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ANALYSIS OF THE GENERAL RING CAVITY BISTABLE SYSTEM IN THE DISPERSION AND CAVITY DETUNING CASE

Xiangsuo Fan

Published Jan 1, 1993• 0 citations
OpenAlex

Abstract

In this paper the steady state solutions of the general ring cavity bistable system in the dispersion and cavity detuning case are given, and the stationary properties of the system are analyzed. The difference between the ordinary ring cavity bistable system and the general ring cavity bistable system is pointed out in the pure absorption and resonance case.

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Physical Review A•Jul 1, 1992•3 citations
In this paper the steady state solutions of the general ring cavity bistable system in the dispersion and cavity detuning case are given, and the stationary properties of the system are analyzed. The difference between the ordinary ring cavity bistable system and the general ring cavity bistable system is pointed out in the pure absorption and resonance case.
The ring cavity optical bistable system with single output is presented and analyzed. The steady state equation in the purely absorptive and resonant condition is given. The steady state curves in the mean field limit all exhibit a reverse S shape, and the critical value of the bistable cooperative coefficient C is equal to 2. The central section of the reverse S-shaped steady state curve proves to be always unstable. Moreover, a part of the steady state curve on the right hand of the central section may also lose its stability.
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.
In Chapter 9 we discussed the case of a nonlinear cavity containing an active medium. In this framework, the outstanding phenomenon which arises is laser emission, and we calculated the stationary solutions for the ring laser. In this chapter, instead, we turn our attention to the passive nonlinear cavity and in this framework the outstanding phenomenon is optical bistability , i.e. the existence of two distinct stable stationary states that coexist for the same fixed values of the parameters in play. This phenomenon can arise also in the case of an active system contained in a cavity, as we have already noted in Section 9.1 and as we will discuss further in connection with the laser with injected signal, but it became popular from the studies of nonlinear passive optical cavities in the 1970s and 1980s. In contrast to the laser case, in the passive configuration we use an input coherent field, which is injected into the cavity. We discussed this case in Chapter 8 and derived a general equation for the transmission of the cavity (Eq. (8.23)), which we used for an empty cavity and for a linear cavity in Sections 8.4 and 8.5, respectively. In this chapter we will discuss the full nonlinear configuration. It is customary to identify two extreme cases of optical bistability called absorptive optical bistability and dispersive or refractive optical bistability . In both cases an essential ingredient to obtain the bistable behavior is the feedback action exerted by the mirrors of the cavity. In the purely absorptive configuration, in which there is exact resonance among the frequencies of the input field, of the atoms and of the cavity, the other essential ingredient is the saturable nonlinearity of the absorption. In the dispersive case, instead, the main feature is the nonlinearity of the refractive index. These two cases will be illustrated in Sections 11.1 and 11.2, respectively, both “exactly” and in the low-transmission limit.
Using a simple model of a ring cavity comprising a cubically nonlinear medium, we analyze dispersive optical bistability in the presence of more than one spectral component. We show the phenomenon of so-called competition for resonance. In addition to presenting cavity characteristics for the cases of two and three different frequencies, we also discuss the general method for finding steady-state solutions and checking their stability. A simple and efficient algorithm, based on a relaxation method, is devised to find steady-state solutions satisfying appropriate boundary conditions. The relaxation dynamics is physically related to a finite response time of the medium.