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Acta Optica Sinica

A cusp catastrophe model of optical bistability

Li C

Published Jan 1, 1983• 0 citations
OpenAlex

Abstract

A simple and clear catastrophe theory model of optical bistability is proposed, which indicates the threshold conditions for the occurrence of optical bistability and the methods for the control of the bistable characteristics.

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A general theory of optical bistability for a homogeneously broadened two-level system in a Fabry-Perot interferometer is presented. Both absorptive and dispersive mechanisms are included, and in the mean-field approximation a cubic state equation is derived relating transmitted intensity to all physical parameters. From the perspective of catastrophe theory, this equation describes an elementary cusp catastrophe. We show that bistable switching may follow not only from sweeping the incident laser intensity, but also with continuous variation of atomic or cavity detuning, or atomic density, with the laser intensity fixed. For the case having incident intensity as the variable control, the domain of bistability is studied in some detail as a function of the remaining fixed parameters. Stability criteria are considered for the general case including both absorption and dispersion.
The behavior of the three-level single-mode laser in the presence of an applied field and a saturable absorber is revealed near the losing -threshold. It is shown by quantitatively calculating that nonlinearity of laser field and introduction of applied field cause the correspondence of steady states of the laser with the canonical cusp catastrophe manifold. In this paper the physical meaning of the cusp catastrophe manifold is explained in more detail. The quantitative condition for optical bistability generation is given.