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Acta Physica Sinica

THE GENERALIZED DYNAMICAL EQUATION OF OPTICAL BISTABILITY AND LASER AND ITS STABILITY ANALYSIS

Fa Ou, Yong Qiang Cai, 华南工学院物理系

Published Jan 1, 1988• 0 citations
Publisher

Abstract

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.

DOI
10.7498/aps.37.330

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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.
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.
We analyze instabilities in mixed absorptive and dispersive optical bistability in the rate-equation approximation and the mean-field and good-cavity limits. Our starting point is a set of multimode equations derived from the Maxwell-Bloch equations for ring-cavity boundary conditions. We obtain analytic expressions for the instability conditions. In a plane-wave analysis, we find that a portion of the lower transmission branch can be unstable in addition to the upper-branch instability found in purely absorptive bistability. Also, a new disconnected region of instability can exist on the upper branch. Our analysis becomes particularly simple for equal and opposite cavity detunings and we explore this case in detail. We extend our treatment to include a Gaussian transverse intensity profile and show that the instabilities remain in the presence of Gaussian averaging. We also show that many of the results obtained in the rate-equation approximation hold when the atomic linewidth and atomic decay rate are of the same order.
In this paper, the general ring cavity model of passive and active optical systems is presented. In the mean field and the Gaussian one transverse mode approximations, the steady state and stability properties of the systems are analyzed for mixed absorptive and dispersive cases. It is found that when the transmissivity ratio M (equals T1/T2) varies, the bistable loop changes its size and even the systematic behavior varies from the bistability mode into the amplification mode, and the instability domain on the steady state curve varies obviously. The mode-pulling formula and bistable threshold with varying values of M are also discussed.