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Applied Optics

Criteria for optical bistability in ring cavities with two orthogonal modes of polarization

A. Korpel, Adolf W. Lohmann

Published Jul 15, 1986• 12 citations
Publisher

Abstract

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.

DOI
10.1364/ao.25.002253

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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.
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.
We analyze a simple model of dispersive optical bistability in a ring cavity filled with a Kerr medium in the presence of two and three (carrier and one sideband pair) different frequencies. The steady-state characteristics are shown and the condition for selective switching is studied. We show the phenomenon of the so-called competition for resonance between different frequencies. The characteristic phenomenon of locking of the output intensities is presented. The model of two frequencies may also be used to describe bistability in the presence of two different polarizations. For three frequencies our discussion is based on the rigorous propagation equations, which admit a real Hamiltonian description and are completely integrable. We also discuss a general numerical approach, based on a relaxation method, for finding steady-state solutions and checking their stability. The relaxation dynamics is physically related to a finite response time of the medium. The effect of this finite response time on the stability of the steady states and on the dynamics is also discussed.
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.
The instabilities of a nonlinear optical medium with induced absorption in a ring cavity are theoretically analyzed. Stable, bistable, and unstable stationary solutions are found for various values of incident intensity and detuning. The dynamic treatment yields, in the unstable regime, oscillations of the transmitted intensity in various modes for constant incident intensity. If the medium relaxation time is short compared with the round-trip time, oscillatory solutions are obtained, which show strong locking of the oscillation frequency to multiples of the inverse round-trip time. If the round-trip time is comparable with the medium relaxation time, numerical integrations yield periodic solutions with substructures because of the mismatch of the two characteristic times.
In a recent paper1, a quantum theory of multiwave interactions with a two-level medium is presented. In this paper we apply this theory to sidemode instabilities pertinent to cavity con figurations in optical bistability and ring lasers. We assume the cavity to oscillate on a single mode, and we evaluate the gain and spontaneous emission at other frequencies. Because of the saturating presence of the strong, laser mode, two symmetrically situated sidemodes can grow together, inducing populations pulsations that influence the other sidemode. The instability must therefore be treated as a double sidemode problem.