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Physical Review A

Guide to fabricating bistable-soliton-supporting media

Richard H. Enns, Darran E. Edmundson

Published May 1, 1993• 24 citations
Publisher

Abstract

A theoretical guide to fabricating materials which could support bistable bright optical solitons in the sense of Kaplan's definition is presented. The approach is to build up the requisite nonlinearity by combining different media which are known to display saturable Kerr behavior. Conditions on the Kerr coefficients and saturation intensities for bistability to occur are derived.

DOI
10.1103/physreva.47.4524

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A theoretical guide to fabricating materials which could support bistable bright optical solitons in the sense of Kaplan's definition is presented. The approach is to build up the requisite nonlinearity by combining different media which are known to display saturable Kerr behavior. Conditions on the Kerr coefficients and saturation intensities for bistability to occur are derived.
In this complement we discuss several examples of optical phenomena in media where the refractive index depends nonlinearly on the intensity , known as optical Kerr media. This nonlinear effect exists in all materials, even isotropic ones, like glass or fused silica, but it is particularly marked in certain physical systems to be exemplified in Section 7B.1. After investigating the propagation of light through such media in Section 7B.2, we shall discuss three applications of the optical Kerr effect (which can be studied in any order). We begin by describing a bistable optical system , when this nonlinear medium is inserted in a Fabry–Perot cavity (Section 7B.3). We then study phase conjugate mirrors and examine their potential applications in adaptive optics (Section 7B.4). Finally, we discuss certain effects occurring during the propagation of an isolated wave, bounded either transversely or temporally, in a Kerr medium, and describe self-focusing effects (Section 7B.5) and self-phase-modulation effects (Section 7B.6). In particular, we shall show that nonlinear effects and dispersion effects can compensate to produce stable structures known as solitons , which maintain their shape during propagation. Examples of third-order nonlinearities Nonlinear response of two-level atoms We begin by studying a simple case of a nonlinear interaction, namely a two-level quantum system under the effects of a plane wave.
Calculations are presented which describe approximately the behavior of optically bistable devices based on the self-focusing of light. A simple heuristic calculation and a more complicated calculation which incorporates saturation of the material nonlinearity are presented. Both give a good qualitative description of situations in which a single hysteresis loop is observed. More complicated types of behavior, some of which have been observed, are predicted by the calculations which incorporate saturation. The results provide useful guides for the design of such devices.
The calculus of variations is applied to electromagnetic fields in a layered nonlinear structure supporting a guided wave. The system also includes a phase-conjugate mirror (PCM). By introducing a variational dimension and using a collection of plane waves as a trial function, we approximate the exact solution of the nonlinear Kerr–Maxwell equation. The formalism is new, and it involves the nonlinear interference of multiple plane waves. A simple analytical expression for the nonlinear field in the presence of the PCM is derived, and the fact that the scattered intensities may become bistable when the angle of incidence is varied is demonstrated. In particular, our theory predicts the angular bistability in the backscattering direction, where the effect of the guided waves is subtle. Our numerical results are also in good agreement with other theoretical approaches and with the experimental data.