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Physical Review A

Instability in injected-laser and optical-bistable systems

Guang Hu, Guojian Yang

Published Aug 1, 1988• 19 citations
Publisher

Abstract

An analytical function is derived which can serve as a criterion of the instability boundary of both optical-bistable (OB) systems and laser systems with an injected coherent signal (LIS). By means of the criterion, we analyze, in various asymptotic limits, the instability regions of OB and LIS in the parameter space. In both good- and bad-cavity conditions of LIS a full hysteresis loop between coexisting stable states is observed for the first time.

DOI
10.1103/physreva.38.1979

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An analytical function is derived which can serve as a criterion of the instability boundary of both optical-bistable (OB) systems and laser systems with an injected coherent signal (LIS). By means of the criterion, we analyze, in various asymptotic limits, the instability regions of OB and LIS in the parameter space. In both good- and bad-cavity conditions of LIS a full hysteresis loop between coexisting stable states is observed for the first time.
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 single-mode dynamical equation is obtained from the Maxwell equation with the slowly varying amplitude approximation and the boundary conditions of the cavity, here the mean field limir and the good quality cavity case have been used. This equation is useful in describing the dynamical behavior of intrinsic optical bistable systems and/or lasers with injected sig-nals for any kinds of materials including two-level atoms. Furthermore, according to the li--near stability analysis, a generalized instability criterion is derived.
A single-mode dynamical equation is obtained from the Maxwell equation with the slowly varying amplitude approximation and the boundary conditions of the cavity, here the mean field limir and the good quality cavity case have been used. This equation is useful in describing the dynamical behavior of intrinsic optical bistable systems and/or lasers with injected sig-nals for any kinds of materials including two-level atoms. Furthermore, according to the li-near stability analysis, a generalized instability criterion is derived.
Based on the instability criterion of semi-classical Maxwell -Bloch equations of single-mode optical systems, the global distribution of instability region is depicted in △-θ parameter space (△ detuning of the atoms, θ mistuning of the cavity). In the instability region predicted, various bifurcations and chaos are disclosed. We find that chaos may appear in both upper and lower branches of one bistable curve Moreover, a new time-dependent solution coexisting with the stable stationary solution is found.