Journal of Luminescence 83}84 (1999) 127}130

Spectral di!usion within exciton line in GaSe

Atsushi Hasegawa!,*, Fujio Minami"

!Communications Research Laboratory, Nukui-Kita 4-2-1, Koganei-shi, Tokyo 184-8795, Japan"Graduate School of Science and Engineering, Tokyo Institute of Technology, Meguro-ku, Tokyo 152-8551, Japan

Abstract

The spectral di!usion across the exciton line in GaSe is observed in two types of four-wave-mixing experiments. In thestimulated photon echo experiment, the signal shows a non-exponential decay as the waiting time between the secondand third pulses increases. This behavior begins clearly from a few 10 ps of the waiting time. The deformation of the signalpro"le depending on the delay time of "rst two pulses is also observed in the transient grating-type signal. These resultsare in good agreement with the result of a theoretical calculation based on a stochastic model. ( 1999 Elsevier ScienceB.V. All rights reserved.

PACS: 42.50.Md

Keywords: Spectral di!usion; Stimulated photon echo; Transient grating

1. Introduction

Time-resolved degenerate four-wave-mixing(DFWM) is a powerful technique to obtain in-formation about relaxation processes in solids. Inparticular, photon echo is frequently used to un-cover the detail of homogeneous dephasing that ismasked by inhomogeneous broadening [1]. Thedecay of photon echo is taken to indicate thehomogeneous dephasing time [2]. Furthermore,three-pulse photon echo, i.e., stimulated photonecho (SPE) provides us with information concern-ing an additional dephasing introduced by the"nite waiting time, known as `spectral di!usiona,in addition to homogeneous dephasing. In thispaper, we study ultrafast spectral di!usion across

*Corresponding author. Fax: #81-42-327-6694.E-mail address: hasegawa@crl.go.jp (A. Hasegawa)

an exciton line in GaSe through SPE experiments.As the waiting time of SPE increases, the spectraldi!usion plays an important role in optical dephas-ing. The deformation of the SPE signal begins from&10 ps of the waiting time [3]. It means that thedecay curve is no longer exponential and changesdrastically on increasing the incident time of thethird pulse.

The spectral di!usion can also be seen in thedecay signal of transient grating-type (TGT) experi-ment. In this experiment, we scan the third pulsecontinuously while changing the interval of the "rstand second pulses discretely. The experiment givesa combination of the exciton lifetime and the spec-tral di!usion. On increasing the interval of the "rsttwo pulses, the signal intensity near 10 ps of delaytime changes drastically. It means that TGT signalreceives a large deformation from the ordinal tran-sient grating one, as predicted by the result of theSPE. These results can be simulated well witha stochastic model analysis.

0022-2313/99/$ - see front matter ( 1999 Elsevier Science B.V. All rights reserved.PII: S 0 0 2 2 - 2 3 1 3 ( 9 9 ) 0 0 0 8 5 - X

Fig. 1. ¹8

dependence of the time-integrated SPE signal at 5 K.The solid lines are the calculated curves derived from Eq. (1) asa function of q.

2. Experiment

The sample used here was layered semiconductorGaSe grown by the Bridgman method. At 5 K, the1S exciton line peaked at &2.11 eV (588 nm) andhad a width of &5 meV, which is broadened in-homogeneously as a result of the stacking disorder,as discussed by Forney et al. [4]. The excitationsource was Optical Parametric Oscillator (OPO)system based on the mode-locked Ti sapphire lasergenerating pulses with &200 fs. The wavelength ofthe pulses was tuned to the 1S exciton resonance.All three pulses had the same polarization (s-polar-ization). We assume that the relative delay timebetween the "rst and second pulses is q, and thatbetween the second and third pulses is ¹

8in this

paper. In the SPE experiment, ¹8

was changeddiscretely. In the TGT experiment, ¹

8was scanned

continuously and q was changed discretely. Allmeasurements were performed at 5 K.

3. Results and discussion

The ¹8

dependence of the time-integrated SPEsignal pro"le is shown in Fig. 1. On increasing ¹

8,

the signal intensity decreases quickly at longer-delay time. Further, the peak near-zero-delaysharpens and shifts to the zero-delay time. Theseresults can be explained by the spectral di!usion. Inthe SPE process, the "rst two pulses interfere intime and generate a periodic frequency modulationof the exciton population. The third pulse reachedat time ¹

8after pulse two, scatters o! this grating

and the amplitude of the resulting echo depends onthe extent to which this modulation has decayed atthe time of the third pulse. The loss of contrastresults from spectral di!usion washing out the grat-ing modulation depth set up by the initial pulses.This shallowing of the grating depth causes thedecrease of SPE signal.

At ¹8"0 ps (two-pulse photon echo), the echo

curve shows a single exponential decay with a risedetermined by the temporal resolution (&200 fs)because of the absence of spectral di!usion. At¹

8"5 ps (the stimulated photon echo case), the

spectral di!usion does not signi"cantly a!ect thesignal pro"le. In this case, the asymmetry of the

curve indicates that inhomogeneous broadening isdominant in GaSe. From the decay time of&0.85 ps, therefore, the homogeneous line width isestimated to be &0.38 meV [5]. If spectral di!u-sion is present, however, a non-exponential decayoccurs for a longer waiting time ¹

8. It is found

from the "gure that the role of spectral di!usion inthe optical dephasing is more important for largervalues of q. This dependence results from thegrating fringe spacing being proportional to 1/q.For larger q, the frequency interval of the

128 A. Hasegawa, F. Minami / Journal of Luminescence 83}84 (1999) 127}130

Fig. 2. q dependence of TGT signal at 5 K. The ordinate takesthe logarithm scale.

fringe becomes shorter. Therefore, the depth of themodulation disappears more rapidly as comparedto shorter q case.

The peak shift is caused by the integrated e!ectof the photon echo signal. When the in-homogeneous width is not so broad, this e!ect isstrongly emphasized [5]. At ¹

8"0 ps, the peak

shift is determined only by this e!ect. With increas-ing ¹

8, as will be seen, the photon echo signal

becomes weak due to the spectral di!usion. Thesignal that peaked at the time of the incidence of thethird pulse appears and dominates the time-integ-rated signal. The decay of this signal is determinedby the free induction decay time of exciton. This iswhy the signal peak shifts to zero delay for larger¹

8. The variation of the rising time of the signal

with ¹8

is also explained similarly. On increasing¹

8, the spectral di!usion e!ect becomes dominant.

In such a case, the temporal order of the two pulsesis lost because of the fading away of the frequencymodulation. This leads to the appearance of thesignal at negative delay.

In Fig. 2, the results of the TGT experimentis shown. In the case of q"0 ps, the signal showsthe usual transient grating pro"le: a sharp peak(coherent artifact) followed by a long-decay re#ect-ing population relaxation. In this case, the fre-quency modulation cannot be formed because ofthe simultaneous excitation of two pulses. There-fore, the di!raction signal is not in#uenced by thespectral di!usion. On increasing q, the signal pro"legradually changes with q because of the spectraldi!usion across the frequency modulation made bythe "rst two pulses. The signal has the coherentartifact which is generated by the interference with-in the excitation pulses. This coherent artifact in-vites us to observe the variation of the signal pro"lenear-zero delay. Therefore, we focus our attentionon the signal in the temporal region where thee!ect of the coherent artifact does not reach.Around 10 ps of delay time ¹

8, the signal change is

remarkable. This is predicted from SPE experi-ment. The SPE signal also gradually changes after¹

8"10 ps.To study the e!ects of the spectral di!usion on

the SPE and TGT experiments, we also performeda theoretical calculation within the framework ofa Gaussian stochastic model, where the system is

subject to a random perturbation by interactionwith the bath [6]. In this model, the signal intensityincluding the spectral di!usion e!ect is written forq(¹

8as

I(q, ¹8)Jexp [!Aq!D2q2M1!exp (!R¹

8)N

!¹8/¹

1] (q(¹

8). (1)

Here, D and 1/R are parameters corresponding,respectively, to the strength of the system-perturberinteraction and to the correlation time of the per-turbation. The "rst term of Eq. (1) corresponds tothe dephasing process and the parameter A deter-mines the dephasing rate in the absence of spectraldi!usion. We "tted our experimental results usingD and R as adjusting parameters. Firstly, wecalculate for the SPE case. The solid lines on thedotted signal in Fig. 1, show the theoretical curvescalculated from Eq. (1) as a function of q. Thevalues of the parameters used are D"500 GHz,R"70 GHz, A"1.17 THz, 1/¹

1"1 GHz. Here,

A and 1/¹1

is derived from the signal pro"le in the

A. Hasegawa, F. Minami / Journal of Luminescence 83}84 (1999) 127}130 129

Fig. 3. Calculated curves derived from Eq. (1) as a functionof ¹

8.

absence of spectral di!usion. The curves are "ttedwell to the experimental data. It is thus found thatthe change in the SPE signal can be explained bythe spectral di!usion.

The calculated results for the TGT case areshown in Fig. 3 as a function of ¹

8. At q"0 ps, the

transient grating has only the populational relax-ation channel. However, on increasing q, the extraspectral di!usion channel opens in the relaxationprocess. This di!usion a!ects the decay process forseveral 10 ps. After that the signal comes back tothe original populational relaxation pro"le. There-fore, the signal approaches asymptotically to thepopulational decay signal. These calculated curvesgive a good simulation of the experimental results.

4. Conclusion

The non-exponential decay caused by the spec-tral di!usion is observed in the SPE involving theexcitons in GaSe. Because of the spectral di!usion,the photon echo signal is found to disappear in thelonger-delay region. In the TGT experiment, signalintensity decreases, especially in an early time of¹

8due to the spectral di!usion. At a long-delay

time of ¹8, the signal goes back to the ordinal

transient grating one. The theoretical calculationbased on the stochastic model is found to repro-duce both the experimental results well.

Acknowledgements

This work was supported partially by aGrant-in-Aid for Scienti"c Research and SpecialCoordination Funds for Promoting Science andTechnology from STA (Science and TechnologyAgency) of Japan.

References

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[2] For example, F. Minami, A. Hasegawa, S. Asaka, K. Inoue,J. Lumin. 45 (1990) 409.

[3] T. Mihashi, M. Mizuno, F. Minami, A. Hasegawa, Proceed-ings of the 24th International Conference on The Physics ofSemiconductors, World Scienti"c, Singapore, 1999, II-C-2(CD-ROM).

[4] J.J. Forney, K. Maschke, E. Mooser, J. Phys. C 10 (1977) 1887.[5] T. Yajima, Y. Taira, J. Phys. Soc. Japan 47 (1979) 1620.[6] Y.S. Bai, M.D. Fayer, Phys. Rev. B 39 (1989) 11066.

130 A. Hasegawa, F. Minami / Journal of Luminescence 83}84 (1999) 127}130