The behaviour of a F P resonator filled with a nonlinear medium and irradiated by a strong e.m. field nearly resonant with bo th one cavi ty mode and with the medium is bistable (optics1 bistability), the main characteristic feature being tha t the outgoing power can have two distinct values for a proper choice of the parameters defining the state of the entire system. I n view of the interest both from a fundamenta l point of view and from the potent ial applications r the field of integrated optics of bistable devices, a very intensive effort has been made to s tudy the various aspects of OB (1).
The behaviour of a F P resonator filled with a nonlinear medium and irradiated by a strong e.m. field nearly resonant with bo th one cavi ty mode and with the medium is bistable (optics1 bistability), the main characteristic feature being tha t the outgoing power can have two distinct values for a proper choice of the parameters defining the state of the entire system. I n view of the interest both from a fundamenta l point of view and from the potent ial applications r the field of integrated optics of bistable devices, a very intensive effort has been made to s tudy the various aspects of OB (1).
In the last chapter, we examined the effect of cubic nonlinearity on selfrefraction of an optical beam. We have also seen that the presence of a quadratic nonlinearity can also contribute to change in the profile of a Gaussian beam in a crystal. In this chapter we will see how the effect of nonlinearity, alongwith the proper feedback, can give rise to optical bistability and hysteresis. This is not unexpected as hysteresis and bistability are also observed in nonlinear electronic circuits with feedback, such as in the Schmitt trigger, as well as in hybrid optical devices, such as an acoustooptic device with feedback (Banerjee and Poon, 1991). In what follows, we will examine two different types of optically bistable devices based on optical nonlinearities. The first is a nonlinear ring resonator comprising a two-level gain medium as the nonlinear element. We will treat both absorptive and dispersive bistability. Absorptive bistability is the case when the incident optical frequency is close to or equal to the transition frequency of the atoms from one level to another. In this case, the absorption coefficient becomes a nonlinear function of the incident intensity. On the other hand, if the frequencies are far apart, the medium behaves like a Kerr-type material and the system exhibits what is called dispersive bistability. In this case the material can be modeled by an effective n2 or v (3), meaning that the refractive index becomes a nonlinear function of the optical intensity. The second configurationwewill examine is a linear-nonlinear interface. In this case, the interface provides the feedback due to refractive index mismatch. In fact, the reflection coefficient (as well as the transmission coefficient) is modified due to the nonlinearity, which, as we shall see later, is responsible for demonstrating optical switching and bistability.
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.
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.
Summary form only given. Optical bistability is basically a nonlinear response of the medium (here confined electrons in a QW) to an external oscillating field, in which there are three possible responses (two stable and one unstable). Which one the system chooses depends on the history of the adiabatically varying control parameters (usually electric field amplitude). The OB we consider is an intrinsic feature of the electron gas in the QW, and does not rely on the use of a Fabry-Perot resonator. Another feature of OB is that it is not a ubiquitous nonlinear response such as superharmonic generation; it can be observed only at some restricted values of the parameters. Furthermore the nonlinear response changes abruptly from one value of the output to the other. This effect can be measured by detecting the different transmitted intensities of the FIR field to the same input field. These features of OB make it a relevant choice for applications to optical switching and the realization of optical logic gates.
Abstract An optical bistable device can be useful not only for optical memory but also for optical sensing by using its binary signal process characteristics. In this case, if a nonlinear Faraday medium is used in the optical bistable device, some interesting features can be obtained as already shown by the present author. Those unique characteristics are that, by controlling the polarization direction by an external magnetic field, a multiple interference can also be controlled not only by the phase associated with an optical path variation but also the polarization direction. This paper describes a theoretical analysis of the fluctuation of transmission and reflection as a function of an absorption in a medium besides the incident intensity reduction and discusses the bistability characteristics and the threshold values against the parameters. It is shown that the control of the bistable function, the realization of a low threshold value, and the increase of a discontinuous power variation ratio (= optical intensity ratio between on and off in the binary signal process) at the threshold value are accomplished as the result of the introduction of the external magnetic field control method. Therefore, it can be concluded that a Faraday medium is very useful for an optical bistable device.