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Journal of the Optical Society of America B

Photon echo in semiconductors: a stochastic approach

W. Vogel, Frank Herzel, K. Henneberger

Published Sep 1, 1991• 1 citation
Publisher

Abstract

Femtosecond photon echos in semiconductors are studied on the basis of a stochastic description of the polarization decay. A satisfactory agreement with experimental results [ Phys. Rev. Lett.61, 1647 ( 1988)] is found with respect to the nonexponential decay of the echo energy as a function of the time delay between the laser pulses. Moreover, the shape of the echo is studied, and the detuning of the laser frequency with respect to the band edge is found to depend significantly on the shape of the light pulses.

DOI
10.1364/josab.8.001947

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•May 21, 1990•0 citations
Femtosecond photon echos in semiconductors are studied on the basis of a stochastic description of the polarization decay. A satisfactory agreement with experimental results [ Phys. Rev. Lett.61, 1647 ( 1988)] is found with respect to the nonexponential decay of the echo energy as a function of the time delay between the laser pulses. Moreover, the shape of the echo is studied, and the detuning of the laser frequency with respect to the band edge is found to depend significantly on the shape of the light pulses.
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.
The semiconductor Bloch equations are solved numerically for a two-pulse photon-echo configuration. The time-dependent diffracted signal is computed and the significance of many-body effects, carrier relaxation, and dephasing is investigated in detail. Assuming femtosecond-pulse excitation at various intensities and frequencies, distinctly different results are obtained if the exciton or the continuum electron-hole-pair states are excited. It is shown that pure exciton excitation produces a free-induction decay signal and no photon echo. An echo signal is obtained only if continuum states are excited either directly by choosing the central pulse frequencies appropriately or if the band-gap renormalization is sufficiently strong to shift continuum states into resonance. A continuous transition between free-induction decay and photon-echo signal is obtained with increasing excitation amplitude. A perturbative analytical analysis of the equations allows one to identify the role of the many-body effects in producing the different features.
The availability of femtosecond pulses in the optical-frequency regime allows the study of coherent effects in the interaction between semiconductors and light. Because the properties of the exciting pulses become important ingredients in spectroscopy, the theoretical analysis must treat the complete time dependence of the system. For this purpose we use the semiconductor Bloch equations (SBE),1-3 which are the coupled equations of motion for the interband polarization and the electron and hole populations for an interacting electron-hole system in the random-phase approximation. The equations describe the electron-hole Coulomb attraction leading to excitonic features; they contain phasespace filling and band-gap renormalization effects, as well as the dipole interaction with the applied light field.
Experimental results of observations of a femtosecond photon echo excited in an ensemble of quantum nanometer-sized objects in thin semiconductor (ZnO, SiB, SiP) films at room temperature are presented. The observed properties of the photon echo are discussed. Recorded relaxation times of exciton quantum transitions and beats at the photon echo decay as a function of the increasing interval between the exciting pulses reveal the role played by the defects of the thin film in the formation of its exciton structure of quantum transitions investigated using angular optical echo spectroscopy.
The phase relaxation of optically excited electronic states can be studied in fourwave mixing experiments where three excitation pulses at t = 0, t =t21, and t = T, respectively, interact via the third-order polarization of the medium to generate a nonlinear signal whose intensity depends on the dephasing time T2. For inhomogeneously broadened optical transitions the signal will be emitted as a time delayed photon echo pulse at t = T + t21 provided the pulse duration is short compared with T2. The echo amplitude decays as exp(−4t21/T2).1