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Philosophical Transactions of the Royal Society of London Series A Mathematical and Physical Sciences

Dynamic effects in optical bistability

Paul Mandel, Thomas Erneux

Published Dec 18, 1984• 3 citations
Publisher

Abstract

Abstract In the first part we give a brief review of some theoretical problems that still hinder the practical use of bistable optical devices in logic circuits. In the second part we study the influence of a time-dependent control parameter on the solution of differential equations. We prove that even for small sweeping rates large delays can be expected, resulting in the dynamical stabilization of unstable solutions. Examples are given for dynamically induced optical bistability in a laser and dynamical stabilization in a laser with saturable absorber.

DOI
10.1098/rsta.1984.0108

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Abstract In the first part we give a brief review of some theoretical problems that still hinder the practical use of bistable optical devices in logic circuits. In the second part we study the influence of a time-dependent control parameter on the solution of differential equations. We prove that even for small sweeping rates large delays can be expected, resulting in the dynamical stabilization of unstable solutions. Examples are given for dynamically induced optical bistability in a laser and dynamical stabilization in a laser with saturable absorber.
Optical bistability in a CO2 infrared laser containing SF6 as a saturable intracavity absorber has been studied under dynamic conditions as a function of a time-dependent laser control parameter. The width of the optical bistability region, the fluctuations in the bistability switching values, and the dependence on the initial conditions have been investigated in this transient optical bistability. A numerical solution of the laser rate equations provides a good interpretation of the experimental results, but some experimental observations cannot be completely explained.
A simple mathematical model to describe the action of a saturable absorber in a laser cavity (LSA) was developed. The approach considered here takes in a phenomenological way into account the essential physical processes which makes it possible to determine the principal parameters in a LSA and their influences on the optical bistability. We will study theoretically optical bistability in a trimodale laser containing a saturable absorber in the case that the active medium and absorber show a homogeneous broadening. We determine the densities of photons as function of the pumping of the active medium and analyze the linear stability of the solutions obtained.
Introduction Lasers are part of a large class of non-linear systems which covers a great deal of scientific domains, including physics, chemistry, biology, sociology, etc. All these non-linear systems have common properties and present universal features which become more and more extensive as new studies are performed. In recent years, the interest in these non-linear systems has considerably increased. In particular, it is now well established that the role of fluctuations in non-equilibrium systems is far more relevant than in systems at thermodynamical equilibrium, and the study of their influence on stationary and transient states has become very important. Among the different aspects presented by the non-linearity in lasers, two of them will be particularly studied here: (i) The first one is the optical bistability (OB). An optical system is bistable if it has two output states I for the same value of the excitation A over some range of excitation values (see Gibbs, 1985, for a recent review). A typical response curve of such a system is given in Figure 5.1. Here, the system is defined as bistable between A ↓ and A ↑ , where the effectively occupied state depends on the history of the input parameter (see the caption to Figure 5.1). If OB is a common phenomenon in different fields, the OB transient phenomena have far more general features.