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Journal of Modern Optics

Surface Effects in Optically Bistable and Transphasor Devices

W. J. Firth, Ian Galbraith

Published Jan 1, 1987• 5 citations
Publisher

Abstract

We present an analysis of the effect of surface recombination on the behaviour of optically bistable and transphasor devices. We derive analytic expressions for the longitudinal carrier profiles and the input/output intensity characteristics for a plane wave input. We also examine the frequency response of such devices and find qualitative agreement with experimental results. Finally, we present preliminary calculations modelling bistable devices including both longitudinal and transverse carrier diffusion, and surface recombination.

DOI
10.1080/09500348714550201

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We present an analysis of the effect of surface recombination on the behaviour of optically bistable and transphasor devices. We derive analytic expressions for the longitudinal carrier profiles and the input/output intensity characteristics for a plane wave input. We also examine the frequency response of such devices and find qualitative agreement with experimental results. Finally, we present preliminary calculations modelling bistable devices including both longitudinal and transverse carrier diffusion, and surface recombination.
Abstract : The interaction of a light beam with matter has varying degrees of dependence on the transverse profile of the beam. Two topics are considered here. The first topic, superfluorescence, involves the coherent emission generated by an initially inverted two-level medium. Calculations in the past have included either quantum fluctuations in the initial conditions or transverse effects, but never both. The calculations presented here include both transverse effects and quantum fluctuations. The results of the theoretical calculations are in good agreement with previous experimental results, both quantitatively in terms of time delay averages and distributions and also qualitatively in terms of pulse shapes. The second topic considered, optical bistability, involves devices which exhibit two stable output light intensities (a high and a low branch) over a limited range of input light intensities. Simulations performed here show the effect of diffraction, measured in terms of the Fresnel number, on how much of the device becomes bistable. It was found that for small Fresnel number cases, the entire device become bistable. For high Fresnel number cases, only part of the device becomes bistable while the rest of the device remains low transmitting. The results of an experiment performed are consistent with the simulations. (Author)
Optically bistable devices may be physically pixelated, and this may reduce cross talk or power requirements. When the bistability is of electronic origin, the rate of recombination of carriers at the surface is of great importance. We show how the surface recombination affects the speed of the element, first for a one-dimensional model and then for a cylindrical rod pixel with recombination at the curved surface. In some cases pixelated and unpixelated elements operate at the same speed, which indicates that the surface recombination in the former is equivalent to the diffusive loss from the latter.
Abstract For reasons of speed and economy, applications of optical bistability are likely to concentrate on solid-state devices of small volume. In this paper we discuss the modelling and optimization of such devices. We report calculations of surface reflectivity optimization in the presence of absorption, and show that optical bistability in reflection offers significant advantages over transmission. Small transverse dimensions, i.e. dense packing, are limited by cross-talk between neighbouring devices. We show that diffraction and diffusion give rise to qualitatively similar effects
Transverse beam-profile variations are investigated for a system which shows cavityless optical bistability due to increasing absorption. Coupled transport equations for the light field and the excitation density are derived and solved numerically for the case of an optically thin sample, where longitudinal density variations can be neglected and where diffusion of the excitation is the dominant transverse coupling mechanism. Assuming a Gaussian input beam, the increasing absorption is shown to cause substantial profile modifications when the medium undergoes the transition from low to high absorption. The formation of spatial ring structures is predicted and it is shown that transverse carrier diffusion plays an important role in determining both the steady-state and the temporal response of the system.
Of the Lorenz-type instabilities expected in optical systems, the single-mode instability in optical bistability has been the subject of detailed theoretical and experimental work by our groups. A treatment employing the plane-wave and mean-field limits of the Maxwell-Bloch equations predicts a rich variety of higher-order bifurcations including period doublings and intermittency.1 An extension of this work to include the transverse dependence of the intracavity field reveals no significant qualitative differences between the plane-wave theory and the Gaussian beam theory as regards the stability boundaries obtained from a linearized analysis.2 The instability persists in the presence of a Gaussian transverse profile and the boundaries are not radically modified compared with those obtained from the plane-wave theory. However, numerical integration of the Maxwell-Bloch equations in the single transverse mode approximation does not show the wealth of higher-order dynamic states present in the plane-wave case. An experimental investigation of optical bistability for two-level atoms in a single transverse, single longitudinal mode cavity exhibits limit cycle oscillation with stability boundaries that agree well with the boundaries obtained from the work in Ref. 2. However, for the range of values C < 300, |Δ| < 5, |θ| < 50, X ~ 102, the experimental results do not show the diversity of higher dynamic states expected from the plane-wave theory, in agreement with our numerical results. In addition the measurements support the existence of a single transverse mode oscillation. The sum of our theoretical and experimental work provides a quantitative statement for the role of the transverse effects in optical instabilities.