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Journal of Physics C Solid State Physics

Landau level non-linear refraction in semiconductors

Brian S. Wherrett, N A Higgins

Published Mar 20, 1982• 9 citations
Publisher

Abstract

Detailed comparisons are made of the results of two approaches to the problem of non-linear refraction at frequencies just below the band edge of a semiconductor. The magnetic field case discussed is shown to give potentially larger non-linearities than the zero-field situation. The physical origin of the non-linear dispersion is taken to be direct saturation of T 2 broadened band states in the first model. In the second the refraction associated with a dynamic Burstein-Moss shift of the absorption edge is considered. Both models predict an extremely large non-linearity, of importance in the field of dispersive optical bistability. The results are also consistent with experimental observations of non-linear Faraday rotation and interband saturation in InSb.

DOI
10.1088/0022-3719/15/8/020

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Detailed comparisons are made of the results of two approaches to the problem of non-linear refraction at frequencies just below the band edge of a semiconductor. The magnetic field case discussed is shown to give potentially larger non-linearities than the zero-field situation. The physical origin of the non-linear dispersion is taken to be direct saturation of T 2 broadened band states in the first model. In the second the refraction associated with a dynamic Burstein-Moss shift of the absorption edge is considered. Both models predict an extremely large non-linearity, of importance in the field of dispersive optical bistability. The results are also consistent with experimental observations of non-linear Faraday rotation and interband saturation in InSb.
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.
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.
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.