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Journal of Applied Physics

Band-edge nonlinearities in direct-gap semiconductors and their application to optical bistability and optical computing

Stephan W. Koch, Nasser N. Peyghambarian, H. M. Gibbs

Published Jan 15, 1988• 66 citations
Publisher

Abstract

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.

DOI
10.1063/1.340098

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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.
Starting from a Hamiltonian which describes the interaction of the many-electron system of a crystal with the quantized light field, we derive nonlinear coupled equations of motion for the light-field amplitude, the electron-hole-pair amplitude, and the inversion. These equations yield the basis for the investigation of space-dependent nonlinear interaction effects between light and electrons in direct band-to-band transitions. With the aid of these equations we investigate the saturation behavior of direct band-to-band transitions for an incident monochromatic electromagnetic plane wave. We determine the nonlinear absorption coefficient and nonlinear refractive index. We compute the nonlinear transmissivity taking into account the boundary conditions at the end faces of the crystal and discuss the effect of optical bistability.
This dissertation studies the physics of room-temperature optical nonlinearities in GaAs and their application to the optical logic gates. The microscopic origins of the room-temperature optical nonlinearities in GaAs are investigated experimentally and theoretically. The data of nonlinear absorption measurement are analyzed in the framework of a semiconductor plasma theory in combination with excitation-dependent line broadening. The importance of the plasma screening of the continuum-state Coulomb enhancement and band filling are emphasized for GaAs at room temperature. Optical bistability and optical logic gating are direct consequences of the nonlinear refractive index changes in etalons. The nonlinear index changes are directly measured by a new technique of observing the Fabry-Perot transmission peak shift using the self-photoluminescence as a broad-band source. The validity of a Kramers-Kronig technique under quasi-steady state conditions is crosschecked by an independent measurement of Δn under identical pumping conditions. Thermal index changes are also directly measured to establish the criteria on the temperature stability condition that is needed for reliable operation of devices based on dispersive nonlinearities. Optical logic gates based on dispersive optical nonlinearities may be the critical components of an all-optical computer in the future. Five optical logic functions are demonstrated in a nonlinear GaAs/AlGaAs MQW etalon. Specially designed dielectric mirrors are used to observe low-energy (3-pJ) operation of optical logic gates. Parallel operation using as many as eight optical logic devices is achieved with Wollaston prisms. Toward practical devices, optical logic gating using diode lasers is demonstrated in a setup much smaller than the usual argon-laser pumped dye laser setup. The cycle time of optical logic devices is limited, not by the switch-on time, but by the switch-off time which depends on the carrier relaxation rather than the switch-on time. To reduce the carrier relaxation time windowless GaAs is employed to take advantage of the faster surface recombination of carriers at the GaAs/dielectric mirror interface compared to that at the GaAs/GaAlAs interface. The speed and effectiveness of the windowless GaAs are compared with those of the proton-bombarded GaAs as optical logic gates.
Abstract Detailed comparisons are made of the results of two approaches to the problem of nonlinear refraction at frequencies just below the band edge in semiconductors. The physical origin o f the nonlinear dispersion is taken to be direct saturation of independent, T2-broadened band states in the first model discussed. In the second model the refraction associated with a dynamic Burstein-Moss shift of the absorption edge is considered. Both models predict an extremely large nonlinearity, X(3) ≈ 1 e. s. u., of importance in the field of dispersive optical bistability and consistent with experimental observations of bistability, two-beam differential gain and four-wave mixing.
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.
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.