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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Photon echo in direct-gap semiconductors

Indrani Majumdar, Pranay K. Sen

Published Apr 28, 1999• 0 citations
Publisher

Abstract

Based upon the time dependent perturbation theory for coherent radiation-semiconductor interaction, the possibility of occurrence of the phenomenon of two-pulse photon echo has been investigated analytically in a bulk direct-gap semiconductor under near resonant transition regime below the absorption edge of the crystal. The excitation intensity is chosen to be in the low-to-moderate power regime such that the photoinduced electron-hole pair density remains below the Mott transition limit and the weakly bound Wannier-Mott excitonic structure of the crystal absorption edge is manifested. The band gap renormalization effect is also taken into account. Numerical estimation of the transmitted intensity has been made for electron-hole transition to the 1s excitonic states in the bulk CdS crystal. The analytical results demonstrate the occurrence of photon echo in direct-gap semiconductors.

DOI
10.1117/12.347989

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Based upon the time dependent perturbation theory for coherent radiation-semiconductor interaction, the possibility of occurrence of the phenomenon of two-pulse photon echo has been investigated analytically in a bulk direct-gap semiconductor under near resonant transition regime below the absorption edge of the crystal. The excitation intensity is chosen to be in the low-to-moderate power regime such that the photoinduced electron-hole pair density remains below the Mott transition limit and the weakly bound Wannier-Mott excitonic structure of the crystal absorption edge is manifested. The band gap renormalization effect is also taken into account. Numerical estimation of the transmitted intensity has been made for electron-hole transition to the 1s excitonic states in the bulk CdS crystal. The analytical results demonstrate the occurrence of photon echo in direct-gap semiconductors.
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 coherent excitation of a Wannier-exciton system by a short resonant light pulse is described through a simple model that takes into account explicitly the phase-space-filling effects due to the fermion nature of the electrons and holes composing the excitons. This formalism can describe both coherent-transient experiments, such as photon echoes, and optical observations at time scales longer than dephasing, such as absorption saturation. At high excitation densities the optical response of hydrogenic excitons deviates significantly from the response of the two-level model used traditionally to describe resonant effects. This suggests that coherent-optical-transient experiments, such as photon echoes, may be used to probe exciton interactions due to their internal structure, in addition to the relaxation processes that they probe in traditional experimental arrangements.
An overview on photon echo spectroscopy under resonant excitation of the exciton complexes in semiconductor nanostructures is presented. The use of four-wave-mixing technique with the pulsed excitation and heterodyne detection allowed us to measure the coherent response of the system with the picosecond time resolution. It is shown that, for resonant selective pulsed excitation of the localized exciton complexes, the coherent signal is represented by the photon echoes due to the inhomogeneous broadening of the optical transitions. In case of resonant excitation of the trions or donor-bound excitons, the Zeeman splitting of the resident electron ground state levels under the applied transverse magnetic field results in quantum beats of photon echo amplitude at the Larmor precession frequency. Application of magnetic field makes it possible to transfer coherently the optical excitation into the spin ensemble of the resident electrons and to observe a long-lived photon echo signal. The described technique can be used as a high-resolution spectroscopy of the energy splittings in the ground state of the system. Next, we consider the Rabi oscillations and their damping under excitation with intensive optical pulses for the excitons complexes with a different degree of localization. It is shown that damping of the echo signal with increase of the excitation pulse intensity is strongly manifested for excitons, while on trions and donor-bound excitons this effect is substantially weaker.
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.
Using a coherent radiation-semiconductor interaction model based upon the time dependent perturbation technique, the occurrence of optical nutation has been analytically investigated in direct-gap semiconductors such as GaAs, GaSb, InAs, and Hg1-xCdxTe, duly irradiated by near resonant laser beams. The present approach is much more simplified and straightforward than the conventional Maxwell-Bloch approach used so far for the study of coherent optical transient effects in molecular and atomic systems. The dispersion and absorption expressed in terms of the real and imaginary parts of the crystal optical susceptibility\chi_{r}and\chi_{i}exhibit temporally damped ringing behavior of Neumann and Bessel types, respectively. These processes have been identified as dispersive and absorptive optical nutation. The theory is developed for arbitrary laser intensity in presence of damping due to nonoptical processes. To understand the mechanisms of dispersive and absorptive optical nutation, we have restricted only to low-power resonant band-to-band transitions neglecting excitonic and damping effects. While studying analytically the transient behavior of\chi_{r}and\chi_{i}for a given pump field strength, it is noticed that the absorptive component exhibit remarkable qualitative agreement with the experimental observations of optical nutation in13CH3F.
Using the time-dependent perturbation treatment of the density matrix, the authors report the occurrence of first-order free induction decay (FID) in narrow direct-gap semiconductors. The analysis deals with the interaction of a near resonant, ultrashort, moderate power laser pulse with the bulk semiconductor sample. Numerical estimates have been made for intrinsic InSb of micrometre size at 77 K irradiated by a frequency doubled 10.6 mu m CO 2 laser with pulse duration in the picosecond domain. The results reveal oscillations, around the background values, in the decay profiles of both the refractive index as well as the absorption coefficient. The transient transmitted intensity has been found to decay in a time comparable to the inhomogeneous Doppler broadening time, which is much shorter that the dephasing time. The analytical behaviour reported here is in very good agreement with the experimental observations of first-order FID in the atomic caesium vapour systems.