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Chinese Physics Letters

Periodic and chaotic behaviors in optical bistability

Lixue Chen, Li Chun-Fei, Jing Hong

Published Nov 1, 1984• 3 citations
Publisher

Abstract

The periodic and chaotic behaviors for both long and short delay time are demonstrated successfully using a hybrid OBD. The degree of stability S is introduced into the dynamic equations of optical bistability with a delayed feedback. The instability threshold is S = 2 for long delay time and S = 1 + π/2 Q for short delay time.
DOI
10.1088/0256-307x/1/2/011

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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.