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Topical Meeting on Optical Bistability (OB)

Criteria for Polarized Optical Bistability

A. Korpel, A.W. Lohmann

Published Jan 1, 1985• 0 citations
Publisher

Abstract

We consider the usual ring cavity with a nonlinear medium of which the response time is much longer than the period of the light frequency. It is assumed that two polarization modes affect this medium incoherently, i.e. on an additive power basis. We will show by heuristic physical reasoning, based partly on graphical construction, that a sufficient condition for jump type instabilities is that the sum of the inverse relative differential gains for the two modes not exceed unity. We will then briefly sketch how the same result can be obtained from a formal mathematical stability analysis.

DOI
10.1364/obi.1985.md23

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We consider the usual ring cavity with a nonlinear medium of which the response time is much longer than the period of the light frequency. It is assumed that two polarization modes affect this medium incoherently, i.e. on an additive power basis. We will show by heuristic physical reasoning, based partly on graphical construction, that a sufficient condition for jump type instabilities is that the sum of the inverse relative differential gains for the two modes not exceed unity. We will then briefly sketch how the same result can be obtained from a formal mathematical stability analysis.
A ring cavity is considered containing an optical medium of current practical interest, i.e., one of which the response time is much longer than the period of the light carrier wave. It is assumed that two orthogonal polarization modes are present simultaneously and that they affect this medium incoherently, i.e., on an additive power basis. It is further assumed that all other parameters for the two modes are the same but for the detuning of the cavity. Using a phenomenological model, we show, both from a heuristically physical and a formally mathematical point of view, that a sufficient condition for jump-type instabilities is that the sum of the inverse relative differential gains for the two orthogonal modes not exceed unity.
Using a simple model of a ring cavity comprising a cubically nonlinear medium, we analyze dispersive optical bistability in the presence of more than one spectral component. We show the phenomenon of so-called competition for resonance. In addition to presenting cavity characteristics for the cases of two and three different frequencies, we also discuss the general method for finding steady-state solutions and checking their stability. A simple and efficient algorithm, based on a relaxation method, is devised to find steady-state solutions satisfying appropriate boundary conditions. The relaxation dynamics is physically related to a finite response time of the medium.
The transmission characteristics of a Fabry-Perot cavity containing a resonant absorber are described analytically and graphically for internal fields of arbitrary intensity. The multimode instability considered by Bonifacio and Lugiato [Opt. Commun. 19 , 72 (1976)] for the unidirectional ring laser is treated for the standing-wave cavity. In particular, an instability may exist when the medium is located at one of the ends of the cavity, but not if the medium fills the cavity. The results are explained in terms of induced side-mode gain and spatial hole burning.