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Physical Review A

Stability analysis for an optical bistable dye system

Shangqing Gong, Shao-hua Pan, Guo-Zhen Yang

Published Mar 1, 1993• 2 citations
Publisher

Abstract

A different set of the Maxwell-Bloch equations describing optical bistability in a dye ring cavity has been derived. A complete linear stability analysis including propagation effects is given. The corresponding numerical simulations show that the bistable regions are functions of both the frequency detuning and the band-structure parameters such as the bandwidth and the distribution of the dipole moments.

DOI
10.1103/physreva.47.2205

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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.
We study a single-mode laser system, whose active medium consists of molecules with a large difference between excited and ground electrical permanent-dipole moments. In this case, the Maxwell-Bloch equations are further coupled by nonlinear terms involving the ratio between this difference between the dipoles and the transition dipole moment. It is found that these new terms lead to multiple stationary solutions. From the linear stability analysis, we demonstrate the bistable (or multistable) character of the lasing solutions.
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.