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Proceedings of the Royal Society of London A Mathematical and Physical Sciences

Theory of nonlinear refraction near the band edge of a semiconductor

Brian S. Wherrett, N. A. Higgins

Published Jan 8, 1982• 76 citations
Publisher

Abstract

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.

DOI
10.1098/rspa.1982.0005

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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.
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.
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 The results of an experimental investigation ol nonlinearities and bistability at the band gap in InAs are presented. Bistability was observed in reflection at 3 mW with a HF laser by using the large nonlinearity at the band-gap resonance in InAs. The measured nonlinear refractive index is shown quantitatively to agree with the dynamic Burstein—Moss shift as the mechanism, as long as both the full Fermi-Dirac statistics and the effect of light holes are included in the calculation. In a separate study a theoretical analysis has investigated general conditions for intrinsic bistability without cavities. It is shown that bistability can result from a nonlinear constitutive relation. Specific calculations are presented for bistability due to nonlinear polarization.
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.
A detailed study of bandgap resonant optical nonlinearities in n-type InAs and their use in an optical bistable device is presented. The results of measurements of both nonlinear absorption and nonlinear refraction taken with an HF laser show good agreement with a band-filling model in which the contribution from the light-hole band and the effects of large initial free carrier densities are included. Evidence of the saturation of the nonlinear refraction through the carrier-density-dependent recombination rate is presented, and it is shown that this effect together with diffraction effects accounts for the critical power for bistability observed in the reflected signal from an InAs etalon at 77 K.