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Philosophical Transactions of the Royal Society of London Series A Mathematical and Physical Sciences

Diffusion, diffraction and reflection in semiconductor o.b. devices

W. J. Firth, E. Abraham, Ernest Marshall Wright, Ian Galbraith, Brian S. Wherrett

Published Dec 18, 1984• 21 citations
Publisher

Abstract

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

DOI
10.1098/rsta.1984.0110

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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
For reasons of speed and economy, applications of dispersive optical bistability are likely to concentrate on solid-state devices of small volume. In this paper we will discuss the modelling and optimisation of such devices, particularly in relation to possible pixel size and spatial resolution. Diffusion (1,2), rather than diffraction (3), is the dominant transverse coupling mechanism in the two current solid-state systems (InSb etalon (4) and ZnSe-spaced interference filter (5)), capable of cw hold and optical address, but we will argue that in an optimised device diffraction and diffusion will be equally important.
There is an increasing interest in all-epitaxial Fabry-Perot etalons for optical bistability1,2 and optical logic gates.3 To model these devices theoretically, the wave equation, carrier diffusion equation, and heat conduction equation must be solved self-consistently for the layered structure. To investigate the effects of small spot sizes, the wave equation must include diffraction, whereas for the heat conduction equation both longitudinal (perpendicular to the layers) as well as transverse (parallel to the layers) heat conduction must be taken into account.
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.
Detailed results are presented on optical bistability (OB) and two-beam optical transistor (transphasor) action in simple, one-element Fabry-Perot devices, with the semiconductor InSb using a CW CO laser near the bandgap region, and OB for semiconductors in general is discussed. OB and multistability are seen in transmission and reflection at 5 K. At 77 K,n_{2} \simeq 3 \times 10^{-3}cm2/W [corresponding to an effective\chi^{(3)} \sim 1ESU] is measured and OB is observed at ∼8 mW. Transphasor action at 5 K is presented and the influence of degenerate four-wave mixing is discussed. The basic physics of the microscopic mechanism for n2(bandgap-resonant saturation) is summarized and a simplified, generalized model is derived. This model and arguments on cavity optimization are used to predict order of magnitude limits to switching power, energy, and speed, both in InSb and other semiconductors, even in the absence of excitonic enhancement.