Analysis of origin of nonlinear gain in 1.5 μm semiconductor active layers byhighly nondegenerate fourwave mixingK. Kikuchi, M. Amano, C. E. Zah, and T. P. Lee Citation: Applied Physics Letters 64, 548 (1994); doi: 10.1063/1.111099 View online: http://dx.doi.org/10.1063/1.111099 View Table of Contents: http://scitation.aip.org/content/aip/journal/apl/64/5?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Highly nondegenerate four-wave mixing in a tunable dual-mode semiconductor laser Appl. Phys. Lett. 84, 5189 (2004); 10.1063/1.1764604 Nondegenerate four-wave mixing in a semiconductor microcavity Appl. Phys. Lett. 71, 2650 (1997); 10.1063/1.120168 Observation of nearly degenerate and cavityenhanced highly nondegenerate fourwave mixing insemiconductor lasers Appl. Phys. Lett. 62, 2757 (1993); 10.1063/1.109630 Highly nondegenerate fourwave mixing and gain nonlinearity in a strained multiplequantumwell opticalamplifier Appl. Phys. Lett. 62, 2301 (1993); 10.1063/1.109398 Cavityenhanced highly nondegenerate fourwave mixing in GaAlAs semiconductor lasers Appl. Phys. Lett. 55, 519 (1989); 10.1063/1.101865

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Analysis of origin of nonlinear gain in 1.5 pm semiconductor active layers by highly nondegenerate four-wave mixing

K. Kikuchi and M. Amano Department of Electronic Engineering, University of Tokyo, 7-3-l Hongo, Bunkyo-Ku, Tokyo 113, Japan

C. E. Zah and T. P. Lee Bellcore, Red Bank, New Jersey 07701

(Received 21 May 1993; accepted for publication 15 November 1993)

The origin of the nonlinear gain effect in 1.5 pm semiconductor active layers is investigated by using highly nondegenerate four-wave mixing, where the pump-probe detuning is extended up to 2 THz. From the signal intensity measured as a function of the detuning frequency we find that both the spectral hole burning and the dynamic carrier heating contribute to the four-wave mixing. The dynamic carrier heating, however, creates the index grating rather than the gain grating, and hence, the spectral hole burning is the main origin of the nonlinear gain effect.

The nonlinear gain coefficient E in semiconductor lasers is an important parameter which determines the modulation bandwidth.’ The nonlinear gain effect is induced by the re- duction of the occupation probability of carriers due to the presence of intense light. The spectral hole burnin~3 and the dynamic carrier heating4T5 have been proposed as the origin of the occupation probability reduction. However, it has not been fully understood which effect is more dominant.

This letter aims at elucidating the origin of the nonlinear gain in 1.5 ,um semiconductor active layers through a highly nondegenerate four-wave mixing experiment. The pump- probe detuning is extended up to 2 THz in the present ex- perimental setup, making it possible to observe the nonlinear gain effect more clearly than in our previous experiment.6 From the signal intensity measured as a function of the pump-probe detuning, we can discuss third-order nonlinear optical properties of active layers: the nonlinear gain (the imaginary part of the third-order nonlinear optical coefficient ,yC3’), the nonlinear refractive index (the real part of x”‘), and the time constant governing x’“‘. The analysis of the experi- mental results shows that both the spectral hole burning and the dynamic carrier heating contribute to the third-order op- tical nonlinearity; however, as far as the nonlinear gain is concerned, the contribution from the spectral hole burning is about ten times larger than that from the carrier heating.

We assume that the semiconductor active layer under test is operated in the traveling-wave amplifier (TWA) mode. Let the pump, probe, and signal frequencies be fp, fq, and f, respectively. When the pump and probe lights copropagate in the active layer, the light intensity varies at the pump-probe detuning frequency fd( =f,--f,). Then, the gain and refrac- tive index are modulated at fd, generating dynamic gain and index gratings. The pump .light is, in turn, scattered by the dynamic gratings, and the signal light at f,=fp+fd=2f -fq i,sthenproduced.

When ]IzJ%]~J~+]EJ~, the Bragg scattering process mentioned above is described by the following differential equations:“‘7

dEP>~ _ l x-2 Gw-%,~ (1)

dE, 1 d,l-zg&-;g&E;eik.

In Eq. (2), the cross-phase modulation of the signal light due to the pump light is neglected, because it only affects the phase-matching condition. Electric fields Ej (j=p,g,s) de- note the complex amplitude of the pump, probe, and signal lights, respectively, and are normalized so that IEj12=Sj, where Sj is the photon density. Parameters gj are the gain at the pump, probe, and signal frequencies, and Ak denotes the mismatching of the wave vector kj defined as

Ak=2k,-k,-k, (3)

The parameter 5 denotes the scattering efficiency by the dynamic gratings, and is written asbT7

5= ::;;:;s+m~,ch iY;;$;. The first term originates from the carrier density modulation due to the pump-probe beating. In this term, rS represents the carrier recombination lifetime (-1 ns), I, the saturation in- tensity, and a the linewidth enhancement factor. On the other hand, the second term stems from the modulation of the oc- cupation probability of carriers, which may be induced by the spectral hole burning (m = hb) and/or the dynamic carrier heating (m=ch). In this term, E, denotes the nonlinear gain coefficient, and p, the ratio of the real part to the imaginary part of the nonlinear susceptibility. The time constant rhb is determined from the intraband scattering process, and is -0.05 ps. The time constant r& is estimated to be 0.65 ps by the pump-probe experiment.” When deriving Eq. (4), we as- sume that IE,[241,.

We should note that in Eq. (4), Z,+l/e, and ~,%r,. Therefore, the Bragg scattering occurs when lf,j<lOO GHz mainly through the carrier density moduIation [the first term of Eq. (4)]. On the other hand, the contribution from the occupation probability modulation [the second term of Eq. (4)] appears only when 1 fdl %-IO0 GHz, and is much smaller than that from the carried density modulation.

By solving Eqs. (1) and (2) under the approximation that the amplifier gain G‘% 1, we obtain the signal amplitude as

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1 o-23 t 1GHzl 10’ 102 103 fd [GHzl

-fd [GHz]

FIG. 1. Scattering efficiency 14 of the bulk active layer as a function of the pump-probe detuning frequency. (a) fd>O, (b) f&O.

FIG. 2. Scattering efficiency 151 of the M Q W active layer as a function of the pump-probe detuning frequency. (a) fd>O, (b) fd<O.

E.&j = -5 lqMq~)“, (5)

where v is given as

In the present experiment, where the maximum detuning is 2 THz, the phase mismatching Ak is negligibly small.

Equation (5) shows that the scattering efficiency Id is determined from the signal power, the probe power, and the pump power measured at the output of the amplifier. From 1~1 measured as a function of the detuning frequency fd, we can estimate E,?~ and &, by using Eq. (4).

The experimental setup is the same as that used in Ref. 6. We use 1.5 pm InGaAsP TWAs having the bulks and multiple quantum-well (MQW)’ active layers. The MQW ac- tive layers are composed of four Ina.s3Ga0,4& wells, 7 nm thick, each.” The signal light is detected by a heterodyne receiver to improve the receiver sensitivity and the frequency resolution. The pump, probe, and local light generated from distributed feedback lasers, whose- frequency is swept by controlling the laser temperature.b The maximum pump- probe detuning fd of 2 TH?z is obtained by using eight probe lasers. The pump wavelength is 1545 nm, and the gain peak wavelengths of the bulk and MQW active layers are 1490 and 1480 nm, respectively. The bias current is fixed at 90 mA for the bulk WA and 80 mA for the MQW TWA during the experiment.

Small circles in Figs. l(a) and l(b) show the scattering efficiency 14 of the bulk active layer measured for the posi-

tive detuning (fd>O) and the negative detuning (fd<O), re- spectively. The scattering efficiency 161 of the MQW active layer is shown in Figs. 2(a) (fd>O) and 2(b) (fd<O).

When lf,l<lO O GHz, Id in these figures reduces at the rate of 20 dB/decade as shown by the broken lines. This is due to the fact that 5 is approximated as

g-a 2rfdrsl,

(71

when lal~l. On the other hand, when lf,]>lOO GHz, 5 de- viates from the broken lines, showing the contribution from the second term in Eq. (4).

We use phb, &, ebb, and eCh as adjustable parameters for fitting Eq. (4) to the measured values. We assume that $,=0.05 ps and r,,, -0.65 ps, but the theoretical curves are insensitive to the value of rhb, because the cutoff frequency 1/2nr,,b is outside the experimental detuning range. The line- width enhancement factor LY is measured to be 10 in the bulk active layer, and 8 in the MQW active layer at the pump wavelength and the bias currents used in the experiment. Note that these values are very large, because the pump wavelength is much longer than the gain peak (positive de- tuning).

Table I shows values thus obtained, and the solid curves in Figs. l(a) and l(b) and 2(a) and 2(b) are fitted ones. We

TABLE I. The most likely set of E and p in bulk and M Q W active layers obtained by curve fitting.

% (m3) Phb %h cm’) P ch

Bulk M Q W

l.7x1o-D 0.7 3.0x10-24 14 1.7x10-u 0.6 4.6X10-” 6.6

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TABLE II. Another set of E and p in bulk and MQW active layers obtained by curve fitting. et+ becomes negative, and this set of parameters is rejected physically.

%b tm3) f&b ch (m3) P ch

Btllk -1.5x1o-u 1.0 1.7x lo-= -6.8 MQW -l.oxlo-‘J 1.8 1.8x1o-u -2.5

find that another set of parameter values shown in Table II can also give good fitting of Eq. (4) with experiment. How- ever, e,,b becomes negative in this case, and it is most likely that the parameter values given in Table I are the actual ones.

From Table II we find that both the spectral hole burning and the carrier heating contribute to four-wave mixing. The former creates both the index and gain gratings, whereas the latter does the index grating. On the other hand, the norilin- ear gain is induced mainly by the spectral hole burning. The contribution form the spectral hole burning is about ten times as large as that from the carrier heating.

The nonlinear gain effect observed between 1.5 pm bulk and MQW active layers is not significantly different. The nonlinearity originated from carrier transport is not observed. This may be due to the fact that the beating between the

pump and probe lights injected into the MQW active layer directly modulates the carrier density in the quantum wells.

In conclusion, the origin of the nonlinear gain in 1.5 pm semiconductor active layers was investigated by using highly nondegenerate four-wave mixing with the pump-probe de- tuning of 2 THz. We found that both the spectral hole burn- ing and the carrier heating contribute to the nonlinear gain, but the contribution from the former is about ten times larger than that from the latter.

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