We present a theoretical analysis and experimental measurements of broadband optical wavelength conversion by four-wave mixing in semiconductor traveling-wave amplifiers. In the theoretical analysis, we obtain an analytical expression for the conversion efficiency. In the experiments, both up and down-conversion efficiencies are measured as a function of wavelength shift for shifts up to 27 nm. The experimental data are well explained by the theoretical calculation. The observed higher conversion efficiency for wavelength down-conversion is believed to be caused by phase interferences that exist between various mechanisms contributing to the four-wave mixing process

Dawson, Jay W.

Miller, Barry I.

Newkirk, Michael A.

Park, Namkyoo

Vahala, Kerry J.

Zhou, Jianhui

English

Caltech Authors - Main

50 IEEE PHOTONICS TECHNOLOGY LETI’ERS, VOL. 6, NO. 1, JANUARY 1994 
Efficiency of Broadband Four-Wave 
Mixing Wavelength Conversion Using 
Semiconductor Traveling-Wave Amplifiers 
Jianhui Zhou, Namkyoo Park, Jay W. Dawson, Kerry J. Vahala, Member, ZEEE, 
Michael A. Newkirk, Member, IEEE, and Barry I. Miller, Member, IEEE 
Abstmct-We present a theoretical analysis and experimental 
measurements of broadband optical wavelength conversion by 
four-wave mixing in semiconductor traveling-wave amplifiers. In 
the theoretical analysis, we obtain an analytical expression for 
the conversion efficiency. In the experiments, both up and down- 
conversion emciencies are measured as a function of wavelength 
shift for shifts up to 27 MI. The experimental data are well 
explained by the theoretical calculation. The observed higher 
conversion efficiency for wavelength down-conversion is believed 
to be caused by phase interferences that exist between various 
mechanisms contributing to the four-wave mixing process. 
I. INTRODUCTION 
~ C A L  wavelength conversion devices are expected to 0 play an important role in future broadband multichan- 
ne1 lightwave systems. Several techniques for wavelength 
conversion have been demonstrated. These include optically- 
triggered multi-electrode DFB lasers [ 11, optical injection- 
induced frequency shift in DFB lasers [2], gain saturation in 
semiconductor optical amplifiers [3], as well as nondegenerate 
four-wave mixing (FWM) in optical fibers [4], semiconductor 
lasers [5] and traveling-wave amplifiers [6]. 
Four-wave mixing in traveling-wave amplifiers (TWA’s), 
when used for wavelength conversion, has several advantages. 
Owing to their traveling-wave operation, these devices offer 
the potential for very high speed operation as well as contin- 
uous tuning of the input and output wavelengths. In addition, 
since the converted signal is the phase-conjugate replica of the 
input signal, the conversion is transparent to the modulation 
format, and also provides the possibility for fiber-dispersion- 
compensation in lightwave communication systems. 
In a typical FWM wavelength conversion experiment, pump 
and probe (input signal) waves are combined and coupled into 
a TWA. The beating of pump and probe fields in the TWA 
active layer induces dynamic gain and index gratings, and the 
subsequent scattering of the input fields from these gratings 
generates two sideband signals. The important contributing 
Manuscript received July 13, 1993; revised November 1, 1993. This work 
was supported by the Office of Naval Research under contract N00014-91- 
1524 and by Northrop Corporation. 
J. Zhou, N. Park, J. W. Dawson and K. J. Vahala are with the Department 
of Applied physics, Mail Stop 128-95, California Institute of Technology, 
Pasadena, California 91 125. 
M. A. Newkirk and B. I. Miller are with AT&T Bell Laboratories, Holmdel, 
New Jersey 07733. 
IEEE Log Number 9214736. 
1041-1 135/94$04 
mechanisms are carrier density modulation caused by inter- 
band stimulated emission and intraband occupancy modulation 
via dynamic carrier heating and spectral hole buming. Owing 
to its ultrafast nature (relaxation timescl ps), intraband dy- 
namics can play a dominant role in broadband wavelength 
conversion. This has been demonstrated in previous highly 
nondegenerate FWM measurements [7]-[ lo]. 
In this paper, we present a theoretical analysis in which 
coupled-amplitude equations are solved and an explicit expres- 
sion is obtained for the FWM conversion efficiency. We also 
present measurements of wavelength conversion efficiency in 
TWA’s as a function of wavelength shift AA for shifts up to 
27 nm. 
In the copropagation FWM geometq, guided waves in the 
TWA are given by Ej(z)exp [ i ( k j z  - w j t ) ] ,  where j = 
p ,  g, s indicate pump, probe and converted signal, respectively; 
{ E j ( z ) }  are the field amplitudes; and z is the longitudinal 
coordinate along the propagation direction. The influence of 
interband and intraband mixing of pump and probe waves on 
the propagation of the three waves can be modeled using 
coupled-amplitude equations. Following procedures similar 
to those used in Agrawal’s treatment [ l l ] ,  we obtain the 
following set of coupled equations 
= (+ (1 - ia) - CY1 Ep,,(z) (1) 
dz 2 l + r  ) 
x E,(z) - ~ ( z ) E ; ( z ) E , * ( z )  exp ( iAkz)  (2) 
where we have introduced the wave-number mismatch Ak = 
2kp - k, - IC, and a four-wave mixing coupling coefficient 
~ ( 2 ) .  In addition, go is the unsaturated optical gain per unit 
length, with its wavelength dependence negligible for the 
devices tested. P ( z )  is the total optical power at position 
z in the waveguide, P, is the TWA’s saturation power, a 
is the linewidth enhancement factor and al is the TWA’s 
nonsaturable intemal loss per unit length. In deriving Eq. (l), 
we have neglected the power that is coupled to pump and probe 
waves from neighboring wavelengths, since, for broadband 
wavelength conversion, the power transfer is negligible in 
comparison to the power in the pump and probe, themselves. 
1.00 0 1994 IEEE 
MOU et al.: EFFICIENCY OF BROADBAND FOUR-WAVE MIXING 51 
The coupling coefficient K ( Z )  is central to this theoretical 
analysis. To simplify the analysis, we treat contributing mech- 
anisms to FWM-carrier density modulation, dynamic carrier 
heating and spectral hole burning-as independent processes. 
This is justified, in part, by noting that damping effects asso- 
ciated with these mechanisms are caused by interactions with 
independent baths. By evaluating the polarizations induced by 
the above mechanisms at the signal wavelength, ~ ( z )  is found 
to be 
.- 2 ;, 1 90 .(Z) = -- 2 1 + y m = 1  
where m=1, 2, 3, for carrier density modulation, dynamic 
carrier heating and spectral hole burning, respectively. f is 
the detuning frequency, defined as the difference between the 
optical frequencies of the pump and probe waves; {r,} and 
{P,} are the lifetimes and saturation powers associated with 
the mechanisms; and {a,} give the ratio between the real and 
the imaginary parts of the refractive index change induced by 
the mechanisms. 
Using the boundary condition &(O) = 0, we solve Eqs. 
(1) and (2) and find that under moderate TWA saturation the 
converted signal amplitude at the TWA output (z = 1 )  can be 
expressed by 
E; ( Z ) E , *  ( l )K( i )Ze iAk l  
0.23G + iAkl E&) = - (4) 
where G = 4.34Ji(i$L!+ - at)& is the TWA saturated 
gain in dB. The phase dsmatch term can be expressed as 
AkZ = 5 % (y)2 1, where % is the group index 
dispersion. Using % N -0.7 pm-', measured by Hall er al. 
[12], and 1 = 0.8 mm for the devices in this study, the phase 
mismatch for AA = 27 nm is estimated to be -0.27, which is 
negligible in comparison to the first term for a typical optical 
gain of G N 15 dB. 
Using @. (4), the conversion efficiency, defined as the ratio 
between the converted signal power and the input probe power, 
is given in dJ3 by 
1 3  I 
where I, is the input pump power in dBm and where the 
complex coupling coefficient, h, is defined as 
1 - icu, 
901 .- c, = 
0.46G( 1 + y) pm 
We note that the term 3G is present in Eq. (3, which results, 
physically, from the fact that both the pump and probe waves 
experience an optical gain of G (note that G affects the 
pump wave twice due to the form of Eq. (4)). TWA's with 
large optical gain are therefore critical to efficient wavelength 
conversion. 
The experimental arrangement for this study was similar 
to what we have described in Ref. [9]. The TWA's used 
1 1 0  100 
Wavelength Shift (nm) 
Fig. 1. Measured wavelength conversion efficiency relative to 3G + ZIP 
versus up-conversion (circle), and down-conversion (square) wavelength 
shifts, showing theoreticalfit (solid line) and 20 dB/dec line (dashed line). 
Device tested is a tensile-strained TWA biased at 100 mA. 
in the measurements were compressively and tensile-strained 
InGaAsAnGaAsP multiple quantum well devices operating at 
1.5 pm. Details on these devices appear in Refs. 1131 and [141. 
Three, single-frequency, tunable, &-doped fiber ring lasers 
[15] were used as pump, probe, and local oscillators in the 
measurement. The converted signal was heterodyne detected 
by mixing the signal with the fiber-laser local oscillator 
output and tuning the local oscillator relative to the signal 
frequency to provide an IF signal. The IF mixing frequency 
was maintained at 4.00 GHz throughout the measurements 
to eliminate the frequency dependence of the detection elec- 
tronics. The detected photocurrent was measured using an 
electronic spectrum analyzer, and the input wavelengths and 
the optical powers of pump and probe were measured using 
an optical spectrum analyzer. 
Using this experimental setup, both the up and down- 
converted signals were measured, and both compressively and 
tensile-strained TWA's were tested. The maximum wavelength 
conversion spacing measured was as large as 27 nm. The 
conversion efficiency relative to 3G + 21, was then evaluated 
as a function of the wavelength shift. Shown in Fig. 1 are 
the data from the tensile-strained device and the theoretical fit 
based on Eq. (5). 
As can be seen in Fig. 1, IQ. (5) provides an excellent 
fit for both up and down-conversion efficiency spectra. The 
fitting parameters are as follows: 71 = 200 ps, 7 2  = 650 
fs, 7 3  = 50 fs, C1 = 0.24e-i1.30, C2 = 0.0027ei1.30, 
C3 = 0.00048ei1.53. The efficiency asymmetry with respect 
to up and down-conversion is believed to be caused by 
the phase interferences which occur between the various 
contributing mechanisms. The down-conversion shows overall 
higher efficiency because of constructive phase interferences 
which exist on this detuning side. The compressively-strained 
device data, shown in Fig. 2, also exhibit similar features. This 
fit is obtained using the same relaxation time constants as for 
52 
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-40 
-50 
-60 
-70 
-80 
IEEE PHOTONICS TECHNOLOGY LETTERS, VOL. 6. NO. 1, JANUARY 1994 
’ 
’ 
’ 
which incorporates the contributions to the conversion process 
from carrier density modulation, dynamic carrier heating and 
spectral hole burning. The theoretical results and the measured 
efficiency spectra presented in this paper should be of prac- 
tical importance for design and analysis of four-wave mixing 
wavelength converters. 
I 
-90: . . ’ .”; 1 0  1 0 0  
Wavelength Shift (nm) 
Fig. 2. Measured wavelength conversion efficiency relative to 3G + 21, 
versus uptonversion (circle), and downtonversion (square) wavelength 
shifts, showing theoreticalfit (solid line) and 20 dB/dec line (dashed line). 
Device tested is a compressively-strained TWA biased at 150 mA. 
the tensile device, but different complex coupling coefficients: 
C1 = 0.24e-i1.30, C2 = 0.0027ei1.42, C, = 0.00023ei3.13. 
Interpretation of these fitting parameters can be found in 
RefiIO]. 
The relative efficiency spectra measured in this study should 
be useful for the design of four-wave mixing wavelength 
converters. They make it possible to quickly estimate the actual 
conversion efficiency at any AA-shift provided that the optical 
gain and input pump power are known. For example, in the 
case of tensile TWA measurements reported here, the saturated 
TWA gain was w 15 dB and the input pump power was - -9 
dBm, giving a conversion efficiency of -30 dB for AA = 10 
nm (up-conversion). If the saturated optical gain could be 
increased to 25 dB while other parameters remain unchanged, 
the efficiency would become 0 dB or 100%. This illustrates the 
importance of TWA gain for efficient wavelength conversion. 
Additionally, the measured efficiency spectra indicate the 
presence of ultrafast intraband processes in the FWM process, 
and can provide insight into the ultrafast dynamics of the 
semiconductor active layers. We have discussed broadband 
FWM wavelength conversion as a spectroscopic tool in a 
recent paper [IO] and the FWM mechanism assignments used 
here result, in part, from that work. 
In conclusion, we have measured the FWM conversion 
efficiency versus wavelength shift for shifts up to 27 nm. The 
efficiency spectra were well explained by a theoretical analysis 
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Efficiency of broadband four-wave mixing wavelength conversion using semiconductor traveling-wave amplifiers

20 nm Wavelength conversion using ultrafast highly nondegenerate four-wave mixing,”

All fiber, low threshold, widely tunable single-frequency, erbium-doped fiber ring laser with a tandem fiber Fabry-Perot filter,”

Effects of nonlinear gain on four-wave mixing and asymmetric gain saturation in a semiconductor laser amplifier,”

High perfonnance optical wavelength shifter,”

Highly nondegenerate four-wave mixing and gain nonlinearity in a strained multiplequantum-well optical amplifier,”

hnable optical-wavelength conversion using an optically triggerable multielectrode distributed feedback laser diode,”

Observation of highly nondegenerate four-wave mixing in a 1.5 pm traveling-wave semiconductor optical amplifier and estimation of nonlinear gain coefficient,”

Tensile-strained InGaAsAnGaAsP quantum-well optical amplifier with a wide spectral gain region at 1.55 pm,”

Terahertz four-wave mixing spectroscopy for study of ultrafast dynamics in a semiconductor optical amplifier,”

Wavelength conversion experiment using fiber four-wave mixing,”

Wavelength conversion for frequency-modulated light using optical modulation to oscillation frequency of a DFB laser diode,”

http://authors.library.caltech.edu/8879/1/ZHOieeeptl94a.pdf

Efficiency of broadband four-wave mixing wavelength conversion using semiconductor traveling-wave amplifiers

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