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Acta Physica Sinica

The generalized dynamic equation of optical bistability, and the laser and its stability analysis

Fa Ou, Yong Qiang Cai

Published Jul 1, 1989• 0 citations
OpenAlex

Abstract

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.

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Physical Review A•Jan 1, 1986•14 citations
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.
In the first section we discuss the stationary solutions for a laser with an injected signal, the active counterpart of the optical bistability analyzed in Chapter 11. Next, in Section 13.2 we consider another very interesting system, namely a laser with a saturable absorber, a free-running laser in which the optical cavity contains a passive medium in addition to the active medium. The single-mode model for this system can be constructed by combining the single-mode models for the free-running laser and for optical bistability. The discussion is then focussed on its stationary states. In Section 13.3 we return to the single-mode model for optical bistability and, by introducing an appropriate “cubic limit” on the parameters in play, we derive a cubic model for dispersive optical bistability with two-level atoms. The stationary equation for such a model formally coincides with that derived and discussed for a Kerr medium in Section 11.2. In the last section we start from the equations for a quadratic nonlinear medium in the degenerate configuration derived in Chapter 6 and combine them with the appropriate boundary conditions for the two field envelopes in play, assuming that the quadratic medium is contained in a ring cavity as happens in an optical parametric oscillator or in second-harmonic generation in a cavity. Next, by introducing the low-transmission limit and the single-mode limit we derive a two-mode model that describes the dynamics of a degenerate optical parametric oscillator or of second-harmonic generation in a cavity. Finally, for the case of a parametric oscillator we illustrate extensively the stationary solutions of the equations. A laser with an injected signal From a technical point of view, this system is interesting because of the possibility of stabilizing the frequency and the phase of separate lasers by taking advantage of the known affinity of nonlinear oscillators to lock onto a periodic forcing element. In 1972 Spencer and Lamb [125] predicted the possibility of bistable behavior in a laser with an injected signal before the surge of interest in optical bistability in the passive configuration.
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.
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.