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The Journal of Chemical Physics

Slowing down near the critical point in optically bistable ZnSe

Anita N. Wolff, John Ross, Robert H. Harding

Published Jan 15, 1992• 1 citation

Abstract

We measure relaxation rates near the critical point and the left hysteresis limit of an optically bistable system, a ZnSe interference filter. Our ZnSe system has an inhomogeneous geometry where a long, narrow illuminated region has boundaries at a temperature near and below that of the lower state. We determine the critical angle, the angle of incidence of light at which the hysteresis limits coalesce to form a critical point, and perturb the system by changing the input power beyond the critical point. For incidence angles equal to or slightly greater than the critical angle, we find that relaxation rates increase exponentially as the critical point is approached. The critical exponents for perturbations which increase the input power beyond the critical point are greater than those for perturbations which decrease the input power. In either case, the critical exponents increase as the angle of incidence approaches the critical angle. When the hysteresis region is large, we find slowing down near the left hysteresis limit in accordance with our calculations based on a one-dimensional inhomogeneous model.

DOI: 10.1063/1.462144

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We measure relaxation rates near the critical point and the left hysteresis limit of an optically bistable system, a ZnSe interference filter. Our ZnSe system has an inhomogeneous geometry where a long, narrow illuminated region has boundaries at a temperature near and below that of the lower state. We determine the critical angle, the angle of incidence of light at which the hysteresis limits coalesce to form a critical point, and perturb the system by changing the input power beyond the critical point. For incidence angles equal to or slightly greater than the critical angle, we find that relaxation rates increase exponentially as the critical point is approached. The critical exponents for perturbations which increase the input power beyond the critical point are greater than those for perturbations which decrease the input power. In either case, the critical exponents increase as the angle of incidence approaches the critical angle. When the hysteresis region is large, we find slowing down near the left hysteresis limit in accordance with our calculations based on a one-dimensional inhomogeneous model.

We study the semiclassical mean-field theory of absorptive optical bistability in the limit of a fully developed hysteresis cycle, i.e., in the limit of large values of the bistability parameter

C

. We show by multiple time-scale perturbation analysis that it is possible to describe the transition between the two stable branches by simple equations. Near the low-transmission branch, the behavior of the system is governed by an equation for the atomic population, whereas, near the high-transmission branch, it is an equation for the field amplitude which determines the long-time evolution of the system. We then present an analytic study, completed by numerical results whenever necessary, of the time-dependent response of the system when the input field is swept across the bistable region. We study the influence of the initial conditions, the sweeping velocity, and the ratio of the atomic relaxation times on the dynamical hysteresis as well as its relation with the stationary hysteresis.

The optical bistabilities of ZnSe and ZnS interference filters have been studied since 1977 when Karpushko and Sinitsyn reported the first experimental results. We see from papers published that (a) it is appropriate to study and compute optical bistabilities of interference filters by a Fabry-Perot resonator; (b) during the fabrication of bistable optical devices (BOD) the parameters such as incident angles, transmission power, and influence of peak position error on BOD, etc. were not studied in detail; (c) the authors could not resolve the problems of transmission peak height for large absorption materials such as ZnSe. We propose a new method of designing BODs of interference filters to study these problems precisely.