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Analysis of ring cavity optically bistable systems with two partially reflecting mirrors of unequal transmissivity

Liguo Luo, Chen Jishu

Published Jan 1, 1988• 0 citations
OpenAlex

Abstract

The general ring cavity optically bistable systems with two partially reflecting mirrors of unequal transmissivity are analysed. In the mean field approximation, the steady state equation is given, and the linear stability analysis of the steady states is performed. It is found that when the ratio of transmissivity T_1/T_2 varies, the bistable loop changes its size and even the systematic behavior varies from the bistability mode into the amplification mode. It is pointed out that in the mean field approximation there are many systems with (?)≡CT_1/L_v(?)1 and also many systems with (?)1. The self-pulsing instability is observed in the latter systems.

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Acta Physica Sinica•Jan 1, 1988•0 citations
The general ring cavity optically bistable systems with two partially reflecting mirrors of unequal transmissivity are analysed. In the mean field approximation, the steady state equation is given, and the linear stability analysis of the steady states is performed. It is found that when the ratio of transmissivity T_1/T_2 varies, the bistable loop changes its size and even the systematic behavior varies from the bistability mode into the amplification mode.
It is pointed out that in the mean field approximation there are many systems with (?)≡CT_1/L_v(?)1 and also many systems with (?)1. The self-pulsing instability is observed in the latter systems.
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 review and extend the theory of instabilities in absorptive optical bistability for ring cavities containing homogeneously broadened two-level media. The instabilities occur in the high-transmission branch and result in either a precipitation to the low-transmission branch or in pulsed multimode operation. Two numerical approaches are used to predict operation away from the simple mean-field limit. First, an iterative method is used to solve the general field eigenvalue equation for cavity modes with frequencies displaced from the input frequency. This work shows that the instability region decreases in size as the mirror transmission increases. These calculations are confirmed by the second numerical technique, consisting of direct integrations of the coupled Maxwell-Bloch equations. This second approach also provides time histories of the instability evolutions, and divides the instability range into a precipitation regime and a self-pulsing regime. The results are discussed in terms of first- and second-order phase transitions, and agree with the analytical results obtained within the dressed-mode description of optical bistability. They show that when the incident field is adiabatically decreased along the high-transmission branch, the spiking behavior always appears abruptly. By further decreasing the incident intensity, the self-pulsing disappears either continuously if the system remains in the high-transmission branch, or discontinuously if the system precipitates to the low-transmission branch. Connection is made with induced probe gain known in the saturation spectroscopy of absorbers (uninverted media), in which population pulsations transfer energy from a saturating wave to the probe waves. The very close relationship with multimode operation in homogeneously broadened unidirectional ring lasers is also established.
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.