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Topical Meeting on Optical Bistability (OB)

Theory of Resonance-Enhanced Optical Nonlinearities in Semiconductors

H. Haug

Published Jan 1, 1983• 0 citations
Publisher

Abstract

In semiconductors the attractive Coulomb interaction between electrons and holes causes one- and two-photon resonances, known as excitons and exciton molecules, respectively. Large nonlinearities are observed in the spectral vicinity of these resonances. These nonlinearties are well-suited for the realization of optical bistability1),2),3) as has been demonstrated by Gibbs et al. 1)for GaAs and by Miller et al.2) for InSb. The electron-hole correlations, the screening and the energy renormalization are most conveniently calculated by the Green's function formalism. The optical dielectric function can be expressed in terms of the retarded photon self-energy which is also called the polarization function. This connection is not restricted to the linear response regime.

DOI
10.1364/obi.1983.thc1

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In semiconductors the attractive Coulomb interaction between electrons and holes causes one- and two-photon resonances, known as excitons and exciton molecules, respectively. Large nonlinearities are observed in the spectral vicinity of these resonances. These nonlinearties are well-suited for the realization of optical bistability1),2),3) as has been demonstrated by Gibbs et al. 1)for GaAs and by Miller et al.2) for InSb. The electron-hole correlations, the screening and the energy renormalization are most conveniently calculated by the Green's function formalism. The optical dielectric function can be expressed in terms of the retarded photon self-energy which is also called the polarization function. This connection is not restricted to the linear response regime.
The optical spectra of laser-excited semiconductors change with varying laser intensity. Close to exciton or biexciton resonances these optical nonlinearities are, e.g., large enough to obtain optical bistability. The cause for these large nonlinearities are many-body effects in the system of the electron-hole pair excitation. The use of nonequilibrium Green’s functions, or if a quasi-equilibrium exists of thermal Green’s functions, makes it possible to take radiative and Coulomb interactions consistently into account.
Summary form only given. Large-radius excitons in semiconductors suffer strong Coulomb interaction on close approach. This is a distinctive difference in comparison with two-level systems in quantum optics. A mean field theory of interacting excitons in semiconductors leads to purely repulsive interaction, and does not account for spin-dependent polarization mixing and the formation of excitonic molecules (biexcitons). We have developed a theory for the nonlinear optical response, which can account for both. The coherent polarization is driven by exciton-exciton correlation, which can be expressed in terms of spin-dependent retarded memory functions. The effective equation is a generalized Gross-Pitaevskii equation.
Semiconductors exhibit large optical nonlinearities near the band edge because of resonance enhancement. Optical bistability occurs when the optical nonlinearities are coupled with feedback. In bulk GaAs and GaAs–AlGaAs multiple-quantum-well superlattices, the nonlinearity arising from the presence of the free-exciton resonance has produced room-temperature optical bistability with a few milliwatts of power. The formation of biexcitons in CuCl, the saturation of the bound exciton on CdS, and band-filling effects in InSb, InAs, and HgCdTe lead to observation of bistability in these materials. A bistable etalon can be operated in an optical-gate mode to generate optical analogs of electronic gates such as and, or, and nor. It has been demonstrated that a GaAs optical NOR gate responds in ∼1 psec, using only ≲3 pJ of energy. However, because of the carrier lifetime of a few nanoseconds, the repetition rate of the NOR gate is now limited to a few hundred megahertz.
Nonlinear optical properties of laser-excited semiconductors are discussed, and the applications to optical bistability and optical logic are reviewed. The physical origin of the nonlinearities is analyzed in terms of the many-body interactions in the system of electron-hole pairs, causing effects such as plasma screening of the Coulomb interaction, band-gap renormalization, and band filling. Theoretical results for absorption and refractive-index spectra are compared to experimental data obtained for room-temperature GaAs and other semiconductors. The experimental and theoretical results for dispersive optical bistability in semiconductors are summarized, and recent experiments on optical logic gating and pattern recognition are discussed.
Abstract A coherent radiation‐exciton interaction model is employed to study analytically the phenomenon of nonlinear absorption in important III—V semiconductors (viz., GaAs, GaSb, InSb, InAs), the crystals being irradiated by suitable lasers with energies (hω) nearly equal to the band gap energies (hωg). The nonoptical processesare accounted for phenomenologically by introducing a damping parameter into the equation of motion of the probability amplitude of the excited electron—hole pair state. The Wannier‐Mott type of exciton wave function is found to be responsible for the giant nonlinearity of the crystal absorption coefficient in the near resonant optical interband transition regime with h | ω ‐ ωg | of the order of the crystal exciton binding energy. The effect of renormalization of the crystal band gap in the presence of Coulomb interaction and Starkbroadening is also discussed.