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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Absorptive-Dispersive Bistability In Double-Ring Cavities

Rosario Martínez-Herrero, Pedro Martín Mejías, Eusebio Bernabéu

Published Jul 10, 1987• 0 citations
Publisher

Abstract

The behaviour of a double-ring optical bistable configuration in the mixed absorptive-dispersive case is presented. The exact parametric steady-state equation which expresses the output of the system in terms of the input amplitude is determined. New possibilities for hysteresis cycle control are described.
DOI
10.1117/12.937118

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A novel type of optical bistable configuration, namely the so-called double-ring (DR) device, is presented. The stationary solutions in the purely absorptive case for a homogeneously broadened atomic system are derived. In the mean-field limit it has been pointed out that use of a DR arrangement enables us to reduce both the length of the sample of the nonlinear medium and the response time of the device. Linear stability analyses have shown that the position and the length of the unstable regions of a given hysteresis cycle can be controlled, to a great extent, by means of the two new parameters of our DR scheme. Finally, it has been remarked that, in order to observe self-pulsing, the purely absorptive DR system may present a similar behavior to that offered in the dispersive single-ring case.
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.
We analyze the absorptive and hybrid absorptive–dispersive double-cavity optical bistability behavior in a four-level N-type atomic system driven by two optical fields circulating inside two independently unidirectional ring cavities and a trigger field outside the cavities. In this system, the two-photon absorption and cross Kerr nonlinearity play significant roles in the formation of bistability and can be controlled efficiently due to the quantum interference effect, and then the resulting nonlinear behavior exhibits different features from the two/three-level schemes. It is shown that the threshold values and hysteresis cycle width of the bistable curve can be manipulated via the adjustment of the system parameters. Meanwhile, we also obtain double-beam optical multistability. When adding positive and negative pulses to the cavity input, all-optical steady-state switching for the two cavity outputs can be achieved simultaneously. Therefore, the proposed scheme may have potential applications in all-optical communication and computing.
We study the semiclassical mean-field theory of single-mode dispersive optical bistability in the limit of a fully developed hysteresis cycle (i.e., in the limit of large values of the bistability parameter C) and when all decay rates have comparable magnitude. We locate (i) on the upper branch instabilities leading to time periodic regimes, (ii) on the lower branch instabilities leading to a switching before the limit point is reached. None of these instabilities are observed in the case of purely absorptive optical bistability.
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 study the semiclassical mean-field theory of absorptive optical bistability in the limit of a fully developed hysteresis cycle, i.e., in the limit of large values of the bistability parameter CCC. We show by multiple time-scale perturbation analysis that it is possible to describe the transition between the two stable branches by simple equations. Near the low-transmission branch, the behavior of the system is governed by an equation for the atomic population, whereas, near the high-transmission branch, it is an equation for the field amplitude which determines the long-time evolution of the system. We then present an analytic study, completed by numerical results whenever necessary, of the time-dependent response of the system when the input field is swept across the bistable region. We study the influence of the initial conditions, the sweeping velocity, and the ratio of the atomic relaxation times on the dynamical hysteresis as well as its relation with the stationary hysteresis.