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Physical Review Letters

Many-Body Theory of Optical Bistability in Semiconductors

Jan P. Löwenau, Stefan Schmitt-Rink, H. Haug

Published Nov 15, 1982• 84 citations
Publisher

Abstract

A unified microscopic theory of the observed optical bistabilities in narrow-gap semiconductors, such as InSb and GaAs, is developed by calculating the complex, nonlinear dielectric function for arbitrary free-carrier concentrations from an integral equation for the polarization function.
DOI
10.1103/physrevlett.49.1511

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Dispersive optical bistability has been observed in various direct-gap semiconductors. This effect is due to the dependence of the refractive index on the intensity I. A unified microscopic theory of the observed optical bistability in direct-gap semiconductors, such as GaAs is developed by calculating the complex, non-linear dielectric function for arbitrary free-carrier concentrations. The calculation, which includes many-body effects, consists in a very accurate numerical solution of the Bethe-Salpeter equation for the polarisation function. The resulting time-resolved spectra are discussed and are compared with experimental results.
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.
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.
Gives a broad description of optical bistability: from practical applications, as an optical transistor or optical memory element, to its phase transition interpretation. The theory is divided into three parts. The first is a simple discussion that covers most of the basic experimental effects and concepts of practical importance. The second part applies to atomic system where a semiclassical as well as a quantum-mechanical approach is possible. The third one discusses the mechanisms compatible with large nonlinearities observed in InSb and GaAs as semiconductors constitute the most promising materials for applications. Current experimental progress in all-optical and hybrid devices is also discussed and scaling example is presented to indicate the possibilities in high-speed all-optical signal processing.
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.