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Journal of the Optical Society of America B

Dynamics of optical bistability: a simple model

Denis L. Weaire, M. Al-Hourani

Published Jun 1, 1990• 4 citations
Publisher

Abstract

Various computational results of relevance to the dynamics of optical bistability are presented on the basis of an idealized model in which narrow input beams, optically bistable by virtue of a nonlinear refractive index, interact through diffusion. These results include the determination of regimes of stability for various configurations and the outcome of a study of switching waves.

DOI
10.1364/josab.7.001066

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Various computational results of relevance to the dynamics of optical bistability are presented on the basis of an idealized model in which narrow input beams, optically bistable by virtue of a nonlinear refractive index, interact through diffusion. These results include the determination of regimes of stability for various configurations and the outcome of a study of switching waves.
The salient question which arises when light is coupled via a grating or a prism into a waveguide exhibiting an intensity-dependent refractive index is whether switching occurs with or without bistability under appropriate detuning conditions. There are two prevailing theories. In the first1, a plane wave input is assumed leading to a uniform optically induced index change in the coupling region. In the second2, a finite width incident beam is assumed and the growth of the guided field under the coupler leads to an index change proportional to the local guided wave intensity. The first approach leads to optical bistability under certain detuning conditions, whereas the second results in switching only. Although it is known that plane wave analyses are inadequate when dealing with linear-nonlinear interfaces, bistability has been observed experimentally with nonlinear prism couplers3. Fundamentally the finite beam theoretical approaches are unable to predict bistability because no longitudinal feedback is included. Recently we showed that when non-locality is introduced into the optically induced refractive index change, longitudinal feedback occurs and bistability is predicted for the growing mode case4. However, the model used for the non-locality was artificial and resulted only in qualitative predictions. In this paper the nonlocality is modelled by the same equation used to describe heat transfer and carrier diffusion, leading to a quantitative estimate of the minimum diffusion length required for bistability.
In a recent paper1 I formulated a method for calculating propagation through nonlinear media for a number of nonlinear optical phenomena. This method does not use the SVEA and can therefore solve nonlinear propagation problems when refraction and reflection at the boundary interfaces are important. Here, I report the first calculation using this exact (albeit numerical) method. For this first test of the utility of the method, I have chosen to study optical bistability in a thin film whose index of refraction is intensity dependent.
Monolithic bistable microcavities with a GaAs/Al0.3Ga0.7As multiple quantum well active layer and AlAs/Al0.1Ga0.9As Bragg reflectors have been fabricated by metalorganic vapor phase epitaxy. The design of the whole structure is such that a good cavity finesse and a high contrast in the reflective mode are simultaneously obtained. This results in a bistability power threshold of less than 3 mW at 838 nm and a contrast ratio as high as 30:1. A new method is proposed, which allows to measure the nonlinear refractive index in a quasi-continuous regime, and in the operating conditions for bistability. The nonlinear index is shown to saturate at higher power, which evidences the need of a good cavity finesse for such bistable devices. Memory effect is then demonstrated: the sample can stay in either of its two stable states for more than 1 ms without spontaneously switching, and for input pulses as short as 60 ns. Finally we describe two-beam experiments with a new experimental configuration, also in reflection, which allows to mix the two input beams and extract the output beam with an ideal 100% efficiency.