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Physical Review Letters

Coherent optical polarization of bulk GaAs studied by femtosecond photon-echo spectroscopy

A. Lohner, Kai Rick, P. Leisching, Alfred Leitenstorfer, Thomas Elsaesser, T. Kühn, Fausto Rossi, W. Stolz

Published Jul 5, 1993• 80 citations
Publisher

Abstract

The nonlinear polarization close to the band gap of GaAs is studied by spectrally and temporally resolved four-wave mixing. Excitonic and free carrier contributions both excited within the bandwidth of the 100 fs pulses are distinguished for the first time. The excitonic part dominates at carrier densities below ${10}^{16}$ ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}3}$. At higher density, nonthermalized free carriers give rise to an additional component resonant to the pulse that shows a photon-echo-like time behavior. Monte Carlo simulations including the coherent polarization and the scattering dynamics of the carriers account for the data.

DOI
10.1103/physrevlett.71.77

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The nonlinear polarization close to the band gap of GaAs is studied by spectrally and temporally resolved four-wave mixing. Excitonic and free carrier contributions both excited within the bandwidth of the 100 fs pulses are distinguished for the first time. The excitonic part dominates at carrier densities below 1016{10}^{16}1016 cm\ensuremath−3{\mathrm{cm}}^{\mathrm{\ensuremath{-}}3}cm\ensuremath−3. At higher density, nonthermalized free carriers give rise to an additional component resonant to the pulse that shows a photon-echo-like time behavior. Monte Carlo simulations including the coherent polarization and the scattering dynamics of the carriers account for the data.
Summary form only given. Even one decade after the pioneering photon echo experiments by Shank et al. (1988,1991) in which GaAs was investigated at room temperature using /spl ap/10 fs optical pulses, not a single experiment has actually shown directly that the coherent real-time response of semiconductor band-to-band transitions under these conditions is a photon echo indeed. Recent experiments with /spl ap/10 fs pulses exciting GaAs at low temperatures have explicitly shown that the response is not a photon echo for low excitation densities (/spl ap/10/sup 15/ cm/sup -3/). From these experiments it has also become clear that the coherent response after excitation with 10 fs pulses is distinctly different from that after excitation with 100 fs pulses. We investigate the coherent real-time response at elevated carrier densities using transient four-wave mixing and an up-conversion scheme with a time resolution of 5 fs. We focus on approximately resonant excitation (50 meV above gap) of a 0.6 /spl mu/m thin film of bulk GaAs at T=300 K.
We report the first observation of femtosecond photon echoes from the band-to-band transitions in a bulk semiconductor. The time decay of the echo, found to vary from 3.5 to 11 fs, has allowed us to determine the polarization dephasing rate in GaAs. This rate was found to depend on the carrier density in the experimental range covered, 1.5\ifmmode\times\else\texttimes\fi{}1017{10}^{17}1017 to 7\ifmmode\times\else\texttimes\fi{}1018{10}^{18}1018 ${\mathrm{cm}}^{\ensuremath{-}3}$, indicating the dominance of carrier-carrier scattering as the principal dephasing mechanism. The observed functional dependence of the dephasing rate on the carrier density has yielded previously unavailable information on Coulomb screening in a nonequilibrium carrier distribution.
We report a strong (300:1) excitonic resonance in time-resolved (100 fs) four-wave mixing in GaAs quantum wells as a function of the incident photon energy and show that it results from the large difference in the dephasing rates of excitons and free carriers. We conclude that excitons dominate even when they make up only a small fraction of the excited states. These results, in conjuction with new results in exciton-phonon scattering, provide new insights into previous studies performed with spectrally broad ultrashort pulses.
We have studied the coherent emission from bulk semiconductors by spectrally resolved and spectrally integrated four-wave mixing (FWM) with broadband 16-fs pulses in the carrier density range from $1\ifmmode\times\else\texttimes\fi{}{10}^{16}{\mathrm{cm}}^{\mathrm{\ensuremath{-}}3}$ to $6\ifmmode\times\else\texttimes\fi{}{10}^{17}{\mathrm{cm}}^{\mathrm{\ensuremath{-}}3}.$ In GaAs, only continuum transitions are excited, while both excitonic and continuum transitions are excited in Al0.06Ga0.94As.{\mathrm{Al}}_{0.06}{\mathrm{Ga}}_{0.94}\mathrm{As}.Al0.06​Ga0.94​As. The decay of the FWM signal for positive time delays unambiguously reflects the dephasing of the continuum, irrespective of the excitation of excitonic transitions. We find identical ultrafast sub-20-fs decay times of the coherent emission from continuum transitions in GaAs and Al0.06Ga0.94As,{\mathrm{Al}}_{0.06}{\mathrm{Ga}}_{0.94}\mathrm{As},Al0.06​Ga0.94​As, independent of the excess excitation energy. These decay times depend only weakly on the carrier density for densities below ${10}^{17}{\mathrm{cm}}^{\mathrm{\ensuremath{-}}3}.$ The continuum dephasing is analyzed considering carrier-carrier and carrier-LO-phonon scattering in a relaxation rate approach. The excitonic transitions in Al0.06Ga0.94As{\mathrm{Al}}_{0.06}{\mathrm{Ga}}_{0.94}\mathrm{As}Al0.06​Ga0.94​As dominate the FWM signal at negative time delays.
Excitonic nonlinearities in the weak-excitation limit condition are examined with time-integrated and time-resolved four-wave mixing (FWM). Below an excitation of 3\ifmmode\times\else\texttimes\fi{}109{10}^{9}109 excitons/cm2{\mathrm{cm}}^{2}cm2, coherent third-order processes prevail. Echo-type signals are observed in parallel and perpendicular polarization configurations. The coherent process induced by the two-photon coherence of the two-exciton state is attributable to signals in the perpendicular configuration. The polarization dependences of a temporal profile and the intensity of FWM signals are well explained with third-order perturbational analysis that takes into account the two-exciton states and inhomogeneity.