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Topical Meeting on Optical Bistability (OB)

Instability Condition and Frequency-Locking in Hybrid Optical bistability

Lixue Chen, Chunfei Li, Jing Hong

Published Jan 1, 1985• 0 citations
Publisher

Abstract

In the linear instability analysis of the difference-differential equation which describes the dynamic behaviors of optical bistability with delayed feedback, introducing degree of stability S, which is defined as the ratio between relative variations of input and output intensities(1), we find that for long delay time instability condition is S≥2 and possible oscillation periods are approximately T ¯ = 2 T / ( 2 n + 1 ) but for short delay time the condition is S≥1 + πτ/2T and the periods are T ¯ = 4 T / ( 4 n + 1 ) . So the generation of instability for long delay time is easier than for short one, as shown in Fig.1.

DOI
10.1364/obi.1985.we6

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In the linear instability analysis of the difference-differential equation which describes the dynamic behaviors of optical bistability with delayed feedback, introducing degree of stability S, which is defined as the ratio between relative variations of input and output intensities(1), we find that for long delay time instability condition is S≥2 and possible oscillation periods are approximately T ¯ = 2 T / ( 2 n + 1 ) but for short delay time the condition is S≥1 + πτ/2T and the periods are T ¯ = 4 T / ( 4 n + 1 ) . So the generation of instability for long delay time is easier than for short one, as shown in Fig.1.
The degree of stability which describes intensity of feedback is introduced into the dynamic equations of optical bistability with delayed feedback. In addition to relative delay time, the degree of stability also affects the instability behaviors of the system, including threshold condition and oscillation modes of instability. The threshold condition of instability is (S≥2 for long delay and S≥1+π/2Q for short delay. The experiment by a hybrid OBD shows oscillation, bifurcation and chaos and verities theoretical analysis. The results show the close relation between Ikeda instability and stability in OBD. New basis to realize Ikeda instability in intrinsic OBD has been provided.
In a previous paper1an empirical and analytical study of instabilities in hybrid optical bistable systems was reported by us. At the end of that paper and in order to study the theory, a triangular voltage bias was added to the feedback, instead of the usual constant one. In that way the workline is displayed with the same slope, tg−1βIIN. Because the slope transmission ( dT dV ) was negative, the output, for a constant input, was periodic oscillations having a delay time larger the material response time. The nomenclature is explained in ref. 1.
A single-mode dynamic equation is obtained from the Maxwell equation with the slowly-varying amplitude approximation, and the boundary conditions of the cavity. Here the mean-field limit and the good-quality cavity case have been used. This equation is useful in describing the dynamic behavior of intrinsic optical bistable systems and/or lasers with injected signals for any kinds of materials, including two-level atoms. Furthermore, according to the linear stability analysis, a generalized instability criterion is derived.
A possible new way to drive hybrid optical devices based on a differential two-channel feedback configuration is presented. To verify the feasibility and characteristics of this approach, comparisons between two-channel and single-channel arrangements are reported. Several analogies and differences in operating conditions are also proved. From the point of view of application possibilities, the optical image obtained of an optical pulse exhibits time-discrimination characteristics, whereas in the single-channel case it shows discriminated intensity levels. This fact can be profitably used in parallel image processing systems.