Four-wave mixing in semiconductor optica

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Four-wave mixing in semiconductor optical amplifiers for terahertz spectroscopy and wavelength conversion
Citation
Zhou, Jianhui
(1995)
Four-wave mixing in semiconductor optical amplifiers for terahertz spectroscopy and wavelength conversion.
Dissertation (Ph.D.), California Institute of Technology.
doi:10.7907/vmke-sz45.
Abstract
Four-wave mixing in semiconductor gain media from GHz to THz detuning rates was used as a frequency-domain technique for analysis of carrier relaxation mechanisms having relaxation times extending from nanosecond to femtosecond time scales. Measurements of four-wave mixing in various semiconductor traveling-wave amplifiers were performed for detuning frequencies as large as 1.7 THz. Ultrafast intraband mechanisms having relaxation time constants of 650 fs, in agreement with dynamic carrier heating, and of less than 100 fs, in agreement with intraband carrier-carrier scattering, were determined in the measurements.

A novel cross-polarized four-wave mixing technique was also developed to study the inter quantum well carrier transport process in quantum well amplifiers. A semiconductor optical amplifier having a structure of alternating tensile and compressively strained quantum wells was used. Polarization selection rule of the strained quantum wells enables selective excitation and probing of adjacent quantum wells according to polarization, thereby enabling study of inter-well carrier transport. A one-dimensional diffusion model was developed to illustrate the different transport efficiencies for carrier number and temperature modulations, thereby qualitatively explaining the experimental data. The inter-well carrier number transport rate in the device measured was determined to be greater than 100 GHz.

Four-wave mixing in semiconductor optical amplifiers was also studied as a wavelength conversion technique. Conversion efficiency over spans up to 65 nm was measured, and wavelength conversion with gain was also demonstrated. It was found theoretically and confirmed experimentally that the conversion efficiency varies with the cube of the saturated amplifier gain. Noise characteristics of four-wave mixing wavelength converters and their dependence on various device and operational parameters were also studied. Noise reduction by introducing a filter between the preamplifier and the mixer was demonstrated and significant noise reduction was achieved. Finally, wavelength conversion of modulated signals at data rates of 2.5 Gb/s and 10 Gb/s was demonstrated.
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:
11 May 1995
Record Number:
CaltechETD:etd-09082005-105846
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DOI:
10.7907/vmke-sz45
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9)

Four-Wave Mixing in Semiconductor Optical Amplifiers
for Terahertz Spectroscopy

and Wavelength Conversion

Thesis by

Jianhui Zhou

In Partial Fulfillment of the Requirements
for the Degree of

Doctor of Philosophy

California Institute of Technology
Pasadena, California
1995

(Defended May 11, 1995)

Jianhui Zhou

The C

iii

To My Wife, Xiaoyu

The C

Acknowledgments

First and foremost, I wish to express deep thanks to my advisor, Professor Kerry
Vahala. I have thoroughly enjoyed working with him and learning from him. His
keen physical insight has continually provided invaluable guidance. His dedication
and enthusiasm has set an example for me of how to do science, and any professional
work. I will always look back with pride on what I have accomplished with him at
Caltech in the past five years.

Some of the measurements in this thesis were performed using Erbium-doped fiber
ring lasers developed by Dr. Namkyoo Park and Dr. Jay Dawson, then graduate
students in the group, to whom I owe special thanks. Thanks are also due to David
Geraghty for his collaboration on the wavelength conversion system measurement.
I would also like to thank other members, present and past, in the Vahala group
who have shared with me many stimulating discussions and have helped make my
Ph.D. pursuit an enjoyable and rewarding experience: Robert Lee, Roberto Paiella,
Guido Hunziker, Charles Tsai, Minyu Yao, Masashi Fukazawa, Hunsuk Kim, Renato
Camata, Dr. John Lebens, Dr. Winston Saunders, Dr. Pete Sercel, and Dr. Steve
Sanders. The assistance of Rosalie Rowe on day to day matters is much appreciated.

The semiconductor optical amplifiers used in the measurements were supplied by
AT&T Bell Laboratories. Special thanks are due to Drs. Michael Newkirk, Barry
Miller and Tom Koch who have donated their time and expertise. Michael has also

made valuable comments at the early stage of this thesis research. Ortel Corporation

has donated some of the DFB lasers and photodetectors used in the experiments

| The C

described in this thesis. In addition, the Advanced Research Projects Agency, the
Office of Naval Research and the National Science Foundation provided funding for
much of the research in this thesis.

My growth as an independent scientist in the past five years has also benefited
greatly from interactions with scientists and researchers outside Caltech. In particu-
lar, my appreciation goes to Dr. Tingye Li of AT&T Bell Labs, Dr. Norman Kwong of
Ortel, Dr. Antonio Mecozzi of FUB, Italy, Dr. Tien-Pei Lee of Bellcore, Dr. Katie Hall
of MIT and Prof. Kam-Yin Lau of UC-Berkeley. I especially thank Dr. Tingye Li who
has generously spent his valuable time giving me much appreciated encouragement
and advice.

I would also like to thank my parents, brother and sister for their unwavering
support throughout the years of my education. Finally, my deepest thanks go to my

wife, Xiaoyu. Her understanding, support, encouragement and love during these past

five years have been the greatest.

| The

Abstract

Four-wave mixing in semiconductor gain media from GHz to THz detuning rates
was used as a frequency-domain technique for analysis of carrier relaxation mecha-
nisms having relaxation times extending from nanosecond to femtosecond time scales.
Measurements of four-wave mixing in various semiconductor traveling-wave amplifiers
were performed for detuning frequencies as large as 1.7 THz. Ultrafast intraband
mechanisms having relaxation time constants of 650 fs, in agreement with dynamic
carrier heating, and of less than 100 fs, in agreement with intraband carrier-carrier
scattering, were determined in the measurements.

A novel cross-polarized four-wave mixing technique was also developed to study
the inter quantum well carrier transport process in quantum well amplifiers. A semi-
conductor optical amplifier having a structure of alternating tensile and compres-
sively strained quantum wells was used. Polarization selection rule of the strained
quantum wells enables selective excitation and probing of adjacent quantum wells
according to polarization, thereby enabling study of inter-well carrier transport. A
one-dimensional diffusion model was developed to illustrate the different transport
efficiencies for carrier number and temperature modulations, thereby qualitatively
explaining the experimental data. The inter-well carrier number transport rate in the
device measured was determined to be greater than 100 GHz.

Four-wave mixing in semiconductor optical amplifiers was also studied as a wave-

length conversion technique. Conversion efficiency over spans up to 65 nm was mea-

sured, and wavelength conversion with gain was also demonstrated. It was found

|The €

Vii

theoretically and confirmed experimentally that the conversion efficiency varies with
the cube of the saturated amplifier gain. Noise characteristics of four-wave mix-
ing wavelength converters and their dependence on various device and operational
parameters were also studied. Noise reduction by introducing a filter between the
preamplifier and the mixer was demonstrated and significant noise reduction was

achieved. Finally, wavelength conversion of modulated signals at data rates of 2.5

Gb/s and 10 Gb/s was demonstrated.

Contents

1 Introduction 1

2 Semiconductor Lasers and Amplifiers 7
2.1 Introduction... .. 1... 2. ee 7
2.2 Optical Gain in Semiconductors ..........0. 00004 eee 10
2.3 Gain Saturation and Nonlinearities ................04. 16

3 Four-Wave Mixing in Semiconductor Optical Amplifiers 24
3.1 Introduction... 2... 0. 2 24
3.2 Theoretical Analysis .. 2... . ee 25
3.38 Discussion... 0. 32

4 Terahertz Four-Wave Mixing Spectroscopy of Intraband Dynamics 36
4.1 Introduction... 1... 2. 36
4.2 Four-Wave Mixing Measurements ..................06. 37
4.3 Analysis of Experimental Results .................00. 44
44 Conclusion... 2... 0. A9

5 Inter-Well Carrier Transport Dynamics . 52
5.1 Introduction... . 2... 2 52

| 5.2 Cross-Polarized Four-Wave Mixing Experiments ............ 55
5.3 Analysis of Experimental Results ................2004% 58
5.4 Conclusion... 2... 63

6 Broadband Four-Wave Mixing Wavelength Conversion 68
6.1 Introduction ... 2... 2... 2 ee 68
6.1.1 Fiber-Optic Communications ................204 68

6.1.2 All-Optical Network and Wavelength Conversion. ....... 70

6.2 Wavelength Conversion Efficiency ................2008. 72
6.3 Noise Properties and Noise Reduction. ................0. 78
6.3.1 Noise Properties... .. 2... 2.2... 00. eee ee ee 78

6.3.2 Noise Reduction............... 0.0.0... 20050.4 82

6.3.3 Optimal Converter Structure................0-4 85

6.4 Wavelength Conversion of Modulated Signal .............. 86
6.5 Conclusion... 2... 91

| The

List of Figures

2.1

4.1
4.2
4.3

4.4

4.5

5.1

5.2

0.3

Illustration of physical processes involved in intraband gain saturation

Schematic structure of Erbium-doped fiber ring lasers ........
Band diagram of a tensile strained SOA... .......-2-0-4
Experimental setup for four-wave mixing measurements........
Normalized four-wave mixing signal power spectra measured on a ten-
sile strained SOA... 2... ee
Normalized four-wave mixing signal power spectra measured on a com-

pressively strained SOA ... 2... . ee

Conceptual band diagrams illustrating carrier transport in quantum
well lasers and amplifiers... ........0.. 0000002 ee eee
Band diagram of an alternating-strained SOA and diagram of co- and
cross-polarized four-wave mixing. ............. 2.000008

Normalized four-wave mixing signal power spectra for co- and cross-

polarized configurations ............. 0.0000 2s

6.1

6.2

6.3

6.4

6.5

6.6

Measured conversion efficiency versus tandem amplifier gain and versus
wavelength shift (tandem amplifier with two SOA’s) .........
Measured conversion efficiency versus tandem amplifier gain and versus
wavelength shift (tandem amplifier with three SOA’s) ........
Measured converted signal power, spontaneous noise, and optical SNR
versus total input power... 2... ee
Noise reduction versus input spontaneous noise power density

Experimental setup used to demonstrate wavelength conversion of mod-
ulated signal... 2...

Converted data pattern and eye diagrams...............-.

Chapter 1

Introduction

Semiconductor optical amplifiers (SOA’s) are of increasing interest for applications
in broadband lightwave communication systems such as broadband wavelength con-
version and ultrafast optical signal processing [1]. It is interesting to note that most
of these applications are not due to the SOA’s amplifying nature, but rather due to
their nonlinearities. While the linear characteristics of these devices have been well
understood, their nonlinear properties are not yet well established.

In this thesis, four-wave mixing experiments in SOA’s and accompanying theory
are presented which explore intraband dynamics of semiconductor active layers and
inter quantum well carrier transport dynamics. Broadband wavelength conversion us-
ing four-wave mixing in SOA’s is also studied for applications in future multichannel
lightwave communication networks. Results concerning conversion efficiency, noise
properties, and system impact are presented. The SOA’s used in this thesis research
are InGaAs/InGaAsP strained multiple quantum well traveling-wave amplifiers op-

erating at 1.5 wm. This is the most important communication band since it is where

silica fibers exhibit minimum attenuation (~ 0.2 dB/km) and where high-performance
Erbium-doped fiber amplifiers are available [2].

Chapter 2 is an introduction to semiconductor lasers and amplifiers. It contains
basic semiconductor laser physics necessary to understand the four-wave mixing spec-
troscopy work described in this thesis.

In Chapter 3, the theory governing the four-wave mixing process in SOA’s is
presented which accounts for contributions to four-wave mixing from both interband
and intraband dynamics. Coupled-amplitude equations are solved and an analytical
expression for four-wave mixing signal strength is obtained.

Chapter 4 describes four-wave mixing experiments in which four-wave mixing sig-
nal spectra are measured at detuning frequencies up to 1.7 THz. Analysis of these
signal spectra reveals ultrafast intraband dynamics in agreement with dynamic carrier
heating and intraband carrier-carrier scattering processes.

Chapter 5 describes a novel cross-polarized four-wave mixing technique that we
developed to study inter quantum well carrier transport. The experimental data are
qualitatively explained by noting the different transport efficiencies for carrier number
and temperature modulations. In addition, the inter-well carrier number transport
rate in the device measured is determined to be greater than 100 GHz.

Chapter 6 first presents an introduction to fiber-optic communications and on-
going efforts for next generation multiwavelength all-optical networks. This review
is intended to help explain the application of SOA four-wave mixing wavelength con-

version described in this chapter. Results concerning the conversion efficiency over

spans up to 65 nm, as well as a demonstration of wavelength conversion with gain
are presented. Issues concerning the noise properties of four-wave mixing wavelength
converters are also addressed. Finally, a demonstration of wavelength conversion
of modulated signals at data rates of 2.5 Gb/s and 10 Gb/s is described and the
experimental results are discussed.

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

proceedings [3]-[21].

Bibliography

[1]

[2]

[3]

[6]

S. Shimada, K. Nakagawa, M. Saruwatari, and T. Matsumoto, “Very-high-speed
optical signal processing,” Proc. IEEE, vol. 81, pp. 1633-1646, 1993.

T. Li, “The impact of optical amplifiers on long-distance lightwave telecommu-
nications,” Proc. IEEE, vol. 81, pp. 1633-1646, 1993.

J. Zhou, N. Park, J. W. Dawson, K. J. Vahala, M. A. Newkirk, U. Koren, and
B. I. Miller, “Highly nondegenerate four-wave mixing and gain nonlinearity in
a strained multiple-quantum-well optical amplifier,” Appl. Phys. Lett., vol. 62,
pp. 2301-2303, 1993.

J. Zhou, N. Park, J. W. Dawson, K. J. Vahala, M. A. Newkirk, and B. I. Miller,
“Terahertz four-wave mixing spectroscopy for study of ultrafast dynamics in a
semiconductor optical amplifier,” Appl. Phys. Lett., vol. 63, pp. 1179-1181, 1993.

J. Zhou, N. Park, J. W. Dawson, K. J. Vahala, M. A. Newkirk, and B. I. Miller,
“Efficiency of broadband four-wave mixing wavelength conversion using semi-
conductor traveling-wave amplifiers,” IEEE Photon. Technol. Lett., vol. 6, pp.
50-52, 1994.

J. Zhou, N. Park, K. J. Vahala, M. A. Newkirk, and B. I. Miller, “Broadband
wavelength conversion with amplification by four-wave mixing in semiconductor
traveling-wave amplifiers,” Electron. Lett., vol. 30, pp. 859-860, 1994.

J. Zhou, N. Park, K. J. Vahala, M. A. Newkirk, and B. I. Miller, “Four-wave
mixing wavelength conversion efficiency in semiconductor traveling-wave ampli-
fiers measured to 65 nm of wavelength shift,” IEEE Photon. Technol. Lett., vol.
6, pp. 984-987, 1994.

(8)

[9]

[10]

[11]

[14]

J. Zhou, N. Park, K. J. Vahala, M. A. Newkirk, and B. I. Miller, “Study of
inter-well carrier transport by terahertz four-wave mixing in an optical amplifier
with tensile and compressively strained quantum wells,” Appl. Phys. Lett., vol.
65, pp. 1897-1899, 1994.

K. J. Vahala, J. Zhou, N. Park, J. W. Dawson, M. A. Newkirk, and B. I. Miller,
“Measurement of gain nonlinearity in a strained multiple-quantum-well optical
amplifier by highly nondegenerate four-wave mixing,” Conference on Lasers and
Electro-Optics, Baltimore, Maryland, May 2-7, 1993, paper JTHA6.

K. J. Vahala, J. Zhou, N. Park, J. W. Dawson, M. A. Newkirk, and B. I. Miller,
“Terahertz four-wave mixing spectroscopy of intraband dynamics in quantum
well amplifiers,” Conference on Lasers and Electro-Optics, Baltimore, Maryland,
May 2-7, 1993, paper CPD2.

J. Zhou, N. Park, J. W. Dawson, K. J. Vahala, M. A. Newkirk, and B. I. Miller,
“Efficiency of broadband wavelength conversion by four-wave mixing in semicon-
ductor traveling-wave amplifiers,” IEEE Lasers and Electro-Optics Society 1993
Annual Meeting, San Jose, California, November 15-18, 1993, paper OS3.2.

J. Zhou, N. Park, K. J. Vahala, M. A. Newkirk, and B. I. Miller, “Inter quantum-
well carrier transport probed by THz four-wave mixing spectroscopy in a semi-
conductor optical amplifier,” Conference on Lasers and Electro-Optics, Anaheim,
California, May 8-13, 1994, paper CThF1.

J. Zhou, N. Park, K. J. Vahala, M. A. Newkirk, and B. I. Miller, “Wide-band
lossless wavelength conversion by four-wave mixing in semiconductor traveling-

wave amplifiers,” Conference on Lasers and Electro-Optics, Anaheim, California,
May 8-13, 1994, paper CThA7.

K. J. Vahala, J. Zhou, N. Park, M. A. Newkirk, and B. I. Miller, “Broadband
optical wavelength conversion with gain by four-wave mixing in a semiconductor
traveling-wave amplifier,” Conference on Lasers and Electro-Optics, Anaheim,
California, May 8-13, 1994, paper CPD4.

K. J. Vahala, J. Zhou, N. Park, M. A. Newkirk, and B. I. Miller, “Four-

wave mixing in semiconductor traveling-wave amplifiers for efficient, broadband,

wavelength conversion up to 65 nm,” 1994 IEEE Nonlinear Optics Conference,
Waikoloa, Hawaii, July 25-29, 1994, paper TuA2.

[16]

[17]

[18]

[19]

[21]

J. Zhou, N. Park, K. J. Vahala, M. A. Newkirk, and B. I. Miller, “High effi-
ciency, broadband, wavelength conversion by four-wave mixing in semiconductor
traveling-wave amplifiers,” Optical Amplifiers and Their Applications Topical
Meeting, Breckenridge, Colorado, August 3-5, 1994, paper FC3.

J. Zhou, N. Park, K. J. Vahala, M. A. Newkirk, and B. I. Miller, “Efficient, broad-
band, wavelength conversion by four-wave mixing in semiconductor traveling-
wave amplifiers,” Optical Society of America 1994 Annual Meeting, Dallas,
Texas, October 2-7, 1994, paper THOOS.

J. Zhou, N. Park, K. J. Vahala, M. A. Newkirk, and B. I. Miller, “Terahertz
four-wave mixing in semiconductor optical amplifiers: physics and applications,”
SPIE Photonics West, San Jose, California, February 6-10, 1995. (Invited)

K. J. Vahala, J. Zhou, N. Park, M. A. Newkirk, and B. I. Miller, “Four-wave mix-
ing in semiconductor optical amplifiers for wavelength conversion and terahertz
spectroscopy,” Conference on Lasers and Electro-Optics, Baltimore, Maryland,
May 21-26, 1995, paper CThF5. (Invited)

J. Zhou and K. J. Vahala, “Spontaneous noise reduction in four-wave mixing
wavelength converters,” Conference on Lasers and Electro-Optics, Baltimore,
Maryland, May 21-26, 1995, paper CThT1.

K. J. Vahala, J. Zhou, M. A. Newkirk, and B. I. Miller, “Wavelength shifting by

four-wave mixing in semiconductor optical amplifiers,” IEEE Lasers and Electro-

Optics Society 1995 Annual Meeting, San Francisco, California, October 30 —
November 2, 1995. (Invited)

Chapter 2

Semiconductor Lasers and

Amplifiers

2.1 Introduction

Optical amplification and feedback are two essential requirements for lasing oscilla-
tion. In semiconductor lasers, amplification is accomplished by an electrically pumped
active region sandwiched in the middle of a p-n junction, and in the simplest laser
device, i.e., Fabry-Perot laser, feedback is provided by the reflection of the cleaved
facets of the laser chip. More sophisticated feedback structures have also been devel-
oped for better laser performance, for example, distributed-feedback (DFB) devices
are lasers in which optical feedback, as the name implies, is not provided by the lo-
calized facet mirrors but by a built-in grating that is distributed throughout the laser

cavity.

The semiconductor material systems for laser fabrication are generally of two main

types, the GaAs/GaAlAs system and InP/InGaAsP system. GaAs/GaAlAs devices
typically have lasing wavelengths in the range 0.7 — 0.9 um while InP/InGaAsP
devices generally lase at longer wavelengths within the 1.1 — 1.6 wm range. The longer
wavelength lasers are important for long-haul optical communication because at these
wavelengths silica fibers have extremely low attenuation (as low as 0.2 dB/km at 1.55
ym). Other material systems have been investigated extensively in recent years for
laser operation in other regions of the optical spectrum, for example, in the visible
spectrum for applications in medical diagnostics, bright displays and high-density
optical data storage and also for replacement of bulky and expensive solid and gas
lasers.

Laser operation of a semiconductor p-n junction device was first demonstrated
by four independent research groups within six weeks of one another in 1962 [1]-
[4]. Initially, due to the severe heating problems caused by the high lasing threshold
current, lasing action could only be generated continuously at low temperature or in
pulsed operation at room temperature, and device lifetimes were also short. Since that
time, semiconductor lasers have developed at a remarkable pace [5]-(8]. Fabrication
technology and device design have progressed to the point where highly reliable lasers
with extrapolated room temperature lifetimes of a century are routinely produced.

Because of their low cost, reliability, low power consumption, and capability for
high-speed modulation, among other features, semiconductor lasers are technolog-

ically attractive sources of coherent optical radiation for a variety of applications.

Most notably, semiconductor lasers are playing an integral part in the ever-expanding

lightwave communication industry. One of the most important characteristics for
semiconductor lasers used in lightwave communication systems is the direct modula-
tion bandwidth. Part of this thesis studies two physical mechanisms that can limit
semiconductor laser modulation bandwidth: ultrafast intraband dynamics and inter
quantum well carrier transport.

When the cleaved facets of a semiconductor laser are anti-reflection coated, the
device is referred to as a semiconductor optical amplifier (SOA). Two types of SOA’s
can be distinguished, Fabry-Perot amplifier and traveling-wave amplifier. The former
is essentially a laser biased above transparency but below lasing threshold. The result
is an amplifier having a series of narrow bandpasses with the resonant-enhanced gain
as the envelope. With the latter, on the other hand, great care is exerted to make
the reflectivity of both facets as low as possible, typically as low as 1074 - 107°. The
device will amplify the incident signal in a single pass through the active region, thus
with little cavity-resonance effects in the gain spectrum.

Research on SOA’s dates back to the 1960’s, soon after the invention of semi-
conductor lasers [9],[10]. However, it was only during the 1980’s that SOA’s were
developed for practical applications, largely motivated by potential applications in
lightwave communication systems [11]-[15]. Early studies were conducted on Fabry-
Perot amplifiers [9]-[11], but more recent research has concentrated on traveling-wave
amplifiers [16]|-[18]. Several ways of suppressing the end reflectivity have been demon-

strated to obtain traveling-wave operation. These include multi-layer anti-reflection

coating [16], angled facet [17], and window facet structures [18].

SOA’s have been used as pre-amplifiers [19] and in-line amplifiers [20] in a number
of lightwave transmission system experiments. They have also been employed to
overcome distribution losses in the local area network applications [21]. However,
SOA’s, initially developed for optical amplification, have in recent years largely given
up the role in the 1.5 um communication window to Erbium-doped fiber amplifiers
which are far superior as optical amplifiers [22]. SOA’s have nevertheless found other
“unconventional” applications to which a large body of research has been devoted
in recent years [23]-[26]. These efforts include using SOA nonlinearities to achieve
important functionalities for lightwave communication systems such as broadband
wavelength conversion [23],[24], all optical clock recovery [25] and ultrafast optical
signal processing [26]. In addition, SOA’s are important components in photonic
integrated circuits [27].

In this chapter, optical gain in semiconductors is reviewed. Gain nonlinearities,
which are responsible for nonlinear applications of SOA’s, and the physical processes
associated with these nonlinearities, i.e., dynamic carrier heating and spectral hole

burning, are also analyzed.

2.2 Optical Gain in Semiconductors

The wave function of an electron in a given band (conduction or valence) in semicon-

ductors can be written as

Veo(r) = Ucuk(r)e** (2.1)

where the subscripts c and v denote for conduction and valence bands, respectively,
and Uevk(r) has the periodicity of the crystalline lattice. The “propagation” constant

k is quantized and its components are given by

_ 27m

= (2.2)

where j = 2, y, Z; mis an integer; and L, is the length of the crystal in the 7 direction.
The k space volume for each electronic state is thus 87°/V where V is the crystal’s
physical volume. The number of electronic states per band for a value of k between

k and k + dk is given by

k2
p(k)dk = “tak (2.3)

where a factor of two has been added accounting for the two spin states of electrons
for each k eigenvalue.
Using the parabolic band approximation

_ WR

E() 2m*

(2.4)

where m* is the effective mass and the energy FE is measured from the band edge

extremum, the density of states per unit energy interval can be readily expressed as

dk 1 (2m*,\*”
Pool Se = saz (pet) BM (2.5)

Pov (E) = V
The above expression gives the density of states for 3-dimensional (3-D) electrons

and holes, i.e., available k-states in the 3-D space are counted. In quantum well

structures, where electrons and holes are confined to planes of motion, we instead

count the 2-dimensional (2-D) availability of k-states and find that the 2-D density

of states (per unit energy and unit area) can be expressed as

oo H(E — Eno 2.6
et H(E - Enew) (2.6)

p(B) = )>
n=1

where H(z), the Heaviside function is equal to unity when x > 0 and is zero when
z < 0, and where E,,,. is the eigen energy value for the n“ transverse quantum state
in the conduction or valence band.

The density of states defines how many states exist for a given energy interval
KE — E+dE. The probability that a given state is actually occupied by an electron

is governed by the Fermi-Dirac law

f(E) = 1 + e(E—E;)/keT

(2.7)

where Ey is the Fermi energy, kg is the Boltzmann’s constant and T is the temper-
ature. In thermal equilibrium, a single Fermi energy applies to both conduction and
valence bands. Under conditions in which the thermal equilibrium is disturbed, for
example, by electrical pumping, two separate Fermi levels Ey, and Eyy, called quasi-
Fermi levels, are used for each of the bands. In this case the electron density N and

hole density P can be written as
N = |" f.(B)pe(B)dE (2.8)
P= [° f(B)p(B)de (2.9)

To calculate the optical gain for a semiconductor system, we start from a two-level

discrete atomic or electronic medium. Let us assume that the population densities of

lower and upper levels are N; and No, respectively, and the energy difference between

the two levels is fiwo. The complex susceptibility of such a system can be found using

the density matrix formalism and it is given by [28]

_ _ T2(No — Ni) [(wo — w)To — @
x(w) = eli + (w — w)°T]

(2.10)

where pz is the momentum matrix element and T> is a phenomenologically introduced
dephasing time.

In a direct-gap semiconductor, the minimum in the conduction band and the max-
imum in the valence band occur at the same value of the wave vector k. Since the
photon carries negligible momentum compared with the carrier momentum hk, radia-
tive transitions occur between electrons and holes of essentially same wave vectors.
In the case of such a semiconductor system, modification to the density inversion
(N2 — N,) can be achieved by first considering the contribution from electrons with
a value of the wave vector between k and k + dk. Their contribution to the density

inversion is found to be

d(No ~~ N;) = Golk)dk{ f(a) ~ Ful s)] ~ fo( Fs) [1 ~ fe(Ea)|}

= Zolk)dklfe(Ba) — fol Ea)] (2.11)

where E, = h?k?/2m* and E, = h?k?/2m* are the energy levels corresponding to the
wave vector value k in the conduction and valence bands, respectively. Substituting
Eq. (2.11) for (No — Ni) in Eq. (2.10) gives the total complex susceptibility in a

semiconductor

x(w) = [fe( Ea) ~ fu( Ee) p(k) dk (2.12)

Vso eoh[l + (w — w)?T?]

We note that there exists the following relation
hwo = (Ep +E.) — (Ey — Ey) = Ey + tk? /2m* (2.13)

where E,, Ey are energy levels of the conduction band minimum and the valence band
maximum, respectively; EH, = E, — E, is the band gap; and m7 is the reduced mass
given by the relation m*~! = m*~! + m*~!. Using Eqs. (2.3) and (2.13), we change
the independent variable of Eq. (2.12) to wo and obtain the following expression for
the complex susceptibility

1 aed (wo _ w)T> —1

— Tp.
x(¥) €oh JEy/t 1 (wo) Tap; (wo) 1+ (w —wy)?T?

where we have introduced the joint density of states p;(wo), which is given by

1 (2m:

3/2
pj(Wo) = on Kh ) (wo — E,/h)\? (2.15)

In addition, the explicit expressions for the Fermi functions appearing in Eq. (2.14)
are given by

fe(wo) = = 2.16

fo(wo) = 3 2.17

1 + elk (two Eg) + Bo — Byo]/keT (2.17)

It follows that the gain constant can then be expressed as

yu) = Simpx(u)}
nn a Tdevg
= Deck Ip, nt “odes (o)l felwo) — folwo)l wow 8)

where n is refractive index of the semiconductor material and k = wn/c is the wave

number of the incident optical field at optical frequency w/27. Since w and E,/h are

on the order of 10! s~!, and Ty! is typically on the order of 10" s~!, ——2,
2 1+(w—wo)?Tz

can be approximated as 76(w — wp) when the integral in Eq. (2.18) is evaluated. This

leads to

2 m*\3/2
(e) = <2 (=E) w= By/h)*Lfalw) — folw) (2.19)

In a similar fashion, we can derive the gain constant for a pumped quantum well

structure having a well thickness of L,. It is given by

2m p2m*

= OT [fl) ~ flu] So H he ~ (Ey + Ee + Boe)} (220)

n=1

VP (w)

Eqs. (2.19) and (2.20) give a clear physical picture of optical gain in semiconduc-

tors. The necessary condition for net gain (7 > 0) in either case is that

fe(w) ~ fu(w) >0 (2.21)
If we use the Fermi functions given by Eqs. (2.16) and (2.17), the condition becomes
Eye — Ey > hw (2.22)

Eqs. (2.19) and (2.20) also indicate that the gain profile depends sensitively on
many parameters. First, it depends on the carrier density N, which determines the
quasi-Fermi energies for the carriers via Eqs. (2.8) and (2.9). These quasi-Fermi en-
ergy levels, in the context of the Fermi functions, determine the occupancy probability
and is used in Eqs. (2.19) and (2.20) to calculate the gain. The carrier density can be
varied by electrical injection or optical excitation. Under a given pumping condition,

the carrier density can be calculated by solving a rate equation, as will be presented

in the following section.

The gain profile also depends sensitively on the carrier temperature, which affects
the Fermi distribution functions, as expressed in Eqs. (2.16) and (2.17). In the next
section, saturation of semiconductor optical gain due to carrier temperature increase

will be discussed.

2.3 Gain Saturation and Nonlinearities

Gain saturation, an important property of semiconductor lasers and amplifiers, can
be understood using the rate equation analysis. The carrier density N at an injected
current J and in the presence of optical power P can be obtained by solving the rate
equation

dN I N_ 4(N) ;
GV Ano tDVN (2.23)

where q is the electron charge; V is the active layer volume, 7, is the spontaneous
carrier lifetime, y(N) is the gain constant per unit length as given by Eq. (2.19)
or Eq. (2.20), A is the cross-section area of the optical guided mode and D is the
carrier diffusion coefficient. This rate equation can be derived from the density matrix
formalism combined with the rate equation approximation and can also be understood
intuitively from the viewpoint of carrier number bookkeeping.

In the case of semiconductor optical amplifiers, the carrier density N is also a
function of longitudinal location z. The solution of the above equation is complicated
because of the presence of the diffusion term. The main effect of the carrier diffusion

is to wash out the carrier gradient in the longitudinal direction. To a good degree

of approximation, this term can be ignored in the case of traveling-wave amplifiers.

The carrier density N thus satisfies the simpler rate equation

dN I oN (N)
a = Lp 2.24
dt qV tt Aw (2.24)

To simplify the solution of Eq. (2.24), the optical gain is assumed to vary linearly

with the carrier density N, i.e.,
y(N) = a(N — No) (2.25)

where a is the differential gain and Np is the carrier density at. which the active region
becomes transparent. Under the condition of steady operation, 7.e., injection current
I and optical power P are constant, the carrier density is found to be

_ It./qV + NoP/P;

2.26
1+ P/P, (2.26)
where P, is the saturation power given by
p, = Ah (2.27)
aT.
Gain saturation behavior can thus be expressed
a(It,/qV — Ni
(WN) = a(N — No) = “ete/a — No) _ yg (2.28)

1+ P/P;
where yo = a(I7;/qV — No) is the unsaturated optical gain in absence of input optical
field, and where we have introduced a saturation factor S, which is a function of z
and is given by

5 = Ty PayP,

(2.29)

Physically, the gain saturation is caused by stimulated emission through which

carrier density is reduced by the input optical field. This saturation phenomenon,

usually referred to as interband gain saturation, has been extensively studied and
well understood. There exists yet another type of gain saturation, resulting from
various intraband processes. In this case, the occupation probability of the carriers in
each energy band, rather than the actual carrier population, is altered by the input
optical field. This leads to intraband gain saturation, also known as the nonlinear gain
effect which is often phenomenologically represented by a nonlinear gain coefficient
€p, as defined in the relation y(N, P) = y(N,0)/(1+ epP).

Intraband processes that cause gain nonlinearity typically include dynamic carrier
heating and spectral hole burning. Dynamic carrier heating results from stimulated
emission, which removes “cold” carriers close to the band edges, and free-carrier ab-
sorption, which transfers carriers to high energies within the bands. These nonthermal
carriers thermalize among themselves via the intraband carrier-carrier scattering pro-
cess on a time scale of < 100 fs. The hot carrier distributions relax to the lattice
temperature by emission of optical phonons with a characteristic time constant of
~ 1 ps. For a fixed carrier density N, heating the carrier distribution will compress
the optical gain, as can be understood by using Eq. (2.19) or Eq. (2.20), resulting in
gain nonlinearity. The physical processes of dynamic carrier heating and gain profile
change are illustrated in Figure 2.1.

Spectral hole burning, on the other hand, refers to a spectrally local gain reduction
due to the input optical field. Stimulated emission removes carriers at states in the

band corresponding to the photon energy. The carriers in neighboring states can

not completely replenish the removed carriers due to finite intraband carrier-carrier

J, > ©
aw e
hv
AV AVAVA Vee
hy VN
AV AVAVA Vee
hv
O fe)
(a) Stimulated Emission (b) Free Carrier Absorption

Ta>T1 Spectral
Hole
(c) Carrier Heating Effect (d) Spectral Hole Burning

Figure 2.1: Illustration of physical processes involved in dynamic carrier heating and spectral

hole burning.

scattering time (< 100 fs), which sets the time scale on which non-Fermi carrier
distributions are restored to equilibrium. This process creates a “hole” in the carrier
distribution in the k-space and, consequently, a spectral hole in the gain profile. This
is also illustrated in Figure 2.1.

Gain nonlinearities caused by intraband dynamics are intrinsically weak and gain
reduction is usually much less than 1%. Such a small gain reduction barely affects
the laser characteristics under continuous operation; however, owing to their ultrafast
nature (< 1 ps), intraband dynamics can greatly affect semiconductor laser dynam-
ics, including noise properties and modulation dynamics [29]. For example, nonlinear
gain introduces an additional damping to the relaxation oscillation in semiconductor
laser modulation, severely limiting the maximum modulation bandwidth. In addition,
these gain nonlinearities cause undesirable cross-talk for wavelength multiplexed sig-
nals in semiconductor optical amplifiers. On the other hand, however, they can be

utilized to realize ultrafast switching, wavelength conversion and other useful nonlin-

ear functionalities [23]—[26].

Bibliography

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[2] M.I. Nathan. W. P. Dumke, G. Burns, F. H. Dill, Jr., and G. Lasher, “Stimulated
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[3] N. Holonyak, Jr., and S. F. Bevacqua, “Coherent (visible) light emission from
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[4] T. M. Quist, R. H. Rediker, R. J. Keyes, W. E. Krag, B. Lax, A. L. McWhorter,
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91-92, 1962.

[5] H. Kressel and J. K. Butler, Semiconductor Lasers and Heterojunction LED’s,
Academic Press, 1977.

[6] H. C. Casey, Jr., and M. B. Panish, Heterostructure Lasers: Part A, Academic
Press, 1978.

[7] G. P. Agrawal and N. K. Dutta, Long-Wavelength Semiconductor Lasers, van
Nostrand Reinhold, 1986.

[8] P. S. Zory, Jr., Ed. Quantum Well Lasers, Academic Press, 1993.

[9] J. W. Crowe and R. M. Craig, Jr., “Small-signal amplification in GaAs lasers,”
Appl. Phys. Lett., vol. 4, pp. 57, 1964.

[10] W. F. Kosonocky and R. H. Cornely, “GaAs laser amplifiers,” IEEE J. Quantum
Electron., vol. 4, pp. 125, 1968.

[11] Y. Yamamoto, “Characteristics of AlGaAs Fabry-Perot cavity type laser ampli-
fiers,” IEEE J. Quantum Electron., vol. 16, pp. 1047-1052, 1980.

[12] J. C. Simon, “Semiconductor laser amplifiers for single mode fiber communica-
tions,” J. Optical Commun., vol. 4, pp. 51-62, 1983.

[13] J. C. Simon, “GaInAsP semiconductor laser amplifiers for single mode fiber com-
munications,” IEEE J. Lightwave Technol., vol. 5, pp. 1286-1295, 1987.

[14] M. J. O’Mahony, “Semiconductor-laser optical amplifiers for use in future fiber
systems,” IEEE J. Lightwave Technol., vol. 6, pp. 531, 1988.

[15] N. A. Olsson, “Lightwave systems with optical amplifiers,” IEEE J. Lightwave
Technol., vol. 7, pp. 1071-1082, 1989.

[16] T. Saitoh, T. Mukai, and O. Mikami, “Theoretical-analysis and fabrication of
antireflection coatings on laser-diode facets,” IEEE J. Lightwave Technol., vol.
3, pp. 288-293, 1985.

[17] C. E. Zah, J. S. Osinski, C. Caneau, S. G. Menocal, L. A. Reith, J. Salzman, F.
K. Shokoohi, and T. P. Lee, “Fabrication and performance of 1.5 ym GaInAsP
traveling-wave laser-amplifiers with angled facets,” Electron. Lett. vol. 23, pp.
990-992, 1987.

[18] N. A. Olsson, R. F. Kazarinov, W. A. Nordland, C. H. Henry, M. G. Oberg,
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[19] N. A. Olsson and P. A. Garbinski, “High-sensitivity direct-detection receiver with
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[20] M. G. Oberg, N. A. Olsson, L. A. Koszi, and G. J. Przybylek, “313-km trans-
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Electron. Lett., vol. 24, pp. 38-39, 1988.

[21] W. I. Way, C. E. Zah and T. P. Lee, “Applications of traveling-wave laser-
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[22] T. Li, “The impact of optical amplifiers on long-distance lightwave telecommu-
nications,” Proc. IEEE, vol. 81, pp. 1633-1646, 1993.

[23] M. C. Tatham, G. Sherlock, and L. D. Westbrook, “20 nm wavelength conversion
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1303-1306, 1993.

[24] J. Zhou, N. Park, K. J. Vahala, M. A. Newkirk, and B. I. Miller, “Four-wave
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lasers,” SPIE Proc., vol. 1497, pp. 444-455, 1991.

Chapter 3

Four-Wave Mixing in

Semiconductor Optical Amplifiers

3.1 Introduction

Nondegenerate four-wave mixing in semiconductor optical amplifiers (SOA’s) has
been a topic of increasing interest over the past few years. Four-wave mixing has
been demonstrated as an effective frequency-domain tool to probe ultrafast semicon-
ductor dynamics [1]-[5]. It has also be studied for applications in lightwave systems,
including wavelength conversion [6|-[8], all-optical demultiplexing of high bit-rate
time-division-multiplexed signals [9] and all-optical conversion from time-division-
multiplexing to wavelength-division-multiplexing [10].

Physical mechanisms responsible for four-wave mixing are interband gain satura-

tion, arising from stimulated emission, and intraband gain nonlinearities, resulting

from intraband dynamics. In the former case, carrier density is modulated by the op-

tical beating of pump and probe, while in the latter case, the carrier density remains
unchanged but intraband occupancy probability is modulated. Both mechanisms can
create dynamic gain and index gratings along the amplifier length. The subsequent
scattering of pump and probe fields from these gratings results in the generation of
two new side bands. This is the basic process of four-wave mixing in SOA’s.

In the next section, the theory concerning four-wave mixing in SOA’s is presented
which includes contributions to four-wave mixing from both interband and intraband
dynamics. Experimental investigation of using four-wave mixing to probe ultrafast

intraband dynamics will be presented in the next chapter.

3.2 Theoretical Analysis

Four-wave mixing in a semiconductor medium generated by intraband occupancy
modulation was first analyzed by Agrawal [11]. His theory, based on the density-
matrix equations, included contributions from interband carrier density modulation
and spectral hole burning. A recently published paper by Uskov et al. [12], also based
on density-matrix approach, included both carrier heating and spectral hole burning.
In this chapter, we use some results from the above referenced work and put our
emphasis on an analytical solution to the coupled equations. We also address some
practical issues such as the phase matching condition.

Let us assume that the pump, probe and the four-wave mixing signal all have the

same polarization, and that these guided waves are given by

E;(z,t) = E;(z) exp [i(k;z — w,t)] (3.1)

where 7 = p,q, s denote pump, probe and four-wave mixing signals, respectively; and
{E;(z)} are the slowly-varying amplitudes of the three waves.

The interband and intraband photomixing of pump and probe waves in the active
layer will of course influence the propagation of the four-wave mixing signal wave, as
well as the pump and probe waves themselves. We can describe the propagation of
these waves by means of coupled-amplitude equations. Assuming the validility of the
slowly-varying-amplitude approach, and following procedures similar to those used in
Agrawal’s treatment [11], we find that the slowly varying amplitudes must obey the

following set of coupled equations

dEyq(Z )

Bat) © [ao S(2) (1 — ta) ~ a4] Bya(2) (3.2)
Bue) go S(2) (1 ta) — ey] Bs)
—K(z) E?(z) Ex(z) exp(iAkz) (3.3)

where we have introduced a wave-number mismatch Ak = 2k, — ky — k, and a four-
wave mixing coupling coefficient «(z). In addition, go is the unsaturated optical gain
per unit length, with its wavelength dependence neglected. go is related to the gain
constant Yo by go = Tyo, with I being the optical confinement factor. a is the
linewidth enhancement factor; a; is the SOA’s nonsaturable internal loss per unit
length; and P(z) is the total optical power at position z in the waveguide.

Eq. (3.2) is a simple amplification rate equation where we have neglected the
power depletion of pump and probe waves, since, for detuning frequencies larger than

a few tens of GHz, the power transfer is negligible in comparison to the power in the

pump and probe themselves. In Eq. (3.3), while the first term is the normal amplifi-

cation term, the second term is a nonlinear mixing term giving energy coupling from
pump and probe to the four-wave mixing signal frequency. The coupling coefficient
«(z) measures the strength of this nonlinear mixing precess, and it is related to the
conventional third-order nonlinear coefficient y®) by « = —ig/#2 x),

The coupling coefficient «(z) is of central importance to this theoretical analysis.
To simplify the analysis, we treat the three contributing mechanisms — carrier density
modulation, dynamic carrier heating and spectral hole burning — as three independent

processes. &(z) can then be decomposed as

(2) = Yo j(2) (3.4)
j=l
with 7 = 1, 2, 3 denoting carrier density modulation, dynamic carrier heating and
spectral hole burning, respectively.

Although a formal justification of this assumption is possible based on the density
matrix formalism [12], the separation of the three mechanisms can be justified intu-
itively by noting that, first, all interactions measured are in the small-signal regime in
our four-wave mixing studies and, secondly, each relaxation mechanism results from
bath damping from distinct, independent baths («K; — photon continuum, Kk — phonon
continuum, and «3 — carrier eigenstate continuum).

The first and third terms in Eq. (3.4) are due to carrier density modulation and
spectral hole burning, respectively. They can be found by solving the density matrix
equations and evaluating the induced polarization at the four-wave mixing signal

frequency [11]. Their expressions are given by

Ki(2) = 5+ 90512)

j=lor3 (3.5)

P; 1 — 120 fT;

where 7, = 7,8 is the effective carrier lifetime; a is the linewidth enhancement fact a;
P, is the interband saturation power P,; and 73 and P3 are the intraband population
relaxation lifetime and saturation power associated with spectral hole burning.

The spectral hole burning saturation power P3 is related to the dipole matrix
element, the dipole dephasing relaxation time and intraband population relaxation
lifetime through the expression h?/,?T»73 [11]. It is important to note that P3 is much
greater than the ordinary saturation power P,, since, physically, the gain saturation
due to intraband processes is much weaker than the saturation induced in the carrier
density. The parameter a3 is the ratio of real and imaginary parts of the refractive
index change caused by spectral hole burning, and it should usually have a value
much smaller than unity [11]. Additionally, in Eq. (3.5) for i<3, we have made use
of the fact that the dipole dephasing relaxation time TJ) is much shorter than the
intraband population relaxation time 73.

The second term in Eq. (3.4) represents the contribution from dynamic carrier
heating. Dynamic carrier heating includes at least two processes. The carriers are
heated through a combination of free-carrier absorption and stimulated emission, as
discussed in the previous chapter. These nonequilibrium carriers then thermalize
on a time scale of 73 < 100 fs, and in the meanwhile, the hot carriers relax to the
lattice temperature by emission of optical phonons. Because the heating and cooling
processes occur on very different time scales (~ 1 ps versus < 100 fs), we can treat

them as two distinctive processes: initial heating and subsequent cooling.

The cooling process, which can be regarded as a thermal process, can be char-

acterized with a relaxation (cooling) time constant 72. However, it is intrinsically
more complicated to model the nonthermal heating process. Because our four-wave
mixing studies are in the small-signal regime, we can assign a “virtual” temperature
to the nonthermal carrier distribution and assume that the 6 function response of
the initialization process follows (1 — e~/"3), where 73 is the intraband carrier-carrier
scattering time constant.

The initial carrier heating process can then be described by the following equation

T(t) —T(-—o) = -f Th) -Ti

dt, + af (1 _ em) P(t) dt, (3.6)
—co To —00
where T(t) is carrier temperature (electrons and holes are assumed to have same
temperature) and T; is the lattice temperature. H is the heating coefficient, defined
as carrier temperature increase caused by unit optical power in unit time interval, and
it is determined by the contributing heating mechanisms. Eq. (3.6) can be reduced

dT(t) T(t)-T _ ,,P(t)
dt? T2 7) dt + T97T3 7 T3 (3.7)

@T(t) 1 1
+(—+—

Solving the above equation and following similar procedures as in the derivation

of K1(z), we obtain the expression for k2(z)

1 1 — ia, 1 T3 1
= —.g,S(z)- , — 3,
Kalz) = 5 905(2) 5 (ie 7 ims (3.8)

where P, is the saturation power for the carrier heating effect and is related to the
carrier relaxation (cooling) time 7) and the differential gain with respect to the carrier

temperature. Like the saturation power associated with spectral hole burning P;,

the saturation power P, is much larger than the ordinary saturation power P,. In

addition, a2 is the ratio of the real and the imaginary parts of the refractive index
change induced by dynamic carrier heating. Both interband transitions and electron-
hole plasma absorption may contribute to this parameter.

We can now write an expression for «(z)

1 1- 101 1 1- 109 1
«(2) 2 905(2) P, 1-—i2nfr + Py 1—i2n fT
1- 10:3 T3 1- — 1
— 3, . 3.9

Physically, the first term represents carrier density modulation; the second term rep-
resents the relaxation (cooling) process of the dynamic carrier heating effect; the
third term represents the intraband carrier-carrier scattering process, with first part
for spectral hole burning and second part for the initial heating process associated
with the dynamic carrier heating.

To solve the differential equations, we first rewrite Eq. (3.2) as:

Ey q(Z) = Epq(0) exp if 5 [goS(z1) - (1 — ia) — ay] dz} (3.10)

Substituting Eq. (3.10) into Eq. (3.3) gives

ee) goS(2) «(1 — ion) ~ an) Hale) — wi(2)23(0)B5 (0)
“exp tf (59 _ i900) S(z) - a1 + idk] dz} (3.11)

Using the boundary condition E,(0) = 0, the solution to Eq. (3.11) is found to be

E,(z) = —E?(0)B*(0) [F w(er) exp (R(ar)zi] dar

“exp if ; [go9(z) - (1 — tay) — a] dz} (3.12)

3l
where R(z1) is given by
Lp
R(z1) = ik = a4 + — [ goS(22)d20 (3.13)

Let us examine the integral [¥ «(z,)e*@)*1dz, which appears in Eq. (3.12). The
first part of the integrand «(z1) is proportional to S(z,) as indicated in Eq. (3.9), and
is therefore a slowly-decreasing function of z;. The second part is an exponentially
growing function with a complex growth rate of R(z,), which, as indicated in Eq.
(3.13), is also a slowly varying function of z,. Therefore, the dominant contribution
to the integral comes from the interval near z; = z, and, when £,(1) is evaluated, the
integrand can be approximated by «(1) exp[R(1)z1]

Following the above approximations, F,(l) is found to be

EOE MKD"

E,(l) = 0.23G + iAkl

(3.14)

where G = 10(loge) fi[goS(z) — ay]dz is the SOA’s saturated optical gain in dB. The
underestimation of the four-wave mixing signal £,(/) introduced by the approxima-
tions depends on the SOA saturation level, and it is usually negligible for moderately
saturated SOA’s.

The second term accounts for the phase mismatch caused by material dispersion

and waveguide dispersion. The phase mismatch can be expressed as

aad" fP dig

AN = aD

(3.15)

where ma is the group index dispersion. Using ma s —0.7 wym~!, measured by Hall

et al. [13], and / = 650 wm, the phase mismatch at f = 1.7 THz is estimated to be

—0.22, which can be ignored in comparison with the first term for a typical SOA gain

of about 15 dB. Even for a detuning frequency up to 4 THz, the phase mismatch,
—1.21, can be ignored, since, as shown in Eq. (3.14), the four-wave mixing signal

power is proportional to [(first term)? + (Akl)?]-}.

3.3. Discussion

As indicated in Eqs. (3.9) and (3.14), the four-wave mixing signal power as a func-
tion of detuning frequency gives essentially the frequency-domain response function of
the contributing semiconductor dynamics. Quantitative characterization of the four-
wave mixing spectra can therefore provide important information concerning these
dynamics. Previously, its time-domain counterpart, pump-probe measurement us-
ing ultra-short optical pulses [14]-[16] has been the only direct technique to probe
ultrafast dynamics in semiconductor active layers. Four-wave mixing spectroscopy
of semiconductor dynamics presents data in a form that is complementary to these
femtosecond studies, i.e. frequency-domain versus time-domain. Experimental imple-
mentation of this frequency-domain technique to probe semiconductor dynamics will
be detailed in the next chapter.

Physically, the term «(/)E,(1)E}(l) in Eq. (3.14) represents the strength of the
dynamic gratings induced by optical beating of pump and probe fields. An additional
factor of E,(l) arises from the fact that the four-wave mixing signal is generated
through the scattering of the pump wave from these dynamic gratings. Since both

pump and probe experience an optical gain of G, the SOA’s single-pass gain acts

three times in the expression for the four-wave mixing signal F,(1). This point is

critical to implementation of efficient broadband wavelength conversion in SOA’s.

a We will experimentally illustrate this point in our experimental study of broadband

wavelength conversion described in Chapter 6.

Bibliography

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M. C. Tatham, G. Sherlock, and L. D. Westbrook, “20 nm wavelength conversion
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S. Kawanishi, T. Morioka, O. Kamatani, H. Takara, J. M. Jacob, and M.
Saruwatari, “100 Gbit/s all-optical demultiplexing using four-wave mixing in a
traveling-wave laser-diode amplifier,” Electron. Lett., vol. 30, pp. 981-982, 1994.

M. A. Summerfield, J. P. R. Lacey, A. J. Lowery, and R. 8. Tucker, “All-optical
TDM to WDM conversion in a semiconductor optical amplifier,” Electron. Lett.,
vol. 30, pp. 255-256, 1994.

G. P. Agrawal, “Population pulsations and nondegenerate four-wave mixing in
semiconductor lasers and amplifiers,” J. Opt. Soc. Am. B, vol. 5, pp. 147-158,
1988.

A. Uskov, J. M@rk, and J. Mark, “Wave mixing in semiconductor laser amplifiers
due to carrier heating and spectral hole burning,” IEEE J. Quantum Electron.,
vol. 30, pp. 1769-1781, 1994.

K. L. Hall, G. Lenz, and E. P. Ippen, “Femtosecond time domain measurements of
group velocity dispersion in diode lasers at 1.5 ym,” IEEE J. Lightwave Technol.,
vol. 10, pp. 616-619, 1992.

K. L. Hall, J. Mark, E. P. Ippen, and G. Eisenstein, “Femtosecond gain dynamics
in InGaAsP optical amplifiers,” Appl. Phys. Lett., vol. 56, pp. 1740-1742, 1990.

J. Mark and J. Mérk, “Subpicosecond gain dynamics in InGaAsP optical ampli-
fiers: experiment and theory,” Appl. Phys. Lett., vol. 61, pp. 9-11, 1992.

K. L. Hall, G. Lenz, E. P. Ippen, U. Koren, and G. Raybon, “Carrier heating
and spectral hole burning in strained-layer quantum-well laser amplifiers at 1.5
pom,” Appl. Phys. Lett., vol. 61, pp. 2512-2514, 1992.

Chapter 4

Terahertz Four-Wave Mixing
Spectroscopy of Intraband

Dynamics

4.1 Introduction

As discussed in the previous chapter, four-wave mixing in semiconductor optical am-
plifiers (SOA’s) can be used as a spectroscopic tool for analysis of intraband dynamics
in semiconductor active layers. Important information regarding these dynamics such
as relaxation time constants can be extracted from analysis of measured four-wave
mixing signal spectra, 7.e., four-wave mixing signal power versus detuning frequency.

Early four-wave mixing experiments were limited to detuning frequencies of a few
hundred GHz [1]-|3]. For example, in an experiment reported by Tiemeijer [1], the

four-wave mixing response was found to be consistent with carrier heating, but the

equivalent temporal resolution of the experiment, related to the maximum detuning
frequency fimar by 1/27fmax, was not sufficient to resolve spectral hole burning. In
another study [2], only spectral hole burning was inferred from the data, but no
time constant was determined, also owing to the limited detuning frequency in the
experiment.

The first four-wave mixing experiment that extended detuning frequencies into
THz regime was performed in our group [4]. The maximum detuning in this study
was as large as 1.7 THz, which corresponds to a sub-100 fs equivalent temporal res-
olution (94 fs). Contributions to four-wave mixing from both carrier heating and
intraband carrier-carrier scattering were observed for the first time. This chapter
presents the details of this experiment and a discussion of the experimental results.
Since then, a number of similar experiments with THz detuning frequencies have been
reported by other research groups and these studies also confirmed the simultaneous
presence of carrier heating and spectral hole burning [5],[6]. In addition, we have re-
cently developed a novel four-wave mixing configuration [7] to study inter-well carrier
transport in semiconductor quantum well amplifiers. This work will be detailed in

the next chapter.

4.2 Four-Wave Mixing Measurements

In order to perform four-wave mixing spectroscopic measurements in an SOA, there

are some basic experimental requirements that must be met. First of all, two single-

frequency lasers are needed for the pump and probe sources, and at least one of them

must be tunable. In our four-wave mixing studies, we used 1.5 yum, single frequency,
widely tunable Erbium-doped fiber ring lasers [8]. These ring lasers are unidirectional
laser oscillators in which fiber optical isolators are used to make the laser to operate
in one direction and two tunable fiber Fabry-Perot (FFP) filters are employed as both
wavelength selecting and tuning components.

Figure 4.1 illustrates the schematic diagram of the fiber laser structure and the
concept of cascaded narrowband (free spectral range 6 GHz, finesse 100) and broad-
band (free spectral range 4 THz, finesse 100) FFP filters. These two cascaded FFP
filters forced the laser to lase in a single longitudinal mode. Polarization controllers
and a pigtailed polarizer were used to control the polarization state of the laser,
as well as to eliminate the competition between different polarization modes. The
laser output was coupled out of the resonator through a fiber optic bidirectional cou-
pler. Typical output power was in the range of 1 ~ 2 mW, depending on the lasing
wavelength and pump power. The side-mode suppression and laser linewidth were
measured to be about 70 dB and 4 kHz, respectively [9]. By electrically tuning the
broadband FFP filter, the laser wavelength can be tuned over ~ 30 nm, corresponding
to the free spectral range of the broadband FFP filter. These characteristics make
these fiber lasers ideal sources for the four-wave mixing studies.

The SOA’s used in this four-wave mixing study were tensile strained or compres-
sively strained InGaAs/InGaAsP multiple quantum well traveling amplifiers operat-
ing in the spectrum of 1.5 wm. They were designed and fabricated by M. A. Newkirk

and B. I. Miller at AT&T Bell Laboratories [10],[11].

A A

ieee
AAA

g lasers used

om Ea
ty
ry
kg

The band diagram of the tensile strained amplifier [10] is shown in Figure 4.2.
The structure was grown by atmospheric pressure metalorganic vapor phase epitaxy
(MOVPE). The wells and barriers were approximately 160 and 270 A thick, respec-
tively. The wells were Ing 39Gao.¢;As and were under tensile strain of 1%. The barriers
were compressively strained InGaAsP (E, = 0.95 eV) with about 0.15% of strain to
partially compensate the tension in the wells. After the growth of the wafers, optical
amplifiers were made using two additional MOVPE regrowths for blocking layers and
p-type cladding layers. The amplifiers had 650 wm long gain sections and 20 — 40 um
long window sections at both ends adjacent to the facets. Single SiO layers were used
for anti-reflection coatings on the facets. The residual reflectivities of these amplifiers
were estimated to be about 8 x 10-°. The small signal gain of this tensile strained
amplifier measured at several bias currents is also shown in Figure 4.2. High optical
gain (> 20 dB) for TM-polarized input was obtained and gain ripple was negligible
(< 0.2 dB). We also found in the measurements that the TE gain was very low, about
15 dB below the TM gain at 150 mA.

The compressively strained amplifier [11] was also grown using MOVPE. The base
wafer comprises a strain-compensated 1.5 um wavelength multiple quantum well gain
layer on top of a 2800 A thick InGaAsP passive waveguide. A three quantum well
stack is composed of six 30 A thick InGaAs wells with 1.3% compressive strain sep-
arated by 125 A thick InGaAsP barriers (E, = 1.0 eV) having 0.2% tensile strain.

The device used the semi-insulating planar buried-heterostructure configuration. 3

jm wide mesas were created by standard photolithography and wet chemical etching,

LN
lL Ly
“47
LN
InGaAsP
inp | _ (70.39680.614s e i ° in Eg=0.95 eV
E=-1.0% = ~ €=+0.15%
Vv
y <—>|<—__>|

160A 270A

30 _ v T Ll T hd T . T v T . 1 -
~ C 7
ee j 7
~ 20 FF 7
c C 4
& c 1
2 3 CF
© C a
Cc —
c '
oO z -
€ 10 -e- P (150 mA) J
2 r -&-P (100 mA) 7

oF ~eP(50mA) 4

0 C 1 l 1 i 1 l : l lL 1 l 7

1.44 1.46 1.48 1.5 1.52 1.54 1.56 1.58

Wavelength (um)

Figure 4.2: Upper figure illustrates the band diagram of the tensile strained amplifiers used

in the experiment. Lower figure shows the small signal gain of the amplifiers at several

pump currents.

followed by two MOVPE regrowths for current blocking, cladding and p-type con-
tacting layers. The compressively strained amplifiers had a similar window structure
for suppressing the facet reflectivity. The small signal gain at 1.55 wm for 150 mA
bias current was measured to be about 16.3 dB with negligible gain ripple.

A typical experimental setup for THz four-wave mixing spectroscopy is shown in
Figure 4.3. The optical outputs from the pump and probe fiber lasers were combined
using a 3 dB fiber coupler, and then coupled into the SOA using microscope objectives.
The optical power coupled into the SOA was about 250 wW. Two fiber polarization
controllers were employed to match the polarization state of input pump and probe
to a specific SOA polarization mode, i.e., TM polarization for the tensile SOA, TE
polarization for the compressive SOA. Two optical isolators were placed before and
after the SOA to eliminate feedback caused by the facets of the input and output
fibers, and also to serve as polarization selectors.

During the measurements, the pump laser wavelength was fixed at 1534 nm, while
the probe was tuned to vary the detuning frequency f. The four-wave mixing signal
was measured by a high-sensitivity heterodyne detection system, as illustrated in
Figure 4.3, in which the four-wave mixing signal was mixed with a tunable fiber
laser local oscillator using a beam splitter/combiner. This local oscillator was tuned
relative to the signal frequency to generate an IF beating note at the pin detector, and
the IF mixing frequency was maintained at a constant value of 4.00 GHz throughout

the measurements. This ensured that the frequency response of detection electronics

would not affect the measured results. The detected photocurrent was amplified

Fiber Lasers Fiber Laser
C) (Pump, Probe) (Local Osci.)
50/50 Coupler
: Beam
SOA Splitter
= J
Optical Isolator Detector
Amp
Optical |
Spectrum
Local
Probe Pump Oscillator
Detuning
Frequency
+—— f ——> Afi
| ———
wy i f, Faw

Figure 4.3: Schematic diagram of the experimental arrangement for four-wave mixing spec-

troscopy of intraband dynamics. The lower figure shows the concept of a high-sensitivity

heterodyne detection system.

by a microwave amplifier with 40 dB gain and then measured using a spectrum
analyzer (Tektronix 2782). The detuning frequencies were determined using an optical
spectrum analyzer (Hewlett-Packard 70950A). Optical powers of the pump, probe
and local oscillator were also measured, so that the measured four-wave mixing signal

could be normalized.

4.3 Analysis of Experimental Results

Using the experimental configuration as shown in Figure 4.3, the four-wave mixing
signal was measured for both the tensile and compressively strained SOA’s. The
largest detuning frequency in the measurements was 1.7 THz, limited only by the
tunability of one of the fiber lasers used in the experiment. The signal level at the
maximum detuning frequency was still 10 ~ 20 dB above the noise floor, owing to the
narrow linewidth and low intensity noise of the fiber lasers. The normalized signal
power as a function of detuning frequency is illustrated in Figure 4.4 where a tensile
strained SOA was measured, and in Figure 4.5 where a compressively strained SOA
was measured.

To understand the experimental data, we first need an explicit expression for
the four-wave mixing signal power as a function of the detuning frequency. Using
Eqs. (3.9) and (3.14), the expression for the four-wave mixing signal power can be
written as

1 P

Prwm = PyPa| 20 Ci 7a,

j=l

(4.1)

where FP, and P, are powers of pump and probe at the SOA output; {C;} are complex

coupling coefficients representing contribution to four-wave mixing from carrier den-
sity modulation, carrier heating and intraband carrier-carrier scattering, respectively.

They are given by

Ci = 0.46G B, for j = 1,2
_ _3, 4.2
Cs 0.46G P3 T Pr (4.2)

We then use Eq. (4.1) to fit the experimental data. The dashed line in Figure 4.4
represents the four-wave mixing response accounting only for carrier density modu-
lation, i.e., only the first term in Eq. (4.1) is used. As shown in Figure 4.4, this one
term fit apparently can not explain the measured data. The deviation of the measured
response from this one term fit indicates the presence of contributions from the in-
traband relaxation mechanisms. In addition, the asymmetric nature of the four-wave
mixing signal spectrum with respect to positive and negative detuning is believed to
result from phase interferences which occur between the various contributing mecha-
nisms. Since the positive detuning data show constructive interferences, we estimated
a relaxation time constant of about 650 fs for an ultrafast intraband mechanism using
the positive signal spectrum. We then fit the measured data with these two terms.
However, as shown in Figure 4.4, the two term response is insufficient to provide a
good fit over the whole signal spectrum. It was then found that a third term having
a lifetime of less than 100 fs was required to obtain a good fit.

Using Eq. (4.1), excellent fits were obtained for both positive and negative detun-

ing data with the same parameter set (as shown in Figure 4.4 for the three term fit).

The fitting parameters used in Figure 4.4 are as follows: 7, = 200 ps, 72 = 650 fs,

O Experimental Data
-10F — 1 Time Constant Fit
ay ——~ 2 Time Constant Fit
oS = 3 Time Constant Fit
2-20
{o)
@ -30F
uo]
Oo
73 407
oO
-50f
“6015 100 1000 10000
Detuning Frequency (GHz)
O Experimental Data
. — -1 Time Constant Fit
—~ -10 N
foal —— 2 Time Constant Fit
ZS ~ === 3 Time Constant Fit
= -20t
[o}
FS
BD -30F (b)
77)
ao]
oO
a -40r
{e)
' -50
“6015 100 1000 10000
Detuning Frequency (-GHz)
Figure 4.4: Normalized four-wave mixing signal power versus (a) positive and (b) negative
detuning frequencies showing theoretical fits. The SOA measured was a tensile strained
multiple quantum well amplifier.

Normalized Signal Power (dB)

(a)
-60 : 1
10 100 1000 10000
Detuning Frequency (GHz)
oO
(b)

Normalized Signal Power (dB)

-60 1 1
10 100 1000 10000

Detuning Frequency (-GHz)

Figure 4.5: Normalized four-wave mixing signal power versus (a) positive and (b) negative
detuning frequencies showing theoretical fits. The SOA measured was a compressively

strained multiple quantum well amplifier.

73 = 50 fs, C) = 0.24, Cy = 0.0027e'?, C3 = 0.00048e'? 8°. We note that there can
be an arbitrary global phase factor in the complex coupling coefficients, as can be
seen from Eq. (4.1).

The compressively-strained SOA data, shown in Figure 4.5, are also accompanied
by theoretical fits using Eq. (4.1). The fits were obtained using the same relaxation
time constants as for the tensile device, but using different complex coupling coeffi-
cients: C, = 0.24, Cy = 0.0027e'*:*, C3 = 0.00023e"4*. Very good fits were obtained
for both positive and negative detuning frequencies, as shown in Figure 4.5.

The time constant of 650 fs obtained in this study is in good agreement with
the results of previous measurements of carrier heating in both time-domain [1] and
frequency-domain [12],[13]. The time constant for the fastest intraband mechanism
used in the fit is 50 fs. However, it is important to note that the fit is relatively
insensitive to this parameter (empirically we can obtain good fits provided T3 < 100 fs)
because the time resolution, or equivalently, the detuning frequency, is still limited in
the measurements. Therefore, this time constant and its associated C’ parameter used
in the fit give somewhat qualitative information on the fastest mechanism. However,
the fact that a third term, having a time constant of < 100 fs, is required to obtain
a good fit clearly indicates the presence of additional ultrafast intraband processes.
They are believed to be related to intraband carrier-carrier scattering, i.e., spectral

hole burning and the initial thermalization of carrier heating, as discussed in our

theoretical analysis.

4.4 Conclusion

Since gain and index gratings both contribute to the four-wave mixing process, the in-
terpretation of four-wave mixing experimental results is somewhat more complicated
than in the case of time-domain measurements, where gain and index contributions
can be separated [12],[13]. However, the different interference behaviors present in
positive and negative detuning signal spectra considerably facilitate theoretical anal-
ysis of the experimental data in four-wave mixing. Furthermore, the measurement
presents data in a form that is complementary to femtosecond studies, i.e., frequency-
domain rather than time-domain, and is inherently a small signal approach. This
latter point may explain the good agreement we find between a simple model and our

data.

Bibliography

[1]

[3]

[5]

[6]

[7]

L. F. Tiemeijer, “Effects of nonlinear gain on four-wave mixing and asymmetric
gain saturation in a semiconductor laser amplifier,” Appl. Phys. Lett., vol. 59,
pp. 499-501, 1991.

A. D’Ottavi, E. Iannone, A. Mecozzi, S. Scotti, P. Spano, J. Landreau, A. Ougaz-
zaden, and J. C. Bouley, “Investigation of carrier heating and spectral hole

burning in semiconductor amplifiers by highly nondegenerate four-wave mixing,”
Appl. Phys. Lett., vol. 64, pp. 2492-2494, 1994.

A. Uskov, J. Mérk, J. Mark, M. C. Tatham, and G. Sherlock, “Terahertz four-
wave mixing in semiconductor optical amplifiers: experiment and theory,” Appl.
Phys. Lett., vol. 65, pp. 944-946, 1994.

J. Zhou, N. Park, K. J. Vahala, M. A. Newkirk, and B. I. Miller, “Study of

inter-well carrier transport by terahertz four-wave mixing in an optical amplifier

[10]

[11]

[12]

[13]

with tensile and compressively strained quantum wells,” Appl. Phys. Lett., vol.
65, pp. 1897-1899, 1994.

N. Park, J. W. Dawson, K. J. Vahala, and C. Miller, “All fiber, low threshold,
widely tunable single-frequency, erbium-doped fiber ring laser with a tandem
fiber Fabry-Perot filter,” Appl. Phys. Lett., vol. 59, pp. 2369-2371, 1991.

N. Park, J. W. Dawson, and K. J. Vahala, “Linewidth and frequency jitter
measurement of an erbium-doped fiber ring laser by a loss-compensated, delayed
self-heterodyne interferometer,” Opt. Lett., vol. 17, pp. 1274-1276, 1992.

B. I. Miller, U. Koren, M. A. Newkirk, M. G. Young, R. M. Jopson, R. M.
Derosier and M. D. Chien, “Tensile-strained InGaAs/InGaAsP quantum-well
optical amplifier with a wide spectral gain region at 1.55 wm,” IEEE Photon.
Technol. Lett., vol. 5, pp. 520-522, 1993.

M. A. Newkirk, U. Koren, B. I. Miller, M. D. Chien, M. G. Young, T. L. Koch,
G. Raybon, C. A. Burrus, B. Tell, and K. F. Brown-Goebeler, ” Three-section
semiconductor optical amplifier for monitoring of optical gain,” [EEE Photon.
Technol. Lett., vol. 4, pp. 1258-1260, 1992.

K. L. Hall, J. Mark, E. P. Ippen, and G. Eisenstein, “Femtosecond gain dynamics
in InGaAsP optical amplifiers,” Appl. Phys. Lett., vol. 56, pp. 1740-1742, 1990.

Chapter 5

Inter-Well Carrier Transport

Dynamics

5.1 Introduction

Carrier transport in quantum well lasers and amplifiers is a complicated and nonlinear
process which has been shown to affect both the static and dynamic performance
characteristics of these devices, including the maximum modulation bandwidth of
quantum well lasers [1]. Shown in Figure 5.1 is the conceptual band diagrams of a
bulk laser and a quantum well laser. In a bulk laser, carriers are injected directly
into the gain region where they participate in the lasing process. Gain nonlinearities
in bulk lasers are therefore essentially material dependent, through mechanisms such
as carrier heating and spectral hole burning. In contrast, gain region in a quantum

well laser is embedded in a large optical confinement region. To contribute to the

optical gain, the injected carriers have to take an additional step, i.e., reaching the

bottom of the wells, as illustrated in Figure 5.1. This results in a structure-dependent
nonlinearity, often referred to as well-barrier hole burning [2].

Carriers in the well regions, confined in one dimension and having discrete energy
bands, can be considered as two-dimensional (2-D) carriers. Carriers in the confine-
ment and barrier regions could be treated quantum mechanically, for instance, by the
wave packet formalism [3]. For simplicity, however, these carriers are often treated
as three-dimensional (3-D) carriers whose transport is by diffusion and drift. The
classical treatment has been supported by a number of experimental studies, such
as photoluminescence [4], pump-probe [5],[6] and modulation response measurements
(7],[8]. The overall carrier transport process can thus be considered to include cap-
ture and escape of carriers between unconfined 3-D and confined 2-D quantum states
in the well regions, as well as diffusion and drift of 3-D carriers across the confine-
ment region and between wells in the barrier regions. The overall carrier transport
process is also conceptually illustrated in Figure 5.1. Since Rideout et al. [2] first pro-
posed a well-barrier hole burning model, a number of theoretical and experimental
investigations [4]-[11] have studied these processes.

As presented in the previous chapter, four-wave mixing in semiconductor traveling-
wave amplifiers has in recent years been demonstrated as an important frequency-
domain technique for study of carrier dynamics in semiconductor active layers [12]—
[17]. In this chapter, we describe the first investigation of inter-well transport using a

novel four-wave mixing technique that selectively excites and probes adjacent quan-

tum wells according to strain, thereby studying inter-well carrier transport [18].

| SP: Spontaneous Emission

l ST: Stimulated Emission
3D: Unconfined 3-D Carriers

v 2D: Confined 2-D Carriers

Carrier Transport Processes

Figure 5.1: Upper figure shows the difference between bulk and quantum well lasers. Lower

figure illustrates details of carrier transport in a multiple quantum well laser.

5.2 Cross-Polarized Four-Wave Mixing Experiments

The semiconductor optical amplifier (SOA) used in the measurement was an In-
GaAs/InGaAsP multiple quantum well traveling-wave amplifier operating at 1.5 ym
[19]. The active layer contains six alternating-strain (tensile and compressive) In-
GaAs quantum wells. It is known that the tensile wells provide predominantly TM
gain, while the compressive wells provide TE gain but have vanishing TM gain. The
scheme of both tensile and compressively strained wells in the same active region was
originally designed to eliminate the polarization sensitivity of the amplifier gain [19].
Indeed, the measured gain spectra indicate a gain insensitivity of less than 1 dB on
the average over the amplifier gain bandwidth.

Similar to the amplifiers described in the previous chapter, the alternating-strain
device was grown by atmospheric pressure MOVPE. As shown in Figure 5.2, the base
wafer comprises the tensile/compressive gain layer on top of a 3200 A thick InGaAsP
passive waveguide. The quantum well stack is composed of three 35 A thick InGaAs
wells with 1.0% compressive strain and three 160 A thick InGaAs wells with 1.0%
tensile strain. The wells are alternately tensile and compressive, separated by a 100
A thick lattice matched InGaAsP barrier (EL, = 0.95 eV). 620 zm long active sections
were then defined by selective etching down to the waveguide layer. The device also
used the semi-insulating planar buried-heterostructure configuration. 2.5 um wide
mesas were created by standard photolithography and wet chemical etching, followed

by two MOVPE regrowths for current blocking, cladding and p-type contacting layers.

The passive waveguide extends 15 ym beyond the active section at each end. To

K InGaAs

InGaAs
1.0% Compressive 1.0% tensile
Strain Strain
InP e-hh e-lh e-lh InGaAsP
n=1 n=1 n=2 Eg=0.95 eV
4 Po
pV
! Vv K> Kk —>| , 5 |
35A 100A 160A

Compressive Well
TE Gain

Tensile Well
T< Gain

Co-Polarized
t FWM Signal

Cross-Polarized
FWM Signal

(TE)

Figure 5.2: Upper figure shows the band diagram of the amplifier having alternative tensile

and compressively strained InGaAs quantum wells. The lower figure illustrates co- and

cross-polarized four-wave mixing processes.

minimize reflections from the cleaved facets, the passive waveguide was terminated to
form a 35 ym long window at the input and output. The facets were also antireflection
coated with a single SiO layer to achieve modal reflectivity < 1 x 10+. At a bias
current of 150 mA, the amplifier was measured to have an optical gain of about 14.5
dB at 1.55 um for both the TE and TM polarizations.

We made use of this special device structure to selectively excite and probe ad-
jacent wells according to polarization. As illustrated in Figure 5.2, input beam 1,
having optical frequency f; and a given polarization (either TE or TM), and input
beam 2, having optical frequency f2 and a polarization at an angle of 45 degrees with
respect to beam 1, were coupled into the SOA. For the configuration shown in Figure
5.2, beating of the TM-polarized beam 1 and the TM component of beam 2 excites
carriers in the tensile wells through interband transitions. As a result, a TM-polarized
four-wave mixing signal at 2f.—, was generated. This conventional four-wave mixing
is referred here as co-polarized four-wave mixing. On the other hand, while carriers in
the compressively strained wells do not experience the optical beating because of the
polarization selection rule, the excited carriers in the tensile well regions can be trans-
ported to the neighboring compressive wells. The TE-polarized component of beam
2 then probes this transported carrier dynamic in the compressive wells, leading to
the generation of a TE-polarized four-wave mixing signal also at 2f.—,. We refer to
this process as cross-polarized four-wave mixing. Since the cross-polarized four-wave

mixing process involves inter-well carrier transport, the observed difference between

the co- and cross-polarized signal spectra gives information about inter-well carrier

transport. Measurements of co- and cross-polarized four-wave mixing can therefore
be used as a frequency-domain tool for analysis of the inter-well transport processes.

The experimental arrangement for this study was similar to what we have de-
scribed in the previous chapter except here the input beams were combined using a
beam splitter to allow independent polarization control. The co- and cross-polarized
four-wave mixing signals were measured using the same heterodyne detection system
as shown in Figure 4.3 in which the SOA output, after passing a polarizer (selecting
TE or TM polarization), was mixed with a tunable fiber laser local oscillator. Using
this experimental setup, we carried out co- and cross-polarized four-wave mixing mea-
surements in which either the tensile wells were selectively excited with TM-polarized
pumps, or the compressive wells were selectively excited with TE-polarized pumps.
Figure 5.3 shows the measured four-wave mixing signal powers, normalized by the
pump and probe amplitudes, plotted versus the detuning frequency f2 — f; up to 1

THz for various pump-probe polarization configurations.

5.3 Analysis of Experimental Results

As shown in previous conventional four-wave mixing studies [12]-[17], contributing
mechanisms to four-wave mixing are interband carrier number modulation and intra-
band occupancy modulation. The former is characterized by the interband carrier
lifetime which is on the order of several hundred picoseconds in quantum well ampli-

fier devices. The latter typically includes dynamic carrier heating and spectral hole

burning. For the detuning frequencies measured in this measurement (up to 1 THz),

Relative FWM Signal Power (dB)

-20 ° 7]
S090
Ong 7
-30 4 -30 -|
TM pump, TE Probe TM pump, TM Probe
» 3 4
O10 100 1000 10 100 1000
Detuning Frequency (GHz) Detuning Frequency (GHz)
(a) (b)
10 , TELL r att 10 + erry —
ne 4 oF o 4
— fe]
— 0b 4 to b
= -20- 4 -20 b
rd ° 00, 4
00
g 'd
= 30 F 4 30
4 TEpump, TMProbe TEpump, TEProbe
na 4 5 4
-40 ere | ns 4 ran -40 I .
10 100 1000 10 . 100 1000
Detuning Frequency (GHz) Detuning Frequency (GHz)
(c} (d)

Figure 5.3: Normalized four-wave mixing signal power versus positive (0) and negative (a)

detuning frequencies for various pump-probe polarization configurations: (a) TM pump,

TE probe; (b) TM pump, TM probe; (c) TE pump, TM probe; (d) TE pump, TE probe.

four-wave mixing is dominated by carrier number modulation and carrier tempera-
ture modulation, i.e., the first two terms in Eq. (4.1) provide dominant contributions
to the four-wave mixing signal.

The cross-polarized four-wave mixing signal spectra, as shown in Figures 5.3(a)
and 5.3(c), are symmetrical at low frequencies with respect to positive and negative
detuning, in contrast to the co-polarized signal spectra which exhibit a steady asym-
metry, as shown in Figures 5.3(b) and 5.3(d). Since this asymmetry results from signal
phase interferences between the contributing four-wave mixing mechanisms, namely,
carrier number modulation and carrier temperature modulation in this study, the dif-
ference between the co- and cross-polarized four-wave mixing signal spectra indicates
that phase interferences are stronger in the case of co-polarized four-wave mixing
versus the case of cross-polarized four-wave mixing. This suggests that carrier num-
ber modulation and carrier temperature modulation experience different transport
efficiencies.

The inter-well carrier number transport can be approximately described as a three-
step process, as shown in Figure 5.1. First, 2-D carriers in the excited well are coupled
to the 3-D states in the same well through quantum capture/escape processes. These
3-D carriers are then transported to the nonexcited wells through the combined effect
of diffusion and drift. Finally, also through carrier capture/escape processes, the
transported 3-D carriers fall into the 2-D states in the nonexcited well, where they

contribute to the cross-polarized four-wave mixing signal. For carrier temperature

modulation, in addition to the above-mentioned processes, carrier-carrier scattering

can also assist the temperature transport.

During the inter-well transport process, the two modulations (carrier number and
temperature) experience different damping mechanisms, i.e., transport of carrier num-
ber modulation is damped by spontaneous interband carrier recombination, while the
carrier temperature modulation is damped by carrier-lattice interactions having a
much shorter relaxation time. These widely different damping rates can considerably
affect the corresponding inter-well transport efficiencies.

To illustrate, we calculate the trans-barrier transport efficiency by considering 3-D
carrier transport from an excited well to the adjacent nonexcited well using a simple
one-dimensional (1-D) diffusion equation

aw _ 7) ew _W

a = 5.1

ot Oy? T (5-1)
where W represents either carrier number or temperature. D and 7 are the diffusion
constant and lifetime associated with the respective modulations. The modulation at

the excited well (y = 0) is given by W = Wo exp(—iNt), where 0/27 is the detuning

frequency. The solution to Eq. (5.1) is found to be

W(y,t) = Woexp (-% 3 10—in (5.2)

The trans-barrier transport efficiency is then given by

where s is the separation between adjacent wells.
Since the carrier number damping time (~ 1 ns) is much longer than the tem-

perature damping time (~ 1 ps), carrier temperature modulation transport is much

less efficient than carrier number transport, particularly at low detuning frequencies.
Here we have assumed comparable diffusion constants for the two modulations in the
above discussion. Another contributing mechanism to the trans-barrier transport is
drift of 3-D carriers caused by internal fields. The drift process, like the diffusion
process, also favors the mechanism having the longer time constant so that, assuming
all other factors are comparable, carrier number transport is again expected to be
more efficient than the carrier temperature transport.

Similarly, the efficiency associated with the escape/capture dynamics are also
subject to the damping effect. Widely different relaxation time constants for the two
modulations should lead to very different efficiencies in the escape/capture process.
We would therefore expect overall inter-well transport to exhibit a higher efficiency for
the carrier number modulation than for the temperature modulation. Consequently,
phase interferences are suppressed in the cross-polarized measurement, causing the
highly symmetrical spectra. This qualitatively explains the observed difference be-
tween the co- and cross-polarized spectra shown in Figure 5.3.

The co- and cross-polarized four-wave mixing signals, as shown in Figure 5.3,
exhibit comparable amplitudes at low frequencies. Furthermore, the cross-polarized
four-wave mixing data in Figures 5.3(a) and (c) do not show any roll-off induced by
the carrier number transport, i.e., beyond the 20 dB/decade roll-off caused by the
interband modulation within the excited wells. This indicates that carrier number
modulation, which is responsible for the low frequency data, is coupled from excited

wells to nonexcited wells with little loss. This agrees qualitatively with a calculation

of the trans-barrier transport efficiency function which gives |¢| > 78% for rT = 1 ns,
D =5cm?s~!, s = 100 A and 2./2m < 100 GHz. The data measured in this study
also suggest that the inter-well carrier number transport in the present device is fast
enough so that carrier number modulation in nonexcited wells behaves as if it were
generated within these wells for frequencies at least as high as 100 GHz. Beyond this
frequency the modulation data is obscured by the presence of additional mechanisms,
making prediction of a definitive upper transport rate impossible.

It should be mentioned that carrier heating induced by free-carrier absorption is
not strain selective. Specifically, it can take place in both types of wells when pumps
are TE-polarized, but it is inhibited in all wells when pumps are TM-polarized due to
the quantum well confinement barrier. Therefore, temperature modulation within the
nonexcited wells is potentially significant in the case of TE pumps. This might explain
the observed difference in the two sets of cross-polarized spectra at low detuning
frequencies, where data with TE pumps show an earlier onset of reduced symmetry,

i.e., more phase interference between carrier number and temperature modulations.

5.4 Conclusion

We have presented in this chapter the measurements of co- and cross-polarized four-
wave mixing up to 1 THz in a SOA having alternating tensile and compressively
strained quantum wells. The effect of inter-well carrier transport on four-wave mix-
ing signal spectra is observed and an explanation is provided by noting the different

transport efficiencies for carrier number and temperature modulations. A lower bound

of inter-well carrier number transport of 100 GHz is estimated by analyzing the mea-
sured data. It is important, however, to point out that the complexities of this system

require a more sophisticated theoretical treatment.

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S. C. Kan, D. Vassilovski, T. C. Wu, and K. Y. Lau, “On the effects of carrier
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tn yp amt ape

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Chapter 6

Broadband Four-Wave Mixing

Wavelength Conversion

6.1 Introduction

6.1.1 Fiber-Optic Communications

A communication system transmits information from one place to another, whether
separated by a few kilometers or by transoceanic distances. If information is carried by
an electromagnetic wave in the optical spectrum (carrier frequency ~ 100 THz), such
communication systems are called lightwave systems to distinguish from microwave
systems whose carrier frequency is typically smaller by five orders of magnitude (~ 1
GHz). Fiber-optic communication systems are lightwave systems that employ optical

fibers as the transmission medium.

The key idea for optical fiber communications was proposed in 1966 in a publica-

a .aaaacmanananscissinain {neem pill SSatISt Sues IY emlniNi gay8N USL NMS SNRNINN.. 2, an

tion by Charles K. Kao [1]. In that paper he noted that pure optical fiber was theo-
retically capable of guiding a light signal with very little loss. By 1970, loss of optical
fiber was reduced to about 20 dB/km [2]. At about the same time, GaAs semiconduc-
tor diode lasers, operating continuously at room temperature, were demonstrated [3].
The simultaneous availability of a compact optical source and low-loss transmission
media lead to a worldwide effort for developing fiber-optic communication systems.
The technologies required for fiber-optic communications have progressed since
then at an extremely rapid pace [4],[5]. These technological advances and market de-
mand for cost-effective transmission of large amounts of information have propelled
fiber-optic systems from laboratory research to widespread field deployment. Fiber-
optic transmission systems are now employed in virtually all areas of telecommunica-
tions [6]: undersea cables spanning oceans, terrestrial long-haul networks connecting
cities, trunk lines that shuttle traffic between switching offices in metropolitan ar-
eas, and subscriber loop systems that serve customer premises. More recently, the
cable-television industry has begun deploying fibers for trunking and distribution,
and optical fiber local area networks have been installed for computer networking.
Research continues today on many fronts to explore more efficient use of the ultra-
broad bandwidth of optical fibers for long-haul transport, high-throughput computer
networking and distribution of broadband services. ‘Two distinctive efforts have been
pursued to increase transmission capacity per optical fiber: one is higher speed se-
rial transmission or time-division-multiplexing (TDM), and the other is paralleled

transmission of multiple channels at different wavelengths or wavelength-division-

multiplexing (WDM). The former approach used to be favored since the cost of a
single high-speed optoelectronic regenerator is generally less than that of several low
speed regenerators and a pair of demultiplexer and multiplexer. Although the speeds
of electronic circuits continue to advance and optical TDM techniques are being ac-
tively explored, it is highly unlikely that the tens of THz of available fiber bandwidth
can be spanned by TDM technologies alone. Thus, WDM will be ultimately required.

The advent of Erbium-doped fiber amplifiers (EDFA’s) has hastened the move
to WDM. EDFA’s can amplify WDM signals without the need for demultiplexing
and optoelectronic regenerating the individual channels as in conventional fiber-optic
systems. This simple and elegant function, which is independent of operating data
rate, has greatly accelerated the pace at which high capacity WDM lightwave systems
are being developed. For example, in a recent WDM transmission experiment, 40
Gb/s was sent through a 1420-km-long fiber using 16 channels of 2.5 Gb/s each, with
EDFA spacings ranging from 96 km to 123 km [7]. More recently, a record-breaking
340 Gb/s was transmitted over 150 km as 17 WDM channels of 20 Gb/s each, with

EDFA’s spaced every 50 km [8].

6.1.2 All-Optical Network and Wavelength Conversion

WDM multiwavelength transmission not only increases aggregate network capacity, it
is also attractive for networking applications where wavelength selective devices may
be used for circuit access and routing. The latter point also represents the basis for the

all-optical networking that is being actively explored by researchers worldwide under

various consortia [9],{10]. In these all-optical networks, some of the network routing

sian.

functions are all-optical, making geographical distribution of switching functions more
flexible.

Early multiwavelength all-optical networks were designed around a broadcast-and-
select concept, where all users were connected to a “passive optical broadcast star.”
The central problem in broadcast networks is that all wavelengths share the same
transmission paths. This forces the number of wavelengths to be continually increased
as new users are added to the network. While these passively routed broadcast
networks can be appropriate for local-area networks (LAN’s), they are not suitable
for larger scale networks due to the limited number of wavelengths available.

Large networks can be built by interconnecting many LAN’s based on wavelength
conversion and wavelength routing, with the same set of wavelengths used in each
LAN’s [9],[10]. Routing between LAN’s can be accomplished by shifting one of the
wavelengths from the incoming LAN, using a broadband wavelength converter, so that
it can be routed to the desired recipient LAN. This architecture makes it possible to
build multiwavelength networks in which the number of nodes is completely indepen-
dent of the number of wavelengths. Such networks are truly scalable and overcome
the limitations placed on broadcast networks by the limited number of wavelengths
available. In addition, wavelength conversion, combined with wavelength routing,
makes it possible to dynamically reconfigure the connection paths in an all-optical
network. This can potentially enhance network survivability, a network quality highly

sought after by service providers.

Because of their potential applications in all-optical networks, wavelength con-

Sy asatsemanarne. «named

Pa i: ARSE 7

version devices have been extensively investigated in recent years. Demonstrations
to date of wavelength converters include: optical triggering in distribution-feedback
(DFB) lasers with saturable absorbers [11]; gain saturation in semiconductor optical
amplifiers (SOA’s) [12] and semiconductor lasers [13]; difference frequency generation
in LiNbO3 channel waveguides [14]; and four-wave mixing in dispersion-shifted fibers
[15], semiconductor lasers [16] and traveling-wave amplifiers [17|-[20]. Various limita-
tions with respect to tuning and modulation format are inherent with most of these
wavelength conversion techniques. However, wavelength conversion based on four-
wave mixing in SOA’s allows continuous tuning of input and output wavelengths over
the entire amplifier gain bandwidth, and the process is transparent to the modulation
format and bit-rate of the data.

In this chapter we present our results concerning conversion efficiency over wave-
length spans up to 65 nm [18], as well as a demonstration of wavelength conversion
with gain [20]. We also describe measurements of the signal to background noise ratio
and present a noise reduction technique using a selective noise filter [21]. In addition,
we describe a demonstration of wavelength conversion of modulated signals at data

rates of 2.5 Gb/s and 10 Gb/s.

6.2 Wavelength Conversion Efficiency

Using Eq. (4.1), SOA four-wave mixing wavelength conversion efficiency can be ex-

pressed by the following simple relation:

1 = 3G +21, + R(Ad) (6.1)

where 77 is the ratio in dB of the converted signal output power to the signal input
power in dBm and G is the saturated SOA optical gain in dB. Other parameters
appearing in Eq. (6.1) include the input optical pump-wave power I, (expressed in
dBm), and a quantity we call the relative efficiency function, R(AA), which is given
by

R(AA) = 20log| > em: 1 infin

m=1

| (6.2)

where, as discussed earlier, the three terms in the summation represent contributions
to four-wave mixing wavelength conversion from the various responsible mechanisms.
Ad is the wavelength shift related to detuning frequency by A\ = —2)?f /c.

A crucial point is the presence of 3G in this expression. This term occurs because
the nonlinear field mixing involved in the four-wave mixing process uses the pump
wave twice and the input signal once so that overall the amplifier’s single-pass gain
acts three times. As an aside, we note that 3G in Eq. (6.1) assumes equal gain for
pump and signal waves. In general, we have 2Gpump + Ginput Where Gpump and Ginput
are pump and input signal gains, respectively.

In the present measurement, we employed a novel tandem amplifier geometry in
which two or three 1.5 wm tensile-strained InGaAs/InGaAsP MQW SOA’s [22] (the
same devices used in the spectroscopy study), separated by optical isolators, were
placed in series. This tandem amplifier, having much higher optical gain, provided
a simple method for realizing higher optical gains and testing theoretical predictions
concerning conversion efficiency.

We first measured the dependence of the conversion efficiency 7 on the saturated

single-pass SOA gain G. The experimental setup was similar to what we described
in Chapter 4 except here a tandem amplifier with two SOA’s was employed. For this
measurement, wavelengths and powers of the pump and signal waves remained fixed,
and the single-pass gain was varied by changing the bias currents of the two SOA’s
between 80 mA and 175 mA. Shown in Figure 6.1 is typical conversion efficiency
data plotted versus single-pass saturated optical gain. Conversion was measured
from 1532.0 nm to 1523.0 nm with a pump power of —5.2 dBm and an input signal
power of —11.3 dBm. The measured slope of 3.18 verified the cubic dependence of
efficiency on single-pass gain. Similar values for the slope were obtained for various
other wavelength shifts and input power levels.

The wavelength-shift dependence of the conversion process was also measured for
both wavelength up- and down-conversion. Both SOA’s used in the measurements
were biased at 150 mA. In the down-conversion experiment, the pump was fixed at
1526.0 nm with —5.3 dBm of power coupled into the first SOA wavelength converter.
The maximum wavelength down-shift measured in this study was as large as 65 nm,
corresponding to a frequency shift of 8 THz. In the up-conversion measurement, the
pump was fixed at 1549.0 nm with an input power of —6.0 dBm. Wavelength up-
conversion was measured for shifts up to 47.5 nm, corresponding to a frequency shift
of —6 THz. The conversion efficiency 7 for both positive and negative wavelength
shifts is presented in Figure 6.1, where the efficiency is normalized using Eq. (6.1)

with the typical parameter values in this study: pump power of —5.5 dBm, signal

power of —10 dBm and saturated optical gain G of 18.2 dB (corresponding to the

75
10
cay
GS oF
omg
oO
@ -10F
= % (a)
Po a
nT] SD
fe)
6 -20F 6
7) °
3) P ap
| 2 O®
| & 30
-40 L i. i L i L
-80 -60 -40 -20 0 20 40 60
Wavelength Shift (nm)
-5
oO Slope=3.18
oS ope —>
cond
Ss -10}
Oo
= (b)
nT)
| S
m 15 bt
pa
oo)
5 Ip = -5.2 dBm
oO Iq = -11.3 dBm
-20 ‘ AF ,
15 16 17 18 19

Gain (dB)

tandem amplifier gain G, showing the cubic dependence. A tandem amplifier with two

tensile strained SOA’s was used.

| Figure 6.1: Measured conversion efficiency 7 (a) versus wavelength shift AA, (b) versus

total input power). The normalization may introduce a small, but negligible error
arising from slight spectral variation in the saturated SOA gain for the pump and
input signal over the wavelength spans measured. An efficiency asymmetry with
respect to positive and negative wavelength shifts is caused by phase interferences
which occur between the various contributing inter- and intraband four-wave mixing
mechanisms. The measurement of wavelength conversion up to 65 nm shows that
ultrafast four-wave mixing dynamics in SOA’s are capable of converting signals over
very large wavelength spans.

In a separate measurement where three SOA’s were used, we achieved 7 > 0 dB,
i.e., wavelength conversion with gain. The measured conversion efficiencies versus
wavelength shift are presented in Figure 6.2 for a pump power of —11.5 dBm and a
signal power of —15.2 dBm (SOA optical gain G was saturated to 24.2 dB at this
input power level). Conversion efficiencies greater than 0 dB, as shown in Figure 6.2,
were achieved for down-conversion up to ~ 7.0 nm and for up-conversion over ~ 2.0
nm. Conversion efficiency remained as high as 14% for down-conversion shifts as large
as 23.9 nm. This was the first demonstration of broadband SOA four-wave mixing
wavelength conversion with gain, indicating high conversion efficiency is possible with
SOA four-wave mixing wavelength converters. In addition, we also confirmed the
cubic dependence of conversion efficiency on the single-pass gain, as also shown in

Figure 6.2.

Figure 6.2: Measured conversion efficiency 7 (a) versus wavelength shift AA, (b) versus

20
cS ot oO
| 9 Bo
= 0 #¢------------= eo ---9 ee ne ee ne ee ec ~q (a)
nr} Pree re)
c o® @
fo) oete) fe)
77) fore) (@)
| ® -10 L o fo)
i c Og
| 9 O
/ -20 F 1 1 '
| -30 -20 -10 0 10 20
| Wavelength Shift (nm)
20
i ~
i (an)
ZS 10+
Cc
Lv
= OF (b)
Lu
| 5
| 2
© -10}
| >
Cc
fo}
| S
~ -20 i 4. 4 L
| 20 22 24 26 28 30
| Gain (dB)

tandem amplifier gain G, showing the cubic dependence. A tandem amplifier with three

tensile strained SOA’s was used.

bev

6.3. Noise Properties and Noise Reduction

6.3.1 Noise Properties

In SOA four-wave mixing wavelength conversion demonstrations to date, either the
input signal is preamplified by an EDFA before being coupled into the SOA mixer
[17],[19], or, as described in the previous section, a tandem SOA structure which
provides high single-pass gain is used [18],[20]. In the latter case, the first SOA
essentially serves as a preamplifier since the nonlinear mixing takes place primarily in
the last segment of the tandem amplifier where the pump and input signal fields are
strongest. The preamplification which occurs in each of these approaches is crucial
to improving overall converter performance.

For a preamplifier having linear optical gain G, and spontaneous emission factor
nz, at the preamplifier output, the spontaneous noise power spectral density for one

polarization state is given by
Sal?) = GySh(v) + nly (Gp — 1) hy (63)

where S?,(v) is the spontaneous noise power spectral density at the preamplifier’s
input and hv is photon energy. The two terms in the above formula originate from
amplification of any input excess noise and introduction of spontaneous noise by the
preamplifier. Assuming a coupling efficiency of k,, to the SOA mixer, the spontaneous

noise coupled to the mixer is given by S!™ = kmS5,,.

The spontaneous noise power spectral density of one polarization at the mixer’s

output can be written as
mY) = GrSP(v) + mm(Av)Si(v — Av) + Nsp (Gn _ : hv (6.4)

where G,, and nf, are the SOA’s saturated single pass linear gain and spontaneous
emission factor, respectively; (Av) is the conversion efficiency of the SOA mixer
for frequency shift Av, defined as the ratio of converted signal power at the mixer’s
output to input signal power coupled into the mixer. Physically, the three terms
on the right side in Eq. (6.4) represent amplified input excess noise, converted input
noise, and spontaneous noise introduced by the SOA mixer, respectively.

Normally, a narrowband optical bandpass filter is used at the SOA mixer’s output
to remove the amplified pump and input signal, leaving only the converted signal.
Upon detection of the converted signal, the photocurrent can be written as J = Isig+1,
where Igig = KaRPO(v;5) is the signal and i represents current fluctuations which
include the effects of shot noise, thermal noise and spontaneous noise. Here, Kg is
the coupling efficiency from the mixer’s output to the detector, R is the detector’s

responsivity and P%",.(1.5) is the power of the converted signal (at optical frequency

Ves) at the mixer’s output. Under most circumstances the variance o? = (i?) of

current fluctuations is dominated by signal-spontaneous beat noise in which case the

total current fluctuation (i?) is given by

(i?) = @? = AK R?P™ (Ves) Os (Ves) A fet (6.5)

sp—sig

where Af.; is the receiver’s electrical bandwidth. Signal to noise ratio (SNR) can

therefore be given by

KaRPe (v )
o? AK2R2P™ (Ves) Sr (Ves)A fet AS™ (Ves )Afel
As Eq. (6.6) indicates, optical SNR CONTE (Afop is the normalization optical

bandwidth), i.e., the ratio of converted signal to background spontaneous noise in
the converted signal band, is an important parameter for a wavelength converter.
It directly affects the electrical SNR at the receiver, which in turn affects the bit-
error-rate (BER) performance of a lightwave communication system. In the first
experiment that we described in Section 6.2 where the tandem amplifier with two
SOA’s was used, optical SNR (Af,, = 0.1 nm) for a total input power level of —4.2
dBm (as used in Figure 6.1) was measured to be about 15 dB for —5 nm of shift and
steadily dropped to 0 dB slightly beyond —65 nm of shift.

Improvement in the optical SNR can be expected with higher total input power
(pump plus input signal) because optical SNR increases with the total input power.
Shown in Figure 6.3 is measured converted signal power, spontaneous noise power
(Af.p = 0.1 nm), and optical SNR as a function of total input power for a 5 nm
wavelength down shift. The maximum optical SNR is 20.8 dB for —0.7 dBm of total
input power. It results because of reduction of spontaneous noise in conjunction with
increasing converted signal power as the amplifier saturates. As the total input power
increases, both G, and G’, are reduced as the result of gain saturation; therefore, the
spontaneous noise at the mixer output decreases. The fact that converted signal
power continues to increase in this regime is due to its cubic dependence on total

output power at a fixed pump to signal power ratio, as indicated by the following

-1 5 T
-20
Ee on L
faa} 2s L
oo L
ro) a
= i
-35 =F
-40
-12

Figure 6.3: Measured four-wave mixing signal power, spontaneous noise (0.1 nm band-

width), and optical SNR versus total input power. A tandem amplifier with two tensile

strained SOA’s was used.

Total Input Power (dBm)

(GP) YNS

equation derived from Eq. (6.1):

I” (Ves) = 317, + R(AA) + 10 log (6.7)

arp

where [™

™ (Ves) is the converted signal power in dBm, r is the ratio of amplified input

signal to amplified pump and J, (expressed in dBm) is the total output power, 7.e.,

the amplified pump power plus the amplified input power.

6.3.2 Noise Reduction

Spontaneous noise from the preamplification stage that resides in the conversion fre-
quency band constitutes a major part of the noise at the converter’s output, as indi-
cated in Eq. (6.4). We refer to this component as the direct noise component. Unlike
normal applications of optical preamplifiers in which amplification and spontaneous
noise are inextricably connected, direct spontaneous noise associated with optical
preamplification can, in principle, be eliminated, thereby vastly improving overall
converter function. This can be done by introducing a filter between the preampli-
fier and the mixer which removes the preamplifier spontaneous noise component in
the spectral vicinity of converted signal wavelength. This is possible since removal
of noise components in the converted signal band at the mixer’s input will have no
effect on the subsequent mixing process. Such a filter which attenuates the converted
signal bands by a factor of y but leaves the input signal and pump bands unaffected

will lead to a spontaneous noise reduction in dB given by

Sm 4+ Eby

Noise Reduction = 10 log

Sih/y + 3h hy

where Fy” = 2ng, (1 — a) is the SOA mixer’s amplification noise figure. The con-
verted input noise, which is normally much smaller than the amplified noise and the
spontaneous noise introduced by the mixer, has been ignored in Eq. (6.8). It should
be noted, however, that this converted noise would be the only remaining noise in an
optimal converter scheme, as will be discussed later in this chapter.

Since the spontaneous noise introduced by the SOA mixer can be written as
5GmE" hy, the term 5 Phy can be viewed as the equivalent input noise power spec-
tral density of the SOA mixer. The effectiveness of this noise reduction technique,
as indicated in Eq. (6.8), strongly depends on the relative magnitude of the input
noise power spectral density S/" coupled into the SOA mixer and the equivalent input
noise power spectral density of the SOA mixer 5 F™hy. The former, in turn, strongly
depends on the excess noise of input signal and the preamplification gain, and the
latter depends on the SOA mixer’s noise as characterized by its amplification noise
figure. Using F’" = 8 dB and hv = 0.809 eV, the calculated noise reduction is plotted
in Figure 6.4 versus Sj” for various filter extinction ratios y.

We have experimentally verified this idea of noise reduction. A tunable erbium-
doped fiber ring laser and a DF'B laser were used as pump and input signal sources.
The SOA mixer was the tensile strained InGaAs MQW amplifier [22] used in the
spectroscopy study described in Chapter 4. An EDFA was used as the preamplifier
for both the pump and input signal, followed by a fiber notch filter having 0.96 nm

bandwidth, 14 dB extinction ratio centered at 1529.8 nm and near unity transmission

outside of the filter band. The total optical power of the pump and input signal into

oh
wn

Noise Reduction (dB)
wn °

-60

1527 nm 1537 nm 1527 nm 1537 nm

Figure 6.4: Upper figure shows noise reduction versus the spontaneous noise power density
S™ at the SOA mixer’s input; Lower picture illustrates the spectra of the SOA mixer’s
output for S7*” = —46.0 dBm (left) and S?7) = —36.7 dBm (right) showing spontaneous
noise reduction. The small peak between the pump and input signal is a side mode of the

DFB laser. Vertical scale: 10 dB/div; Horizontal scale: 1 nm/div.

the preamplifier was attenuated to vary the EDFA gain and thus the spontaneous
noise power spectral density S™. The measured noise reduction versus S77 is also
presented in Figure 6.4 where a good agreement with theory can be seen. Also shown
in Figure 6.4 are measured spectra of the SOA mixer’s output where significant noise

reduction is visible.

6.3.3 Optimal Converter Structure

The theoretical analysis and measurements described in this paper also suggest new
considerations for optimal converter structures. Overall optical gain of the preampli-
fier and the SOA mixer has been previously shown to be crucial for high conversion
efficiency. However, spontaneous noise introduced in the overall conversion process
can considerably degrade the signal to noise ratio. To combat this problem, we pro-
pose to completely separate the functions of gain and nonlinearity.

In an optimal converter structure, the first stage would consist of two optical
preamplifiers for the pump and input signal, respectively. Separate amplification of
pump and input signal is advantageous because of better noise performance. Each of
the preamplifiers is followed by a noise filter that removes spontaneous noise outside
the pump band or input signal band. The third stage of the wavelength converter is
the nonlinear mixer, which can be a highly saturated SOA, or a properly designed
semiconductor waveguide with energy gap greater than the photon energy (Eygap >
hy). In the former case the introduced spontaneous noise, as given by n%}(Gm — 1)hv,

depends on the SOA mixer saturation level, while in the latter case virtually no

spontaneous noise is introduced by the mixer.

With this proposed structure, the high-gain preamplifiers provide high optical
power into the mixer thereby maintaining efficient wavelength conversion in the mixer;
however, they do not significantly contribute to the output spontaneous noise since
filters can, in principle, eliminate the direct spontaneous noise in the converted signal
band. Ideally, by using below gap mixing, only the converted spontaneous noise would
remain in Eq (6.4). This would mean that signal to noise degradation would occur
primarily in the preamplifiers, provided that the subsequent nonlinear wave mixing is
efficient enough to ensure that, upon detection of the converted signal , the shot noise
would not be a significant noise source. The mixing efficiency depends not only on the
mixer’s intrinsic parameters including the third order susceptibility and interaction
length, but also on the preamplifier gain which determines powers of the pump and
input signal at the mixer input. High gain preamplifiers are therefore also crucial to

the noise performance of the overall conversion process.

6.4 Wavelength Conversion of Modulated Signal

We have characterized SOA four-wave mixing converters using a CW laser source as
the input signal. These measurements have provided a good physical understanding of
some of the most important converter characteristics such as conversion efficiency and
noise properties. The understanding of these characteristics is essential to the design
and optimization of these converters. In the meanwhile, we have begun to study four-
wave mixing wavelength conversion from system’s perspective. Wavelength conversion

of 2.5 Gb/s and 10 Gb/s ASK data has been demonstrated and preliminary results

of this measurement are presented in this section.

A schematic diagram of the experimental setup used to demonstrate wavelength
conversion of modulated signal is shown in Figure 6.5. The signal laser, a DFB laser
operating at 1559.4 nm, was directly modulated at either 2.5 Gb/s or 10 Gb/s by a
pseudorandom bit pattern of length 2’ — 1 supplied by a signal generator (Hewlett-
Packard 70340A). The pump source was a tunable fiber-ring laser as shown in Figure
4.1, except here a tunable fiber-pigtailed interference bandpass filter with a band-
width of about 1.5 nm was used in place of the broadband fiber Fabry-Perot filter.
The outputs of the pump and signal lasers were combined using a 90/10 fiber-optic
bidirectional coupler (pump 90%, signal 10%), and co-amplified in an Amoco EDFA
with a maximum output power of 18 dBm. This preamplifier was followed by a fiber-
grating notch filter having a 11.5 dB, 3 A notch centered at 1551.5 nm. Although
this converter structure was not quite the optimal structure that we proposed in the
previous section, use of the notch filter, as we have discussed and will demonstrate,
considerably reduced the excess noise from the preamplifier stage.

The SOA employed in the experiment was the tensile strained InGaAs MQW
amplifier [22] used in the spectroscopy study described in Chapter 4. It was operated
at a high injection current of 150 mA, but was strongly saturated by a total power of
~ 13 dBm coupled into this SOA mixer using microscope objective lenses. The ratio
of pump to input signal powers was maintained at about 10 dB, thereby ensuring
that the slight modulation of the SOA gain by the input signal would not introduce

waveform distortion and chirp to the converted signal.

Wavelength
Converter

DFB
Laser

Data

(2.5 Gb/s or 10 Gb/s) , Optical
Attenuator

Signal
Generator

S/S6

Clock Power
Monitor

Bit-Error Eye
Rate Diagram
Analyzer | Analyzer

Bessel- Microwave Microwave
Thompson }—~ Power Preamplifier
filter Amplifier P

Figure 6.5: Experimental setup used to demonstrate wavelength conversion of ASK data at

2.5 Gb/s and 10 Gb/s.

By tuning the pump laser wavelength, the converted signal was set to the center of
the notch filter. This corresponds to a wavelength down shift of 7.9 nm. The optical
spectrum of the SOA output is shown in Figure 6.6(a) where the pump was slightly
offset to illustrate the notch and the optical SNR improvement of the converted signal.
A tunable fiber Fabry-Perot bandpass filter (bandwidth 35 GHz, finesse 100) was used
to select the converted signal.

The converted signal was detected by a receiver consisting of an EDFA pream-
plifier, a pin-based lightwave converter with 15 GHz bandwidth (Hewlett-Packard
11982A), and a microwave preamplifier. A tunable fiber Fabry-Perot bandpass filter
(bandwidth 45 GHz, finesse 100) was placed before the lightwave converter to remove
most of the background spontaneous noise, also to further suppress residual pump, in-
put signal. The detected data pattern was amplified by a microwave power amplifier
(DC — 6 GHz) and analyzed either by a microwave transition analyzer (Hewlett-
Packard 70820A) or by a BER tester (Hewlett-Packard 70843A). In the case of 2.5
Gb/s, a SONET OC-48 filter was used after the microwave amplifier to suppress high
frequency noise.

A test waveform of the converted signal, consisting of repeated pattern 11100100
at 10 Gb/s, is shown in Figure 6.6(b). Typical eye diagrams for 2.5 Gb/s and 10 Gb/s
are shown in Figures 6.6(c) and 6.6(d). These two eye diagrams correspond to BER’s
of approximately 1 x 10~° and 1 x 10", respectively. The greater amount of noise
for 1 bits than for 0 bits, as seen from the measured waveform and the eye diagrams,

indicates that the results were limited primarily by signal-spontaneous beat noise.

S|
™~
3 r’
° \
| SS a a —————_} i
ny |
Vv
2 nm/div
(a)
Loop pd
oe Rak act 1g > re

120 ps/div

(c)

200 ps/div
(b)

30 ps/div

(d)

Figure 6.6: (a) Optical spectrum of SOA output; (b) converted data pattern 11100100; eye

diagrams of converted data at (c) 2.5 Gb/s and (d) 10 Gb/s.

The in-fiber converted signal power in this study was measured to be —26 ~ —28
dBm and the optical SNR was 26 ~ 28 dB (bandwidth 0.1 nm). These optical
parameter would give error-free performance at 10 Gb/s with a high-performance
optically-preamplified receiver. In fact, the optical spectra measured at the EDFA
preamplifier’s input and output show that the amplified spontaneous noise introduced
by the preamplifier, rather than the amplified input excess noise, was the dominant
source of noise at the pin detector. This indicates that the optical preamplifier was

the primary limiting factor in this measurement.

6.5 Conclusion

We have characterized some of the most important converter characteristics such as
conversion efficiency and noise properties. We have also demonstrated wavelength
conversion of modulated signals at data rates of 2.5 Gb/s and 10 Gb/s. Due to the
lack of a high-performance EDFA preamplifier and a sufficiently stable tunable pump
source in this preliminary system measurement, we did not perform measurements of
BER versus received power. Improvement to the receiver’s optical preamplifier, how-
ever, is expected to enable a full characterization of the impact of the SOA four-wave
mixing wavelength converters on fiber-optic communication systems. In addition,
overall optimization of the wavelength converter structure should lead to further im-

provement to the converter performance.

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