characteristic for a fixed slave bias
will saturate as the input power to the control increases. This is most visible in the
low bias characteristic (J, = 28 mA) where the modulation enhancement decreases

for input powers above about 0.1 mW. This type of saturation must be distinct from

101

the photon density related saturation. The reason is that the slope of the J, = 28 mA
characteristic is reduced to about 1.4 when the device output power is 1.8 mW, yet the
slope of the next characteristic (J, = 30 mA) is as large as 3.0 when the output power
is increased to 3.1 mW. The saturation displayed by the J, = 28 mA characteristic
is most likely due to band filling, whereby the carrier density in the control region
increases enough to increase the effective saturation photon density of this region. In
other words, as the control is pumped harder by the Kr laser, the operating point
OP2 in Fig. 3.1 moves up the gain curve to such a degree that the differential gain
and carrier lifetime are decreased. Thus the ratio of saturation photon densities of the
two regions is reduced, resulting in a less effective gain lever. This form of saturation
is not contained in the theoretical results, because it must be remembered that (3.4.2)
was derived by separately linearizing the gain in the control and slave regions. If the
control is modulated too hard, then the linear approximation for the control gain must
be modified. In fact, for a control volume of 3 wm x 5 wm x 100 A and spontaneous
lifetime of 1.5 ns (in accordance with (3.5.2)), then only 0.03 mW of absorbed Kr
power is needed to boost the control carrier density by 1 x 108 cm73. The lesson
is that to avoid band-filling saturation of the control region, the modulation to this

section must definitely be small-signal.

3.7 Improvements and future applications

There are many possible ways to improve the performance of the gain lever. To

enhance the intensity modulation efficiency, one should consider ways to increase the

102

ratio of saturation photon density of the control and slave regions. This may be
accomplished by forcing the slave to run at higher excitation, thus pushing the slave
operating point further out on the gain characteristic, or by n-type doping the slave
region, which tends to further flatten the gain characteristic compared to the undoped
case [5]. To increase the saturation power due to band-filling effects, one could put
multiple quantum wells in the control section, so that the carrier density in each well
is reduced in proportion to the number of wells. For optical modulation, the overall
quantum efficiency could be improved by increasing the absorption cross-section of
the control region and by eliminating the Fresnel reflection from the control region
surface. Furthermore, the control and slave sections should be electrically isolated so
they form independent carrier populations.

While optical modulation of the control section provided a convenient means to
initially demonstrate the gain lever, it should be clear that a more practical way
to implement the effect is by current pumping both the control and slave sections
through separate electrical contacts, as in Fig. 3.3. In this case, the two regions may
be individually biased to force P$* < P3*. Indeed, this approach was demonstrated
by Moore and Lau [13] subsequently to, and independently of, our gain-lever experi-
ments [1], {2}. They observed up to 23 dB enhancement in the intensity modulation
efficiency of a two-section SQW GaAs/GaAIAs laser similar to our device. Gajic and
Lau found that intensity noise from gain-levered lasers is only marginally increased
compared to homogeneous pumping [14].

Finally, although this aspect of the gain lever was not pursued in our laboratory,

103

the gain lever may also enhance the tunability of semiconductor lasers. Because
the slave region carrier concentration can be controlled by gain-levering (unlike a
homogeneously pumped laser where the carrier density is clamped), the longitudinal
cavity resonances, and hence the lasing frequency, may easily be tuned by way of
the carrier-density dependent refractive index. With this in mind, a gain-levered
multiple quantum well DFB laser with 6.1 nm tuning range was fabricated by Wu
and co-workers [15]. Very recently, Lau reported enhanced FM response [16], up to 20
GHz per mA of control current, and large tunability [17], over 90 A, for a gain-levered
SQW laser. This feature of the gain lever may prove to be important for the future

development of tunable semiconductor lasers.

3.8 Conclusion

The gain lever is an effect, discovered in our laboratory, which enhances the modu-
lation efficiency of quantum well semiconductor lasers. Intuitively, the effect occurs
in quantum wells because of the sub-linear dependence of optical gain on carrier con-
centration. Thus, by inhomogeneously pumping the laser, it is possible to create two
regions with unequal differential gain. If the laser is above threshold, then the overall
modal gain is clamped, and by modulating the pumping to the section with higher
differential gain, the output power from the laser can be modulated with greater than
unity quantum efficiency. The gain lever was explained theoretically using simple
rate equations describing a two section laser. It was found in the general case that

the only requirement for a gain lever is that the two regions have unequal saturation

104

photon densities (the saturation photon density is the inverse of the product of differ-
ential gain and carrier spontaneous lifetime). Furthermore, in order that conventional
saturable absorption effects do not occur, it is necessary that the region with smaller
saturation photon density (the control section) occupy a small fraction of the total
cavity volume. Finally, experimental results for a two-section GaAs/GaAlAs single
quantum well laser show modulation enhancement and saturation behavior described

by the gain-lever mechanism.

105

Bibliography

[1] M. A. Newkirk, K. J. Vahala, T. R. Chen, and A. Yariv, “A novel gain mechanism
in an optically modulated single quantum well semiconductor laser,” presented
at Conf. on Lasers and Electro-Optics, April 24-28, 1989, Baltimore, MD, paper
WGl.

[2] K. J. Vahala, M. A. Newkirk, and T. R. Chen, “The optical gain lever: A novel
gain mechanism in the direct modulation of quantum well semiconductor lasers,”
Appl. Phys. Lett., vol. 54, pp. 2506-2508, 1989.

[3] C. H. Henry, R. A. Logan, and F. R. Merritt, “Measurement of gain and absorp-
tion spectra in AlGaAs buried heterostructure lasers,” J. Appl. Phys., vol. 51,
pp. 3042-3050, 1980.

[4] Y. Arakawa and A. Yariv, “Theory of gain, modulation response, and spectral
linewidth in AlGaAs quantum well lasers,” IEEE J. Quantum Electron., vol.
QE-21, pp. 1666-1674, 1985.

[5] K. J. Vahala and C. E. Zah, “Effect of doping on the optical gain and the
spontaneous noise enhancement factor in quantum well amplifiers and lasers
studied by simple analytical expressions,” Appl. Phys. Lett., vol. 52, pp. 1945-
1947, 1988.

[6] M. Mittelstein, Y. Arakawa, A. Larsson, and A. Yariv, “Second quantized state
lasing of a current pumped single quantum well laser,” Appl. Phys. Lett., vol.
49, pp. 1689-1691, 1986.

[7] A. E. Siegman, Lasers, Mill Valley, CA: University Science Books, 1986, p. 538.

[8]

[9]

[10]

[11]

[12]

[14]

[15]

[16]

[17]

106

C. S. Harder, “Bistability, high-speed modulation, noise, and pulsation in
GaAlAs semiconductor lasers,” Ph.D. dissertation, California Instit. Technol.,
Pasadena, CA, 1983, ch. 4.

H. Kawaguchi, “Bistable operation of semiconductor lasers by optical injection,”
Electron. Lett., vol. 17, pp. 741-742, 1981.

Y. Arakawa, H. Sakaki, M. Nishioka, J. Yoshino, and T. Kamiya, “Recombination
lifetime of carriers in GaAs-GaAlAs quantum wells near room temperature,”
Appl. Phys. Lett., vol. 46, pp. 519-521, 1985.

P. L. Derry, “Properties of buried heterostructure single quantum well (Al,Ga)As
lasers,” Ph.D. dissertation, California Instit. Technol., Pasadena, CA, 1989, ch. 2.

B. Deveaud, F. Clerot, A. Regreny, K. Fujiwara, K. Mitsunaga, and J. Ohta,
“Capture of photoexcited carriers by a laser structure,” Appl. Phys. Lett., vol.
55, pp. 2646-2648, 1989.

N. Moore and K. Y. Lau, “Ultrahigh efficiency microwave signal transmission
using tandem-contact single quantum well GaAlAs lasers,” Appl. Phys. Lett.,
vol. 55, pp. 936-938, 1989.

D. Gajic and K. Y. Lau, “Intensity noise reduction in the ultrahigh efficiency
tandem-contact quantum well lasers,” Appl. Phys. Lett., vol. 57, pp. 1837-1839,
1990.

K. Y. Lau, “Frequency modulation and linewidth of gain-levered two-section
single quantum well lasers,” Appl. Phys. Lett., vol. 57, pp. 2068-2070, 1990.

K. Y. Lau, “Broad wavelength tunability in gain-levered quantum well semicon-
ductor lasers,” Appl. Phys. Lett., vol. 57, pp. 2632-2634, 1990.

107

Chapter 4

Amplitude-phase decorrelation:
Reduction of semiconductor laser

intensity noise

4.1 Introduction

The q@ parameter, or linewidth enhancement factor, has been studied extensively in
research on semiconductor lasers. It governs many of the the important features of
semiconductor laser dynamics, among them enhanced linewidth [1] and frequency
chirp under direct modulation (dynamic line broadening) [2], [3].

In a semiconductor laser, the resonant refractive index and the gain are functions
of carrier concentration. The amplitude and phase of the lasing field are therefore
strongly coupled through the carrier population in the active region. The a parameter

is simply a measure of the coupling strength. However, the coupling is not symmetric.

108

Field amplitude fluctuations are coupled into phase fluctuations, but not the reverse.
With regard to laser noise, this one-way coupling causes excess phase noise which
enhances the fundamental laser linewidth by a factor of 1 + a’, but the fundamental
intensity noise level is unaffected. Nevertheless, the coupling further implies that the
amplitude and phase fluctuations are correlated. Because of the inherent correlation
between the fluctuations, an “image” of the intensity noise lies in the phase noise. We
propose that this image can be recovered from the phase fluctuation (more precisely,
the time derivative of the phase fluctuation, or instantaneous frequency fluctuation)
and used to reduce the intensity noise far below its intrinsic level. When the intensity
noise is maximally reduced, the fluctuations become decorrelated.

In this chapter, a discussion of two methods to achieve intensity noise reduction
is presented [4]. The first approach employs a passive element with a frequency-
dependent transmission which is external to the laser cavity [5], [6]. The theoretical
basis of this method is outlined, and the theory is applied to calculate the spectrum
of noise reduction, as well as the correlation properties of the transformed field fluctu-
ations. The effects of a power-independent component of laser linewidth on the noise
reduction are also considered. In the second approach, a frequency-dependent loss
is placed inside the laser cavity. Many of the effects due to such a dispersive intra-
cavity loss have been considered previously in the context of “detuned loading” [17],
but application to intensity noise reduction was not developed. Both methods may
potentially reduce the fundamental intensity noise floor by the factor 1/(1+ a”), well

over an order of magnitude for typical values of a. Finally, results of an experiment

109

which verify the first approach are discussed. The intensity noise level of a DFB laser
at low bias is passively reduced as much as a factor of 28 (14.5 dB) below its intrinsic

level by amplitude-phase decorrelation.

4.2 Semiconductor laser noise

In this section, the main features of intrinsic noise in semiconductor lasers which
will be important for later discussion of noise reduction are outlined. A semiclassical
description of the field fluctuations incorporating Langevin noise sources is used to
derive the relevant noise spectra and their dependence on laser power. At the cen-
ter of this discussion is the a parameter, which characterizes the coupling between
amplitude and phase fluctuations in the field.

The electric field from a single mode laser can be described as follows,
E(t) = po + p(t) etfwett9) (4.2.1)

where p, is the average photon density in the lasing mode, p(t) is the fluctuating part
of the photon density, wz is the cw oscillation frequency, and y(t) is the fluctuat-
ing phase deviation. When p(t)/p, < 1 the field can be represented in terms of a

dimensionless fluctuating amplitude

E(t) = po (1 + p(t)) etlentt ol) (4.2.2)

where p(t) = p(t)/2p,. As depicted in the intuitive model of Henry [7], the fluctuations
arise from spontaneous emission which randomly perturbs the amplitude and phase

of the field phasor. Since a semiconductor laser operates as a detuned oscillator-i.e.,

110

the gain peak lies at a frequency different from the zero dispersion point of the res-
onant refractive index-the amplitude fluctuations cause enhanced phase fluctuations
by modulating the carrier density-dependent refractive index of the gain medium.
This phase noise enhancement is measured by the a parameter, given in terms of the

real and imaginary parts of the complex susceptibility function as

_ dyp(n)/dn
a= dxr(n)/dn (4.2.3)

where n is the carrier density. As defined above, @ is a negative number. For DFB
semiconductor lasers, a may range from -2 to -7 depending on device design [8].
Each of the quantities p(t), y(t), and n(¢), the deviation of carrier density from

the steady-state value, evolves according to the small-signal rate equations, given by

p(t) = G'n/2+Ar (4.2.4)
y(t) = —aG'’n/2+ A; (4.2.5)
n(t) = —n/tr —2p.Gp (4.2.6)

where G is the optical gain, G’ is the derivative of gain with respect to carrier den-
sity, Tr is the relaxation oscillation damping time, and Ag and Ay, are real and
imaginary parts of the Langevin force accounting for spontaneous emission into the
lasing mode [9]. We omit a noise term in the carrier density equation because it has a
negligible effect on the dynamics of p(t) and y(t) when the laser operates at low bias
in the excess noise regime, described below [10], [11]. The Langevin forcing terms are

assumed to come from a zero-mean Gaussian probability distribution and have the

111

correlation relations [12]

(An(ttr)Aal(t)) = <58(7) (4.2.7)
(A(t +r)A,(t)) = Sr) (4.2.8)
(Ar(t+7)Ar(t)) = 0 (4.2.9)

where S is the spontaneous emission rate into the lasing mode, P is the average
photon number in the mode, and 6(7) is the Dirac delta function. The angle brackets
denote ensemble averaging. By Fourier transforming the above rate equations with
respect to frequency 2, the dynamics of n can be absorbed into equations for p and

y, the instantaneous frequency deviation, to obtain the fluctuation spectra

1.
— +210 .
p(Q) = TR — Ar (4.2.10)
(w?. a2) 4 @
R TR
~ 2 ~
g(Q) = Art ad ay An: (4.2.11)

(wR — 2?) + oR
Here, GG’p, has been replaced by w}, the relaxation oscillation frequency squared. By
Parseval’s theorem, the transformed Langevin terms, ArandA 1, are delta-correlated
in frequency with the same normalizations given in (4.2.7)-(4.2.9).

Equations (4.2.10) and (4.2.11) will provide the foundation for the following dis-
cussion of noise reduction. In these equations, the role of a is seen more clearly as
providing the coupling of amplitude fluctuations into instantaneous frequency fluctu-
ations. It should be emphasized that this is a one-way coupling, from p to ¢. The

amplitude fluctuation spectrum is not affected by the a parameter.

112

One consequence of a nonzero a, however, is enhancement of the fundamental
linewidth over its Schawlow-Townes value. Using the low-frequency limit of (4.2.11),

one finds that the power spectrum of the field is a Lorentzian with a linewidth [7]

Aw = Awsr(1 + a?) (4.2.12)
where
Awsr = 55 (4.2.13)

is the modified Schawlow-Townes linewidth. In the ideal case, linewidth is inversely
proportional to laser power. However, at high power, it is often observed that the
linewidth reaches a constant value and thereafter remains independent of power. To
account for this extra component of linewidth, a power-independent term will be

added to (4.2.12), so that
Aw = Awsr(1 + a”) + Aw. (4.2.14)

The origin of this extraneous linewidth is not known, but several potential mechanisms
have been discussed in the literature. These include carrier number fluctuations [13],
thermal fluctuations [14], and spatial hole burning [15]. In any case, the existence of
a power-independent source of linewidth can be incorporated into the instantaneous
frequency fluctuation spectrum by adding a phenomenological noise source A,, such

that Aw, is the spectral density of A,. Equation (4.2.11) then becomes

~ aw?

g(M) = Ay + ay Art Ao. (4.2.15)

2 Q2) 4 Bt
(wR Mw) +—

It is assumed that A, is uncorrelated with the other Langevin sources arising from

113

spontaneous emission. The presence of this term will later illustrate how an indepen-
dent source of linewidth influences our ability to reduce intensity noise.

For a directly detected field, the relative intensity noise (RIN) is defined as the
ratio of the mean square power per unit bandwidth of the fluctuating photocurrent
to the average photocurrent power. By this definition, the RIN spectrum is directly

proportional to the spectral density of the amplitude fluctuations, given by

1 2
7 +
Woo() = (p"(M)p(2)) = —TR— Awsr. (4.2.16)
(h—mrye S

Since the proportionality constant is of no consequence when direct comparisons of

RIN are made, hereafter we will define relative intensity noise as
RIN = W,,(Q). (4.2.17)

The way in which the RIN varies as a function of laser power can be divided into
two regimes. For the moment, consider fluctuation frequencies 2 < 1/Tp, wp, so that

the intensity noise has a flat spectrum given by

(4.2.18)

At low power, Tp is essentially power-independent while w? is always linearly pro-
portional to P. This characterizes the excess noise regime, where the RIN falls as
1/P?. In the high-power limit, Trw?, saturates to a constant value, so the RIN falls
as 1/P, which is defined as the shot noise regime. In practice, both regimes may
be observed by directly detecting the intensity noise with a photodiode followed by

a high-gain amplifier (see chapter 5). However, in this chapter we assume that the

114

laser is operating in the excess noise regime. The fluctuations are then dominated by
spontaneous emission, and the noise level is sufficiently far above the level of photon
shot noise (or vacuum noise) that a semiclassical treatment of the laser noise and

noise reduction is appropriate.

4.3 Intensity noise reduction with a passive, external trans-

mission function

In this section we discuss a scheme to reduce semiconductor laser intensity noise which
exploits the fundamental amplitude/phase coupling in the field fluctuations [5], [6].
The technique relies on the observation that although the intensity noise level is in-
dependent of a, the enhanced instantaneous frequency fluctuations measured by a
contain an image of the intensity noise. It is this image resulting from the correlation
between p(Q) and ~(Q) which can be recovered to reduce the intensity noise below
its intrinsic level. In what follows, we show that an external, passive element with
a frequency dependent transmission (see Fig. 4.1) can accomplish this task by trans-
forming the field in the desired way. We emphasize that no feedback to the laser source
is involved in this scheme. The fluctuating field is passively processed after leaving
the laser cavity. For an ideal laser source with no extraneous component of linewidth,
the intensity noise can potentially be reduced by the amount 1/(1 + a), the inverse
of the linewidth broadening term. This reduction is independent of laser power, and
is achieved by altering the correlation between the fluctuations. We quantify the

effect of the transmission function on the field’s correlation properties by calculating

115

LASER

T(w) - >

Figure 4.1: Free-running laser and passive, external transmission function T(w). The in-

trinsic intensity noise in the input light can be reduced when T(w) has the right slope.

the cross-spectral density of the fluctuations. For the ideal laser mentioned above,
maximum intensity noise reduction coincides with decorrelation of amplitude and in-
stantaneous frequency fluctuations. Even in the case of a laser with an extraneous
linewidth component, large reduction in intensity noise exceeding an order of mag-
nitude is possible. The dependence of noise reduction on output power will then be

discussed.

4.3.1 Transformation of field fluctuations

Before analyzing the noise reduction method quantitatively, we can form an intuitive
picture of how a frequency dependent transmission function affects the field fluctu-
ations. Suppose that the radiation goes through such a function T(w), as shown in

Fig. 4.2. The fluctuations in instantaneous frequency may be viewed as the lasing

116

frequency jittering about the lasing linecenter wz. Assuming that T(w) has nonzero
slope in the vicinity of wz, the frequency jitter is converted into jitter in the trans-
mitted amplitude. Since these new amplitude fluctuations are correlated with the
existing amplitude fluctuations in the field, they can be made to cancel each other
when they are superposed. Thus, the intensity noise can potentially be reduced by
choosing a transmission function with a proper slope.

It is straightforward to evaluate the effect of the transmission function on the
fluctuations [6]. Assume that T(w) is slowly-varying over the range of fluctuation
frequencies we are interested in. It will be seen that this is an excellent assumption
when T(w) is realized by a Michelson interferometer. A Taylor expansion of T(w)

about the lasing linecenter becomes possible, yielding

where T" is the derivative of the transmission with respect to frequency. Let the

slowly-varying complex amplitude of the input field be defined as
A,(t) = (1 + pi(t))e"© (4.3.2)

so that E(t) = A(t),/poexp(twzt) (see (4.2.2)). In terms of a Fourier component of

the input and output fields, (4.3.1) gives

A(Q) = T(wr + 2)A(O)

= T(wz)A(Q) + NT'(wz)A;(O). (4.3.3)
By inspection, (4.3.3) is the Fourier transform of the equation

A,(t) = T(wr)Ai(t) — iT’ (wr) Ai(t) (4.3.4)

117

OUTPUT AMPLITUDE

Figure 4.2: The transmission function, T(w), converts instantaneous frequency noise in the

input field to amplitude noise. T(w) is acting as a frequency discriminator.

118

which can be used to derive the effect of T(w) on the amplitude fluctuation of the

output field, with the result,
po(t) = Trei(t) + Tr(gilt) — t0i(t)). (4.3.5)

where the subscript R denotes the the real part of J. Similarly, the derivative with

respect to time of (4.3.4) in conjunction with (4.3.5) gives
Go(t) = gilt). (4.3.6)

Products of small-signal quantities have been neglected in writing the above relations.

Transforming back to the frequency domain, we find

po(Q) = (Tr+ 2TR)p(2) + Trei(®) (4.3.7)

Po(82) 9i(2). (4.3.8)

Equation (4.3.7) shows that p,() is the sum of two parts depending on both
the amplitude fluctuation and instantaneous frequency fluctuation of the input field.
The inherent correlation between p; and ¥; will enable intensity noise reduction in
the output field by controlling Tp and Tp. The instantaneous frequency fluctuation
of the output field, on the other hand, is not affected by the transmission function,
as (4.3.8) shows. Consequently, it often will not be necessary to make a distinction
between ¢; and go>.

To account for the fact that T(w) attenuates the mean field in addition to trans-

forming the fluctuations, we normalize p,(Q) by Tr and so obtain

po(®) = (1 + €)p(M) + EGO) (4.3.9)

119

where £ = Tp/Tp and will hereafter be referred to as the “slope” of T. By making

this definition, the RIN spectra of the input and output are simply

RIN; = Wy,o,(2) (4.3.10)

RIN, = W,,),(2) (4.3.11)

and we see that RIN, — RIN; as € — 0, that is, in the limit of zero transmission
function slope.

In reality, the factor NE appearing in the transformation equation (4.3.9) is usually
much smaller than unity and can be neglected for the range of frequencies and slopes
that will be encountered. In particular, the results of section 4.5 show that to achieve
noise reduction, € will typically be 0.03 GHz~! or less, so NE < 1 for all frequencies

of interest. With this observation, (4.3.9) becomes
P(X) = pi(Q) + E9i(Q) (4.3.12)

which is the final transformation equation.

4.3.2 Spectral density of transformed fluctuations

If we assume for now that we have an ideal laser source, that is, one without an
extraneous linewidth component, then the spectral density of the output amplitude
fluctuation may be computed using (4.2.10), (4.2.11), and (4.3.12).

(1/Tr + a€w2)? + 0?

Q?
(oh - OY +

Wrop(Q, €) = RIN, = & + Awsr (4.3.13)

120

This expression simplifies if we restrict our attention to frequencies Q < 1/TR, wp,

where the RIN spectrum is flat. In this case

2\2
RIN, = |e? + U/2 + aéwn) Awsr (4.3.14)
WR
and using
RIN, = S28? (4.3.15)
TRWR

the RIN of the input and output fields may be easily related.
RIN, = [(rrwpé)? + (1 + arRw?f)*JRIN; (4.3.16)

By minimizing this function with respect to £, the optimum slope is found to be

—l a
opt = TO 4.3.17
cont TRW, 1 +a? ( )
which gives the maximum noise reduction
RIN, = } RIN; (4.3.18)
o 7 1+ a? te ae

For a typical a = -5, the intensity noise floor can thus be reduced below its intrinsic
level by a factor of 26. This lower limit on noise reduction is governed by the factor
(1+ a?), the same factor which enhances the fundamental linewidth of the laser over
its Schawlow-Townes value. As the slope is changed from the optimum, different
amounts of noise reduction (or enhancement) will occur in accordance with (4.3.16).
This is shown in Fig. 4.3 where the output noise is seen to vary quadratically with
slope about the minimum. According to (4.3.17), the optimum slope is a function
of Taw}, and generally will vary with the laser power level. Even so, the maximum

reduction (4.3.18) remains independent of laser power.

121

4 a he)
on © ou fo)
T , oy an ee

RIN, / RIN; (dB)
nO]

aa
ron)

155 ;

4-3-2 -1 0 1 2 8 4
Normalized Slope /fop:

Figure 4.3: Relative level of output intensity noise vs. normalized slope. For the optimum
slope (4.3.17), noise is reduced below its intrinsic level by 1/(1+ @*), where a = -5 is
assumed. This figure characterizes noise reduction in the flat part of the intensity noise

spectrum.

122

The complete RIN spectrum of the output field is given by (4.3.13). For a given
value of €, the amount of noise reduction is a function of frequency. Figure 4.4
shows the RIN spectrum calculated from (4.3.13) for several values of transmission
slope. Typical values for Tg (2.6 x 107" sec rad’) and wr (9.4 x 10° rad sec™!)
characteristic of a DFB laser at low bias are taken from the literature [16]. An a
of -5 is also used. The heavy curve is the intrinsic intensity noise level of the input
field, corresponding to = 0. When € is at the optimum value given by (4.3.17),
the low-frequency noise is reduced by 1/(1 +a?) in accordance with (4.3.18), but the
amount of reduction diminishes at higher frequencies. If the slope is too large, 3£opt
for this example, then the low-frequency noise is enhanced over its intrinsic value, in
agreement with (4.3.16) and Fig. 4.3. For the range of slopes in Fig. 4.4, the noise
level at the resonance is not significantly affected. We also see that the high-frequency
noise beyond the resonance is enhanced even when the low-frequency noise is reduced.
This is not surprising because at high frequencies the phase noise is dominated by its
independent component (A; term in (4.2.11)) which is being converted by T(w) to
an additive component of intensity noise.

The optimum slope which minimizes the output intensity noise at frequency 2 is

— -l aD)
bope(Q) = rah 1+ DO) (4.3.19)
where
D(Q) = “R oF (4.3.20)
(wh — 07)? + >
TR

The variation in optimum slope is shown in Fig. 4.5, where €,5:(Q) is plotted normal-

ized by the optimum low-frequency slope £,,; from (4.3.17). Noise reduction at higher

123

20 7
10
-_~
ea
To
all
o +O
Z,
-—
es
-10
-20 ; ‘ {__ ' | ‘ {

0.01 0.1 1.0 10
0/27 (GHz)

Figure 4.4: Output intensity noise spectrum for different slopes calculated from (4.3.13).
The heavy curve is the intrinsic noise level (€ = 0). Spectra are measured relative to the
intrinsic noise level at low frequency. Noise is reduced in the flat region by 1/(1+ a?) when
& = font, or enhanced (€ = 3.1) as the slope is varied. High-frequency noise is enhanced

for all slopes.

124

frequencies therefore requires a fairly constant slope as 2 approaches wr. Beyond the
resonance the optimum slope tends to zero, which indicates that noise reduction is
becoming impossible at these high frequencies.

A plot of the spectrum of maximum possible noise reduction also appears in
Fig. 4.5. This function is obtained by evaluating RIN, (4.3.13) at the optimum
slope for each frequency (4.3.19), and is the envelope of minimum noise levels in the
progression of noise spectra in Fig. 4.4, normalized by the intrinsic noise spectrum,

1.€.,

W,.0.(2, bopt(Q2))
Woo (Q)

maximum noise reduction spectrum =

(4.3.21)

The left-hand side of Fig. 4.5 shows that the noise can be reduced by 1/(1 + a”) at
low frequency, the magnitude of reduction decreases as the resonance frequency is

approached, and no reduction is possible at frequencies beyond the resonance.

4.3.3 Correlation properties

To further illustrate the effect of the transmission function T(w) on the field fluctua-
tions, it is useful to compute the symmetric cross-spectral density of p and ¢, defined

Waol) = 5 [(o(O)E"(2)) + (9° H(M)]. (4.3.22)

Using (4.3.22), (4.2.10), and (4.2.11), the cross-spectral density of the input field is

Wrio(Q) = 78 We Awsr. (4.3.23)
(o3, - 97) +
TR

125

F 1.0

= 08t .

do Q,

fu fs)
0.6 + aw

: e

7 0.44 rd

ry up

= 02+

€ 0.0 , fi ,

i 0.01 0.1 1.0 10

2/27 (GHz)

Figure 4.5: Left-hand side: Maximum intensity noise reduction as a function of frequency.
Noise is reduced by 1/(1 + a) where the noise spectrum is flat. Beyond the resonance,
noise cannot be reduced below the intrinsic level.

Right-hand side: Normalized optimum slope to achieve intensity noise reduction vs. fre-

quency. op¢({) tends to zero at high frequency where noise reduction is not possible.

126

This function gives the degree of correlation between the Fourier components of the
field’s intrinsic amplitude and instantaneous frequency fluctuations. For the input
field, a logarithmic plot of the magnitude of (4.3.23) in Fig. 4.6 shows that there is
always correlation except in the high-frequency limit, which fits with the intuitive
model of [7]. Since the fluctuations are coupled through perturbations to the carrier
density, there can’t be any significant correlation at timescales much shorter than
the characteristic response time Tr. As expected, the above function is directly pro-
portional to a. To be precise, the fact that a is negative means that p; and ¢ are
anticorrelated.

After passing through the transmission function, the amplitude fluctuation is

transformed according to (4.3.12), and the cross-spectral density of the output field

becomes ;
arwhé + OUR
Wog(O, €) = E+ Roz | Awsr. (4.3.24)
(R— orp S

The correlation is now a function of £, the transmission function slope. Figure 4.6
also shows the magnitude of this function evaluated at the optimum value of € used
to generate the normalized noise reduction spectrum in Fig. 4.4. By comparing these
two figures we see that noise reduction coincides with reduced correlation in the
fluctuations. In fact, when the noise is maximally reduced at low frequency, the
cross-spectral density approaches zero, indicating that the low-frequency fluctuations
have been decorrelated by the transmission function. (Note: It is useful to take the
log of the magnitude of (4.3.24), as in Fig. 4.6, because the large dynamic range at

low frequencies is clearly seen, but an artifact of this is a sharp feature after the

127

-60 4 l . i ‘ !
0.01 0.1 1.0 10

|Cross-Spectral Density| (dB)

/2x (GHz)

Figure 4.6: Magnitude of the cross-spectral density of p(Q) and ¢g(Q) of the input field
(normalized by the low-frequency value), and of the output field (heavy curve) for = op,
showing decorrelation of the fluctuations at low frequency. The function changes sign after

the resonance, appearing as a sharp feature in this logarithmic plot.

128

resonance where the function changes sign). In addition, a new correlation at high
frequency arises from the independent source of phase noise (A; term in (4.2.11))
which is being converted to additive intensity noise by the transmission function.
The fact that the cross-spectral density is driven to zero at low frequencies when
€ = & 4 can be understood by considering the fluctuations in the time domain. In

the low-frequency limit, we have from (4.2.4) - (4.2.6)

a(t) = Ap (4.3.25)

where A(t) = TRw}p(t) is a rescaled amplitude fluctuation in order that A(t) and :(t)
be dimensionally equivalent. Let 7? = (A}) = (A?) be the variance of the Langevin
terms (directly proportional to the integration bandwidth, since the Langevin forces

have a flat spectral density) so that

(a;(t)?) = 0? (4.3.27)

(g(t?) = o7(1+a’) (4.3.28)

are the variances of the input field variables p;(¢) and ¢,(t).

If the laser were operating in the tuned condition, corresponding to a = 0, then
contours of constant probability density would be circular, as shown in Fig. 4.7. For
the detuned case, the contours are ellipses tilted with respect to the coordinate axes.
As a result of detuning, the variance of the instantaneous frequency fluctuation is
enhanced by 1 + a? but the variance of the amplitude fluctuation is unchanged. This

tilted ellipse represents the state of the fluctuating input field, where the degree of

129

tilt, and corresponding thinness of the ellipse, indicates the correlation between the
fluctuations.

Using (4.3.12),(4.3.25) and (4.3.26), when € = ,,:, the output field variables are

AR aA;

p(t) ipa? Tdi (4.3.29)
g(t) = A;rtadrR (4.3.30)
which are clearly uncorrelated. The variances are given by
o?
(Golt)") = Ta (4.3.31)
(g,(t)?) = o7(1+a7). (4.3.32)

The output field ellipse is also shown in Fig. 4.7. For the optimum slope, we see that.
the transmission function has rotated the ellipse to align it with the coordinate axes.
As a result of the rotation, the output field variables 6,(¢) and ,(t) are decorrelated
while the variance of the amplitude fluctuation is simultaneously reduced by the
factor 1/(1 + a”). Decorrelation of the fluctuations by T(w) therefore coincides with

intensity noise reduction.

4.3.4 Effect of a power-independent linewidth

To complete this discussion, we must consider the effect of an extra, non-Schawlow-
Townes, component of linewidth on the RIN of the output field. We can foresee
that, in general, the amount of noise reduction will diminish, since the extraneous
linewidth is presumed to come from a phase noise source (A, term in (4.2.15)) which ,

is not correlated with the other noise sources. It is straightforward to substitute

130

TUNED °
a= 0 rope
a le p
0 |
| ? ?,
DETUNED it
a#0 Vo Vt+a2

of)

V1+a2
= Output Field

Input Field

Figure 4.7: Contours of constant probability density for tuned (a = 0) and detuned (a # 0)
operation. For the detuned case, the tilted ellipse of the input field is rotated by T(w) to

decorrelate the variables and reduce the variance of fo(t) by 1/(1 + a).

131

this augmented instantaneous frequency fluctuation spectrum into the transformation
equation (4.3.12) to compute the output RIN. In the low-frequency limit, we find

analagous to (4.3.16)
RIN, = [(rpw}E)?(1 + B) + (1 + arawpe)*]RIN; (4.3.33)

where 8 = Aw,/Awsr is the ratio of the power-independent linewidth to the Schawlow-
Townes linewidth. § increases linearly with laser power, since Aws7 has inverse power
dependence. Evaluating the above relation at the slope which minimizes the output

intensity noise,

—1 a

bopt = Tw? 1 + oy) + B’ (4.3.34)
the maximum reduction is now given by
_ 1+
RIN, = ihe + Bini. (4.3.35)

Thus, for nonzero £, the ability to reduce intensity noise is diminished compared
to the ideal case (4.3.18). Furthermore, the amount of reduction is now a function
of laser power, the net reduction becoming smaller as output power increases. This
behavior will be shown to agree with measurements on a DFB laser diode in section
4.5.

For the complete output spectrum it can be easily seen that the presence of the
extra linewidth component will add a uniform offset to the noise level by the amount
&*BAwsr (see (4.3.13)). Thus the magnitude of reduction at any frequency will
decrease as the laser is run at higher bias.

To summarize the results of this section, we have studied the effects of an external,

passive transmission function on the intensity noise of the laser field and found that

132

large reductions below the intrinsic level are possible when the transmission func-
tion has the correct slope. The method works by exploiting the inherent correlation
between the field fluctuations. Optimum intensity noise reduction simultaneously

decorrelates the amplitude and phase fluctuations at the output.

4.4 Intensity noise reduction with a dispersive, intracavity

loss element

A dispersive transmission function external to the laser cavity may reduce intensity
noise, as was just shown. The same is true if the element is placed inside the cavity,
where it then constitutes a dispersive loss. Contrary to the external case where
the element acts on the field but does not affect the laser, the internal loss element
influences the laser dynamics, and must be incorporated into the rate equations. The
underlying mechanism for intensity noise reduction is similar in both cases, however,
and the maximum amount of reduction is again given by the factor 1/(1 + a).

This method for noise reduction will only be discussed briefly, because the effects
of such an intracavity dispersive loss have been studied in work on “detuned loading”
in semiconductor lasers [17], [18]. In fact, it was shown experimentally that phase
noise (linewidth) reduction and modulation speed enhancement could be achieved
simultaneously through such an approach [19]. The application to intensity noise
reduction was not pursued in the literature. Here, our intent is to quantify how well
the intensity noise is reduced when the loss element has the right slope. Intuitively,

this mechanism for noise reduction relies on amplitude/phase correlation, but contrary

133

LASER

ye) -——

Figure 4.8: Laser with frequency-dependent intracavity loss y(w). The intrinsic intensity

noise can be reduced when 7(w) has the right slope.

to the passive case there is a feedback mechanism through the optical gain. In other
words, the enhanced phase noise (frequency jitter), which contains an image of the
intensity noise, causes jitter in the instantaneous cavity loss owing to the dispersive
loss function. The gain dynamically adjusts to compensate the fluctuating loss and
so quiets the intensity noise, assuming the loss function has the right slope. As
mentioned above, there may reduction in the phase noise as well, but we will focus
on the intensity noise here.

The dispersive intracavity loss y(w) is shown schematically in Fig. 4.8. The equa-

tion of motion for the slowly varying field amplitude (4.3.2) is given by [18]

= $(G —1(w))(1 ia) A+ A (4.4.1)

where A = An +724; is the Langevin noise source. A linear expansion of y about the

134

lasing frequency is assumed possible, so that
y(w) = y(wr) + 266w (4.4.2)

where € is the slope of y and éw is the complex instantaneous frequency deviation,

given by
6w = —i—. 4.4,
w iF (4.4.3)

The small-signal equation of motion then results

G’n(t) (1 -—ta)A A

A= ne tne

(4.4.4)

where G’ is the differential gain and n(t) is the carrier density deviation. Substituting

the expression (4.3.2) for A in terms of p and y, we find

_ G'n(t) 1+ a€ Ar—fAr

Dee t ise (4.4.5)

At low frequencies where n(t) and p(t) track each other, this becomes (using 4.2.6)

1 Ar—€Ar
TRwh 1l+aé

p(t) = (4.4.6)

where p — 0 in this low-frequency limit. The spectral density can then be found

using the normalizations given in (4.2.7) — (4.2.9).

1 1+
TRWR (1 + o€)?

Wp = Awsr (4.4.7)

Minimizing the above expression with respect to & gives &.,. = a for the optimum
slope, so compared to the intrinsic RIN (spectral density when £ = 0), the optimum

RIN is

RINopt = Toa? Ul Nintrinsic (4.4.8)

135

which agrees with the theoretical minimum for the passive case (4.3.18). If the laser
has an extraneous component of linewidth not due to spontaneous emission, then the
remarks of section 4.3 would apply here as well, and the maximum reduction would
be diminished.

In summary, we have shown that an intracavity dispersive loss can potentially
achieve the same level of intensity noise reduction as the passive transmission function
studied in section 4.3. In the flat part of the noise spectrum, both methods predict
that reduction by the factor 1/(1+7) is possible, assuming the laser does not possess

a significant power-independent component of linewidth.

4.5 Experimental results

We have described two ways to reduce laser intensity noise below the intrinsic floor:
an extra-cavity approach using a passive transmission element and an intra-cavity
approach which incorporates a dispersive loss. In this section experimental results
which verify the first approach are presented [4]-[6]. The transmission function is
implemented with a Michelson interferometer. Intensity noise from a DFB laser
shows significant reduction which requires only a small optical path difference in the
Michelson. The level of noise reduction as a function of frequency, laser bias, and
transmission function slope agree with the theoretical predictions.

We note that Michelson interferometers are often used to characterize phase noise
in semiconductor lasers [20], [21]. In these experiments, however, the interferometer

is said to be strongly unbalanced, where the path difference is on the order of 10 cm.

136

In our experiment the interferometer is only slightly unbalanced, as optimum path
differences for noise reduction are on the order of millimeters.

A schematic diagram of the experimental setup appears in Fig. 4.9. The single-
mode laser source used in this experiment is an InGaAsP distributed feedback laser
made by Ortel Corporation operating at 1.3 ym. The threshold current is 21.8 mA.
The light is collimated by an antireflection coated lens and sent through an optical
isolator (Newport ISO-13H) with 60 dB isolation to prevent feedback effects. After
passing through a Michelson interferometer with a maximum 87% intensity transmis-
sion, the output light is focused onto a high quantum efficiency (90%) p-i-n detector.
The noise photocurrent is amplified by a low noise, high gain (52 dB) amplifier over
the frequency band .01 - 1 GHz, and input to a microwave spectrum analyzer (HP
8558B). Lock-in detection is also employed to improve the sensitivity. With this ar-
rangement, the intrinsic intensity noise from the DFB laser can be measured in both
the excess and shot noise regimes, well above the thermal noise level of the detection
system.

A linewidth versus power measurement was taken for the DFB laser which appears
in Fig. 4.10. It shows that the linewidth varies inversely with power until it saturates
at high power to a value of 7 MHz. This represents the power-independent linewidth
component which will be shown to affect the magnitude of noise reduction that can
be obtained.

The transmission function for a Michelson interferometer is given by

Tw) = ; _™, (4.5.1)

wo] 3

137

DFB
LASER DIODE
LOCK - IN
ISOLATOR AMPLIFIER
(60 dB) |
MICROWAVE
+> SPECTRUM
OBL IVTER ANALYZER
d.
‘“N
> > »
M1 a Ty P-I-N
CHOPPER DETECTOR

Figure 4.9: Schematic diagram of the experimental arrangement including a Michelson

interferometer.

138

125
100 F ‘aan
xc
= /5T 5
— e
S .
52) e
FS 50 Fr < e 7
Cc e
a e
257 7
0 1 l A n 1 i : l 1
0.0 0.5 1.0 1.5 2.0 2.5

Inverse Power (mW -')

Figure 4.10: Measured linewidth vs. inverse power for the DFB laser used in the experiment.

The high-power linewidth saturates at 7 MHz.

139

where 6 is the optical path difference, c is the speed of light, and m (< 1), the
amplitude visibility, accounts for the imperfect extinction of the interferometer. m is

related to the intensity visibility v as follows

[Tmax —|TInin _ __2™

”= Poe + Pisin mT (452)
The real part of the Michelson transmission function is given by
Tr(w) = ; ( — mcos()) (4.5.3)
and the derivative is
TR(w) = me sin(). (4.5.4)

One arm of the Michelson is controlled by both a micrometer for coarse positioning
and a piezoelectric transducer (PZT) for submicron motion. The dependence of
intensity noise on interferometer slope is characterized by setting the path difference
using the micrometer, scanning the Michelson by one wavelength using the PZT,
and measuring the noise power of the transmitted light at a given frequency and
bandwidth. Figure 4.11 shows Tr(w) in relation to the lasing frequency wz, for two
path differences 6; and 42 (> 6,). If the scan begins at maximum transmission,
for instance, then during the scan the input field samples a transmission slope Tp
(4.5.4) which changes smoothly from 0 to m6/2c to 0 to —m6/2c to 0. In this way,
a continuous range of slopes, both positive and negative, can be tested in one scan,
and the extremes of this range are set by the amount of path difference, 6.

Figure 4.12 shows the results of an intensity noise measurement for a series of

path differences at a laser bias of 23.3 mA. The output power is 0.34 mW and the

140

W, 6)

Figure 4.11: Measuring intensity noise as a function of interferometer slope. The Michelson
is unbalanced by a path difference 6,, so that the lasing field at wz encounters a range
of positive and negative slopes as Tp is scanned by one fringe. For a larger delay 62, the
fringes are pushed closer together, and the field encounters a wider range of slopes as Tp is

scanned.

141

intrinsic RIN level is -130 dB/Hz. The noise was measured in a 100 kHz band at
130 MHz, within the flat region of the noise spectrum. Noise power is plotted as a
function of transmitted intensity, proportional to the mean detector photocurrent.
This is not the RIN, but the directly detected noise power which is related to RIN,
by multiplying the rhs of (4.3.33) by |T|*. At zero path difference we see the intrinsic
noise power level as the light is merely attenuated by the Michelson during the scan.
If the Michelson is unbalanced, then the dependence of noise level on transmission
slope becomes apparent. “Loops” of noise are observed whereby the noise is reduced
below the intrinsic level for positive slopes and enhanced when the slope is negative.
At the extremes of transmitted intensity for a given loop, the noise level returns to
the intrinsic value as it should since this corresponds to zero slope. As the path
difference increases, the loops grow in area and the noise reduction switches to noise
enhancement at some transmitted intensities.

With (4.3.33), (4.5.3), and (4.5.4), theoretical noise loops may be calculated. Using

1 (wR

a = -2.3, a value which is consistent with our data, rpw} = 34 x 10° rad sec~
measured experimentally and tr taken from the literature [22]), and @ = 0.35 from
the linewidth data, the calculated loops in Fig. 4.13 agree well with the measured
loops.

In Fig. 4.14, cross-sections of the experimental and theoretical loops at the half
intensity transmission point are shown in terms of noise power, normalized by the

intrinsic noise level, versus path difference. The optimum reduction is 7 dB for a

4 mm differential delay, which agrees with the theoretical calculation. Also shown -

142

10 wee arr

NOISE POWER (arb. units )

Pee ey ele
oes

— —

0 F jo TI i !

O 014 02 03 04 05 06 07 08 09 1.0
NORMALIZED INTENSITY TRANSMISSION

Figure 4.12: Measured intensity noise power vs. normalized intensity transmission through
the Michelson for optical path differences of 0 mm (intrinsic noise level), 1, 4, and 7 mm.
Loop areas increase with increasing path difference. Both reduction and enhancement of

the noise level are apparent.

143

10 Taare

NOISE POWER (arb. units )

0 O01 02 03 04 05 0.6 07 0.8 0.9 1.0
NORMALIZED INTENSITY TRANSMISSION

0 oo i L i

Figure 4.13: Theoretical noise loops for optical path differences of 0 mm (intrinsic noise

level), 1, 4, and 7 mm. Loop areas increase with increasing path difference.

144

16 t T q i iu T ' T r T iu T T T r
ay : °
oO 12 = ry - s ~

ry ‘a

3 8 a a LJ
Oo. PN
® a s % 7 |
fo) 4 N a 7 7
za . Ny Zi
N 0 S
rr} uv 5
S 4 | ate 1 _

-8 ' i \ { l ! i : L ‘ i ‘ i .

-8 -6 -4 -2 0 2 4 6 8 I

Optical Path Difference (mm)

Figure 4.14: Measured noise power at half-intensity transmission through Michelson vs.
optical path difference for laser bias of 23.3 mA (filled circles) and 25.7 mA (open squares).
Power is normalized by its intrinsic value at zero path difference. Low bias data show 7 dB
noise reduction at 4 mm path difference. Theoretical calculations of noise power (lines)

from (4.3.33) also appear.

145

are data from measurements at a higher bias of 25.7 mA, where @ is 1.08, rpw?, =
82x 10° rad sec~*, output power = 0.83 mW, and the intrinsic RIN level is -140 dB/Hz.
Because f is larger at higher bias, the amount of noise reduction decreases as predicted
by (4.3.35). Also, the increase in Taw? means the optimum slope is decreased and
occurs at a shorter path difference of 1.6 mm, in accordance with (4.3.34). These
data agree well with the theoretical plots. Note that the free spectral range of the
Michelson is 75 GHz for a path difference of 4 mm. The linear approximation of the
transmission function (4.3.1), on which the theoretical analysis of section 4.3 is based,
is therefore justified.

The amount of noise reduction continued to diminish as laser power increased. It
can be seen however that for a laser having a smaller excess linewidth (smaller f at a
given output power), larger amounts of noise reduction are possible at higher powers
and at shorter path differences. These small path differences needed to achieve noise
reduction suggest that a monolithically integrated version of this technique may be
feasible.

For the low bias case at 23.3 mA, Fig. 4.15 shows the maximum measured noise
reduction as a function of frequency. The theoretical curve calulated from (4.3.21) and
the known value of 8 also appears. As predicted, the amount of reduction diminishes
at higher frequencies where the intrinsic noise spectrum is no longer flat. Note that
an additional benefit from a laser with a smaller component of excess linewidth is
that noise reduction becomes possible at higher bias levels. The resonance frequency

is therefore pushed out to higher frequencies, leading to noise reduction over a wider

146

Intensity Noise Reduction

0.4 ) 0.2 0.3 0.4 0.5
Q:/27 (GHz)

Figure 4.15: Maximum noise power reduction vs. frequency for 23.3 mA laser bias. Mea-
sured (dots) and theoretical (line) values are shown. The magnitude of reduction decreases

at higher frequencies in accordance with (4.3.21) and Fig. 4.5

147

bandwidth.

Finally, Fig. 4.16 shows several noise loops for a second InGaAsP DFB laser with a
larger a parameter than the DFB laser described above. Noise power was measured at
17.8 MHz (in the flat part of the noise spectrum) in a 100 kHz bandwidth. The laser
was biased slightly above threshold for the measurement (bias level = 15.5 mA and
threshold current = 14.5 mA), where the output power was 0.22 mW and the intrinsic
RIN level was -119 dB/Hz. For a 6.6 mm differential delay in the Michelson, the noise
is reduced below the intrinsic level as much as a factor of 28 (14.5 dB). Although the
2 parameter was not directly measured for this device, a factor of 28 reduction in
the intensity noise implies that |a| > 5.2 (see 4.3.35). Additional measurements on
the level of noise reduction for this device in relation to the photon shot noise level

appear in chapter 5.

4.6 Conclusion

In conclusion, we have discussed a simple technique, amplitude-phase decorrelation,
for reducing the intensity noise floor in a free-running semiconductor laser. Taking
advantage of the inherent correlation between the amplitude and phase fluctuations in
the laser field, the intensity noise can potentially be reduced by the factor 1/(1+a’),
independent of laser power, by using a passive external element with a frequency-
dependent transmission. Optimum intensity noise reduction results in decorrelation
of the fluctuations. This technique was shown to share some conceptual similarities

with detuned loading, where a dispersive loss function is placed inside the laser cavity.

148

NOISE POWER (arb. units)

O O01 02 03 04 05 O06 O07 O08 O09 1.0
NORMALIZED INTENSITY TRANSMISSION

Figure 4.16: Measured noise loops for a different DFB laser (with a larger |a|) for path
differences of 0.0 mm (intrinsic noise level), 3.0, 6.6, and 9.0 mm. Loop areas increase with
increasing path difference. The loop at 6.6 mm delay (dashed line) shows a factor of 28

reduction in noise power at half-intensity transmission.

149

In that case the maximum intensity noise reduction is also 1/(1 + a”). In practice,
the presence of a power-independent component of linewidth will limit the amount
of reduction that can be achieved. The magnitude of reduction will thus diminish as
laser power increases. However, we verify that the intensity noise from a DFB laser
diode at low bias can be reduced by as much as 14.5 dB when the passive technique
is implemented with a Michelson interferometer. The measured dependence of the
noise level on interferometer slope, laser bias, and frequency are in agreement with

theory.

150

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the linewidth of single frequency cw (GaAl)As diode lasers,” Appl. Phys. Lett.,
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[2] Ch. Harder, K. Vahala, and A. Yariv, “Measurement of the linewidth enhance-
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[3] T. L. Koch and J. E. Bowers, “Nature of wavelength chirping in directly modu-
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[4] M. A. Newkirk and K. J. Vahala, “Amplitude-phase decorrelation: A method for }

reducing intensity noise in semiconductor lasers,” IEEE J. Quantum Electron.,

vol. QE-27, pp. 13-22, 1991.

[5] K. J. Vahala and M. A. Newkirk, “Intensity noise reduction in semiconductor
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tron. Conf., May 21-25, 1990, Anaheim, CA, postdeadline paper QPDP29.

[6] K. J. Vahala and M. A. Newkirk, “Intensity noise reduction in semiconductor
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[7] C. H. Henry, “Theory of the linewidth of semiconductor lasers,” IEEE J. Quan-
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(8] M. Osinski and J. Buus, “Linewidth broadening factor in semiconductor lasers
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151

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R. J. Lang, K. J. Vahala, and A. Yariv, “The effect of spatially dependent tem-

perature and carrier fluctuations on noise in semiconductor lasers,” IEEE J.
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C. H. Henry, “Theory of the phase noise and power spectrum of a single mode
injection laser,” IEEE J. Quantum Electron., vol. QE-19, pp. 1391-1397, 1983.

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diode lasers due to electron number fluctuations,” Appl. Phys. Lett., vol. 40, pp.
560-562, 1982.

K. Vahala and A. Yariv, “Occupation fluctuation noise: a fundamental source
of linewidth broadening in semiconductor lasers,” Appl. Phys. Lett., vol. 43, pp.
140-142, 1983.

K. Kikuchi and T. Okoshi, “Measurement of FM noise, AM noise, and field
spectra of 1.3 wm InGaAsP DFB lasers and determination of the linewidth en-
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K. Vahala and A. Yariv, “Detuned loading in coupled cavity semiconductor

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sertation, California Instit. Technol., Pasadena, CA, 1985.

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ment, frequency modulation suppression, and phase noise reduction by detuned

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152

[20] B. Daino, P. Spano, M. Tamburrini, and S. Piazzolla, “Phase noise and spectral
lineshape in semiconductor lasers,” IEEE J. Quantum Electron., vol. QE-19, pp.
266-270, 1983.

[21] P. Spano, S. Piazzolla, and M. Tamburrini, “Phase noise in semiconductor lasers:
A theoretical approach,” IEEE J. Quantum Electron., vol. QE-19, pp. 1195-1199,
1983.

[22] R. J. Lang, H. P. Mayer, H. Schweizer, and A. P. Moser, “Measurement of the
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153

Chapter 5

Semiconductor laser intensity
noise reduction and the photon

shot noise floor

5.1 Introduction

In chapter 4 it was shown that the amplitude phase decorrelation technique may po-
tentially reduce the intensity noise of semiconductor laser light by a factor of 1/(1+a7)
below its intrinsic level, where a is the linewidth enhancement factor. This represents
a substantial reduction for typical values of a (~ -5). The question naturally arises:
can amplitude-phase decorrelation reduce intensity noise below the level of the photon
shot noise? The shot noise level represents a fundamental floor for intensity noise,
and the issue of noise reduction below the shot noise level (standard quantum limit)

has been the subject of many theoretical and experimental investigations regarding

154

the generation of sub-Poissonian (squeezed) light [1]-[6].

Because it can be difficult to experimentally establish the photon shot noise level
(SNL) with confidence, a balanced homodyne detector (BHD) is used to accurately
determine the intensity noise level of the lasing mode in relation to the SNL. First,
the performance of the BHD is demonstrated by measuring the intrinsic noise level
of a laser diode and SNL as a function of laser power. Measurements on a distributed
Bragg reflector (DBR) laser show that at high power, the intrinsic intensity noise
level at the device’s output facet is only 0.8 dB above the quantum-limited shot noise
floor. The theoretical dependence of the measured SNL on optical attenuation is also
verified. Second, the BHD is used to complement the amplitude-phase decorrelation
experiments of the previous chapter by measuring the noise reduction in relation to
the SNL. For the DFB laser studied in chapter 4, the decorrelated noise can be reduced
to within 1.3 dB of the SNL. Reduction below the SNL appears to be inhibited by

uncorrelated phase noise in the instantaneous frequency fluctuation spectrum.

5.2 Laser intensity noise measurement with a balanced ho-

modyne detector

At low frequencies (i.e., in the flat region of the noise spectrum), the intensity noise

spectral density for single mode operation has the form

S() = ur ( +B+CI) (5.2.1)

155

where hwz is the lasing photon energy and / is average output power [7]. (Note:
S(I) represents the directly detected noise power which would be measured by a
detector and electronic spectrum analyzer, not the RIN, which is proportional to
S(1)/T’). The coefficients A, B, and C depend on fundamental laser quantities such
as differential gain and spontaneous lifetime, but for now we only wish to consider
the qualitative features of S(J). At low power, where the fluctuations are dominated
by spontaneous emission, the laser operates in the excess noise regime, where S{(/)
has a 1/I dependence. As I increases, the noise level eventually begins to rise as the
- laser enters the shot noise regime. It thus becomes important to relate S(J) to the

fundamental, quantum-limited spectral density of shot noise, given by 2hwzJ [8].

5.2.1 Balanced homodyne detection

Many experimental approaches to establish the SNL involve a fair degree of uncer-
tainty. One may measure the noise power of an incoherent, shot-noise-limited light
source, such as an incandescent filament [9], LED [10], or a highly attenuated laser
beam [11]. This reading of the SNL is then compared to the measured laser noise
level for the same dc photocurrent induced in the detector. However, this approach
has a major drawback. Although the detector dc photocurrents for the SNL cal-
ibration and laser noise measurement may be equal, this does not imply that the
frequency response of the detector is the same in both cases. In particular, a typical
high-performance p-i-n photodiode has both a dc and ac response which separately
depends on the location of the focused spot, the optical intensity, and the spectral

distribution of the radiation. If any of these quantities changes between the SNL cal-

156

ibration and the laser noise measurement, then the meaning of the SNL calibration
is questionable. These issues are not trivial. In our laboratory, we have seen as much
as 4 dB variation in the measured laser intensity noise power as the beam focus on
the detector is adjusted, even though the dc photocurrent remains constant to within
a percent.

Another approach to establish the SNL is to measure the detector current and
calculate the shot noise spectral density using the well-known 2q(/) formula, where q
and (J) are the electron charge and dc photocurrent, respectively. This is an indirect
method, however, which requires precise knowledge of detector response, amplifier
gain and noise figure, losses in the detection system, and the effective integration
bandwidth of the spectrum analyzer. Several dB’s of uncertainty in the location of
the SNL may easily accumulate.

A better approach is to use the laser itself to directly establish the SNL. This may
be accomplished with a balanced homodyne detector (BHD), as shown in Fig. 5.1 [12].
The physical principles of balanced detection are discussed in [13] and [14]. In a
generalized balanced detection scheme, two input modes a and 6 are coupled by a
beam splitter into output modes c and d. In terms of the beam splitter scattering

matrix [14], we have

VRe'?® V1—R a c

e® = (5.2.2)

JI-R —VRe-* b d

where R is the power reflectivity of the beam splitter. The phase angles 6 and ¢

depend on the beam splitter material and coatings, but their actual values are not -

important, as shown below.

157

For noise measurements, the laser light constitutes one input to a 50/50 beam
splitter (R = 1/2 in (5.2.2)), as seen in Fig. 5.1. In a quantum field description, the
laser field is represented by the sum of mean amplitude A; and noise component Aq.
The laser field forms input a in (5.2.2). A vacuum field, with zero mean amplitude
and noise component Aa,, enters the open beam splitter port, forming input 6. These
fields are mixed by the beam splitter and the output fields c and d are detected by
two ideal (unity quantum efficiency) photodetectors, generating currents I, ~ |c|?

and I, ~ |d|?. Using (5.2.2), the photocurrents J, and Jz may be expressed as

which are independent of the phase shifts intrinsic to the beam splitter. To highest
order, the noise-carrying parts of J, and J, are given by
I, ~ Aj(Aa; + Aa,) (5.2.5)
Thus, by coherently adding or subtracting 1; and Iz, followed by detection with a
spectrum analyzer, the measured noise spectra are

(i +12)?) ~ 4A}((Aa;)*) (5.2.7)

(i -h)’) ~ 447((Aa,)*) (5.2.8)

which represent the laser’s intrinsic intensity noise level and the quantum SNL, re-

spectively.

158

DBR
LASER DIODE

ISOLATOR
(60 dB) |

ATTENUATOR

CHOPPER |

11+ [2

| I
I Ait Aa ¥ | LOCK - IN
| HALF-WAVE { AMPLIFIER
| PLATE |
| BEAM |
SPLITTER D2 |
VACUUM__] y > | MICROWAVE
; I SPECTRUM
Aa, I ANALYZER
| D1 . 2 | |
| I
| I
| I
| {

BALANCED HOMODYNE DETECTOR

Figure 5.1: Schematic diagram of the intensity noise measurement setup including the

balanced homodyne detector.

159

5.2.2 Experimental details

In the experimental arrangement shown in Fig. 5.1, the laser output is sent through
an optical isolator with 60 dB isolation to prevent feedback effects. The input light
to the BHD is divided by a half-wave plate and polarization-sensitive beam splitter.
Two matched InGaAs/InP p-i-n photodiodes (BT&D PDH0004) with 0.90 quantum
efficiency are used in conjunction with a bias tee and a high-gain, low-noise amplifier
(Avantek ACT10-213-1). The amplified ac currents are combined in a broadband
hybrid junction [15] which may coherently add or subtract the two inputs. The
combined noise photocurrents are sent to a microwave spectrum analyzer (HP 8558B)
to measure noise power. Lock-in detection is also used to improve the sensitivity and
to filter thermal noise.

The optical powers in the two detector arms are balanced by rotating the half-
wave plate. It is also important that the path lengths of the two arms be made
equal [15]. This is accomplished by current modulating the laser diode at the mea-
surement frequency, subtracting the two photocurrents with the hybrid junction, and
adjusting the differential path length until the modulation peak seen on the spectrum
analyzer is minimized. By this approach, a common mode rejection of 60 dB could be
obtained. Once the BHD is balanced, the noise level of the lasing mode or the SNL
may be observed by switching between the summing and differencing output ports of
the hybrid junction, respectively. No other change to the system is required. Thus,

the uncertainties in establishing the SNL as discussed above are not a factor.

160

5.2.3. Experimental results

The BHD is used to study the intensity noise level of a 1.5 um InGaAs/InGaAsP
strained-layer multi-quantum well distributed Bragg reflector (DBR) laser [16], [17].
Measured noise power at 130 MHz (within the flat part of the spectrum) versus laser
output power is shown in Fig. 5.2. When the detector photocurrents are subtracted,
the SNL is measured, which appears as a line intercepting at zero power, as it should.
When the photocurrents are added, the intrinsic noise level of the lasing mode is
measured. Both the excess noise regime at low power, where the noise level falls with
increasing power, and the shot noise regime at higher power, where the noise level
increases with power, are apparent. A numerical fit to the intrinsic noise data of the
form of (5.2.1) and a linear fit to the SNL data are also shown. This laser appears
to operate extremely close to the SNL even for modest output power. However,
the effect of loss between the laser and detectors, including the non-unity detector
quantum efficiency [14], must be accounted for to relate measured noise to the true
noise level at the output facet.

A lossy optical channel attenuates the mean photon number as follows: (NV) in joss,
(Nout = n(N)in where 7 is the coupling efficiency. The noise statistics are altered
in a less straightforward way. In terms of photon number variance, proportional to

measured noise power, this relationship is [10]

((AN)*)
(V)

((AN)?)
(NV)

out __

m4.—n. (5.2.9)

out in

Equation (5.2.9) is merely an instance of the quantum-mechanical fluctuation dissipa-

' tion theorem, whereby leakage from a system to a reservoir (loss) necessarily couples

161

' | i 1 ' ]

8 =
= LASER INTENSITY NOISE LEVEL -
S 6 ™. 4
2 i " =
a _
i 4 ;
= L NN ;
Oo a SHOT NOISE LEVEL _
tu L (STANDARD QUANTUM LIMIT)
Moe ; -
O L Z
= —

6) 5 " i { at { lL J i |

0 2.5 5 7.5 10
LASER OUTPUT POWER (mW)

Figure 5.2: DBR laser intensity noise (at 130 MHz) vs. output power measured with a
balanced homodyne detector. Both the laser’s intrinsic noise level and shot noise level

(SNL) are shown. A theoretical fit to the intrinsic noise of the form of (5.2.1) and a linear

fit to the SNL are superimposed on the data.

162

reservoir fluctuations into the system. In this case, the reservoir is the vacuum, and
the impact of the vacuum fluctuations is described by the 1 — 7 term in the above
relation.

We see from (5.2.9) that loss affects shot noise and excess noise in fundamentally
different ways. First of all, shot noise has Poissonian statistics, where ((AN)*);, =
(N)in, and hence, when there is loss, the SNL versus incident power is unchanged,
ie., (AN)? )oue/(N)out = ((AN)?)\in/(N),,. In contrast, light with excess noise,
where ((AN)*)in > (N)in, will appear relatively less noisy after experiencing loss,
ie, ((AN)*)out/ (Mout < (AN)*)en/ (NY:

Equation (5.2.9) may be used to verify that the balanced detector is actually mea-
suring the SNL. Fig. 5.3 shows the measured SNL versus mean detector photocurrent
when the currents are subtracted by the hybrid junction. When the laser power is
changed by ramping the laser bias current down to threshold, measured noise power
follows a line which intercepts at zero power, indicative of shot noise, as in Fig. 5.2.
Alternatively, when the laser bias is fixed and the incident optical power to the BHD
is reduced by putting neutral density filters in the beam, the measured noise falls
exactly on the same line. Thus, for a given incident optical power, the measured SNL
is independent of loss before the detector—a fundamental property of photon shot
noise.

Equation (5.2.9) may also be used to factor out the effect of loss on the DBR laser
noise measurement. For the data in Fig. 5.2, 7 = 0.10, which includes losses from the

optical components, a neutral density filter to keep the dc photocurrents below 1 mA,

163

10 T T T l T

ron)

NOISE POWER (arb. units)
tr So fo) .
! ] T I I
SS
“2
l 1 | | j

OPTICALLY ATTENUATE
- LASER LIGHT ~ |

0 0.2 0.4 0.6 0.8 1.0 1.2
DC PHOTOCURRENT (mA)

Figure 5.3: Measurement of the shot noise level (SNL) vs. average detector photocurrent.
To confirm shot noise behavior, the SNL is seen to be a linear function of incident optical
power independent of optical loss before the detector. The incident optical power is varied

either by changing the laser bias or by inserting neutral density filters in the beam.

164

and the non-unity detector quantum efficiency. Fig. 5.4 shows relative intensity noise

(RIN) versus incident laser power where, by definition,

((AN)*)

“a (5.2.10)

RIN =

Because of loss, the measured RIN appears closer to the SNL than the true RIN at the
output facet. Even so, at 10 mW output power, the DBR laser’s intrinsic intensity
noise level at the output facet is seen to be only 0.8 dB above the SNL (a very quiet
laser).

From these results, we see that the balanced detector provides an ideal tool with

which to study laser intensity noise near the quantum level.

5.3 Amplitude-phase decorrelation in relation to the pho-

ton shot noise floor

Using the BHD at the output of the Michelson interferometer (see Fig. 4.9), amplitude-
phase decorrelation experiments were performed on the DFB laser discussed at the
end of chapter 4. Noise loops and the SNL could be measured for a particular laser
bias point by scanning the Michelson (see Fig. 4.11) and either adding or subtracting
the detector photocurrents. Again, because no adjustments are made to the detectors
or laser during the measurement, the balanced detector can unambiguously determine
where the intensity noise reduction stands in relation to the fundamental photon shot

noise level.

165

-120 a a
L a <«—— LASER RIN 7
aa AT OUTPUT FACET
SD -130 - 4
LL
° L A
> -140 F-F 4
oO . A
Ee -150 - ~
iT SHOT NOISE LEVEL
=> (STANDARD QUANTUM LIMIT)
Ee . =
x 160
LL L

. a 7 é) 1 it 1 { 1 j 1 it n i rm

-20 -15 -10 -5 0 5 10
INCIDENT LASER POWER (dBm)

Figure 5.4: Relative intensity noise (RIN) of the DBR lasing mode and the SNL vs. incident
optical power. The effect of loss on the measured noise is factored out to give the true RIN

at the output facet. The RIN falls with increasing power and comes within 0.8 dB of the

SNL at 10 mW output power.

166

5.3.1 Experimental results

Measurements were performed on the DFB laser for a range of bias points from
15.5 mA (near threshold) up to 40.0 mA. Noise power was measured at 17.8 MHz (in
the flat region of the spectrum) in a 100 kHz bandwidth. Figures 5.5 and 5.6 show a
representative series of loops and the SNL, as a function of detector dc photocurrent,
for two different laser bias points. It can be seen that although the noise power
may show a substantial reduction below the intrinsic level, the reduced noise remains
above the shot noise floor. In Fig. 5.7 noise power, as a function of incident laser
power, is shown in terms of RIN for the range of bias points tested. For each bias
point the shot noise level, intrinsic noise level, and maximally reduced noise level are
shown. The intrinsic RIN and reduced RIN describe the noise level at the output of
the Michelson interferometer, where the effect of loss between the Michelson output
and p-i-n detectors has been factored out in accordance with (5.2.9). The detection
quantum efficiency after the Michelson is 0.82, so there is very little difference between
the measured noise level and the true level at the Michelson output. At 15.5 mA bias
(-12 dBm incident power), the noise is reduced by a factor of 28.6 (14.5 dB), as
described in section 4.5. As the bias level increases, the intrinsic noise level falls, in
accordance with (5.2.1), and the amount of reduction decreases as the reduced noise
level approaches the SNL. At 40.0 mA bias (3.7 dBm incident power), the noise level
can only be reduced by 3.4 dB below the intrinsic level, and the reduced noise is
within 1.3 dB of the SNL.

The observed power dependence of the magnitude of reduction is consistent with

167

10-

NOISE POWER (arb. units)
nh

| |
0.48 0.72 0.96 1.20 i
DC PHOTOCURRENT (mA)

0 0.24

Figure 5.5: Noise loops and the shot noise level vs. detector dc current. DFB laser bias
is 24.0 mA (threshold is 14.5 mA). Loops correspond to interferometer path differences of
0.0 mm (intrinsic noise level), 0.4, 0.8, and 1.2 mm. Loop areas increase with increasing

path difference.

168

fo)

NOISE POWER (arb. units)
Bo

0 i | | i i j ! ! |
0 0.6 1.2 1.8 2.4 3.0 id
DC PHOTOCURRENT (mA)

Figure 5.6: Noise loops and the shot noise level vs. detector dc current. DFB laser bias
is 40.0 mA (threshold is 14.5 mA). Loops correspond to interferometer path differences of
0.0 mm (intrinsic noise level), 0.26, and 0.46 mm. Loop areas increase with increasing path

difference.

169

' I ' J t I ' 7 t J t T T T T
{ bs |
—~ 120 a INTRINSIC RIN
—< ™~,
~=- — a _
jan)
® -130 _— “
fe) .
Zz — REDUCED RIN oe _
oP) .
c -140 fF : *% 4
oS) ~
—_— — = J
= .
~ _
g ae a 4
2 oe
s -150 F, a se 4
or SHOT NOISE LEVEL aa Tes
I~ (STANDARD QUANTUM LIMIT) ite
-160 ! i : ! ' L \ i ! I 1 I \ i : j

12 -10 -8 -6 -4 -2 0 2 4

Incident Laser Power (dBm)

Figure 5.7: Intrinsic RIN, reduced RIN, and the shot noise level vs. incident power to the
balanced detector. Laser bias points range from 15.5 mA to 40.0 mA. Intensity noise is
reduced by 14.5 dB at low bias. At high bias, the noise is reduced to within 1.3 dB of the

SNL, but the magnitude of reduction decreases.

170

the presence of an uncorrelated, power-independent source of phase noise (A,) in the

instantaneous frequency fluctuation spectrum (see 4.2.15). The Michelson converts

A, into additive intensity noise, giving a maximum reduction (4.3.35)

RIN, 1+)

= 5.3.1
RIN; l+a?4+8 ( )

where £ is the ratio of the power-independent linewidth (the spectral density of
A.) to the Schawlow-Townes linewidth, so that @ is proportional to output power.
For this DFB laser, it was not possible to directly determine @ from a linewidth
measurement, because the laser could not be taken to high enough power to observe

linewidth saturation. However, from (5.3.1), 8 may be written as

8 = RIN, |
RIN,

-1. (5.3.2)

From the maximum measured noise reduction RIN, / RIN; for each power level (the
data in Fig. 5.7), the power dependence of 8 may be determined. We take |a| to be
5.25, consistent with the factor of 28.6 reduction near threshold. In Fig. 5.8, we see
that 8 as a function of laser power fits to a reasonable line, in agreement with the
simple model incorporating a power-independent source of phase noise in the rate
equations.

Similar measurements with the balanced detector on a variety of DFB lasers and
the DBR laser discussed above showed in all cases that amplitude-phase decorrelation
could reduce the intensity noise to a level very near, but not below the SNL. Insofar
as noise reduction is inhibited by the power-independent linewidth, a specialized DFB

laser with a narrow high-power linewidth, such as described in [18], may provide an

171

Beta

0 0.4 0.8 1.2 1.6 2 2.4

Incident Laser Power (mW)

Figure 5.8: Beta, from (5.3.2), vs. incident laser power. A linear relationship, consistent
with the presence of a power-independent source of phase noise in the rate equations, is

observed.

172

ideal source with which to demonstrate amplitude-phase decorrelation below the SNL.

5.3.2 Amplitude-phase decorrelation at the quantum level

Although the semiclassical formulation of amplitude-phase decorrelation agrees with
all aspects of the observed noise reduction, the issue of reduction below the shot
noise level properly requires a quantum-mechanical treatment. The shot noise level
is a manifestation of the zero-point (vacuum) fluctuations of a quantized radiation
field, and reduction below this level is tantamount to reducing the variance of the
amplitude quadrature of the field below this quantum-mechanical minimum.

Some new issues which would arise in a quantum treatment are briefly discussed
here. Because the Michelson, in order to have a finite slope at the lasing frequency,
must be detuned from maximum transmission, this allows vacuum fluctuations to
couple into the Michelson’s open port. These fluctuations, being uncorrelated with
the lasing mode, dilute the inherent correlation between the lasing mode fluctuations,
inhibiting noise reduction by the decorrelation technique. Sources of loss other than
the Michelson will also couple vacuum into the lasing mode, further diluting the
correlation.

The semiclassical rate equations (4.2.4)-(4.2.6) describe the field fluctuations within
the laser cavity. The output field, the one accessible to measurement, is a replica of
the intra-cavity field. At the quantum level this is no longer true. There are differ-
ences between the intra-cavity and output fields. For instance, a vacuum field which
couples into the cavity can interfere with itself at the laser facet [19]. Furthermore,

pump fluctuations should be taken into account, as these will affect the lasing field

173

fluctuations [20]. Indeed, it has been argued that by suppressing pump noise in a

laser diode, the intrinsic intensity noise can be sub-Poissonian when the laser is at

very high bias [21].

5.4 Conclusion

We have used a balanced homodyne detector to measure intensity noise reduction
by the amplitude-phase decorrelation technique in relation to the photon shot noise
level. For all lasers studied, intensity noise could be reduced close to, but not below
this fundamental noise floor. The observed power dependence of the reduction was
consistent with the presence of a power-independent source of phase noise in the

instantaneous frequency fluctuation spectrum.

174

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