Optical bistability is a phenomenon that arises in the transmission of light by an optical cavity filled with a medium which presents saturable absorption or nonlinear dispersion. From the theoretical viewpoint, optical bistability is a remarkable example of cooperative behaviour in an open system driven far from thermal equilibrium. From the practical viewpoint, optical bistability offers the possibility of realizing memory elements that may perhaps be used to construct an optical computer. We illustrate the basic physical principles of optical bistability at steady state, and the main features of the transient behaviour. The role and the effects of fluctuations (noise) are described in general. Particular attention is devoted to the situations in which the output of the system is not stationary in time, but oscillatory (self-pulsing behaviour), so that the system works as a converter of continuous wave light into pulsed. It is shown that, according to the values of the external parameters, the oscillations can be either periodic in time or completely aperiodic (optical turbulence). The state of the art in the problem of optical bistability is briefly discussed.
Optical bistability is a phenomenon that arises in the transmission of light by an optical cavity filled with a medium which presents saturable absorption or nonlinear dispersion. From the theoretical viewpoint, optical bistability is a remarkable example of cooperative behaviour in an open system driven far from thermal equilibrium. From the practical viewpoint, optical bistability offers the possibility of realizing memory elements that may perhaps be used to construct an optical computer. We illustrate the basic physical principles of optical bistability at steady state, and the main features of the transient behaviour. The role and the effects of fluctuations (noise) are described in general. Particular attention is devoted to the situations in which the output of the system is not stationary in time, but oscillatory (self-pulsing behaviour), so that the system works as a converter of continuous wave light into pulsed. It is shown that, according to the values of the external parameters, the oscillations can be either periodic in time or completely aperiodic (optical turbulence). The state of the art in the problem of optical bistability is briefly 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.
Introduction Lasers are part of a large class of non-linear systems which covers a great deal of scientific domains, including physics, chemistry, biology, sociology, etc. All these non-linear systems have common properties and present universal features which become more and more extensive as new studies are performed. In recent years, the interest in these non-linear systems has considerably increased. In particular, it is now well established that the role of fluctuations in non-equilibrium systems is far more relevant than in systems at thermodynamical equilibrium, and the study of their influence on stationary and transient states has become very important. Among the different aspects presented by the non-linearity in lasers, two of them will be particularly studied here: (i) The first one is the optical bistability (OB). An optical system is bistable if it has two output states I for the same value of the excitation A over some range of excitation values (see Gibbs, 1985, for a recent review). A typical response curve of such a system is given in Figure 5.1. Here, the system is defined as bistable between A ↓ and A ↑ , where the effectively occupied state depends on the history of the input parameter (see the caption to Figure 5.1). If OB is a common phenomenon in different fields, the OB transient phenomena have far more general features.
Theoretical analysis is presented to search for the purely absorptive optical bistability in a Fabry-Perot cavity filled with a saturable absorber. A simple model of singlet absorption is used on numerically solving the relationships between the input and output light fields. The proposed model corresponds well to organic compounds considered as novel optical materials with third-order optical nonlinearities. The effects of saturable absorber parameters on the output light characteristics are studied and purely absorptive optical bistabilities are shown numerically to search for bistable behaviour. The simulated results are indications for promising applications in optical switches for all-optical communication networks.
Introduction Usage has reserved the expression optical bistability mostly for coherently driven passive systems. An atomic system is called passive when there is no population inversion. This is the case, for example, of a system at thermal equilibrium. On the contrary, the laser that we have described in Chapter 1 is a driven active system, because a population inversion is created. The laser equations we have studied so far describe an incoherently driven laser. However, nothing prevents driving a lasing cavity with a coherent field emitted by another laser. This is realized in a whole class of lasers that are used mainly as frequency converters. In optical bistability (OB), the driving field is usually a coherent field. Thus we have to account for two differences between the laser and the optically bistable system: (1) In OB, there is no inversion of population: 〈| A 2 |〉>〈| B 2 |〉, in the notation of Chapter 1. Hence, in the absence of interaction with a field, the population difference D relaxes toward a negative value. (2) The pumping is coherent, meaning that an external laser field is added to the cavity field. Using the single-mode equations (1.48)–(1.50), we have to change the sign of D and D a (which amounts to keeping D defined in (1.34) as it is but changing P into – P and A into – A ) and to add a source term in the equation for the complex field amplitude.
Optical bistability is a quantum optical realization of a first order phase transition far from equilibrium. A nonlinear optical material contained in an optical cavity driven resonantly by an external coherent optical field undergoes a first order phase transition to a new nonequilibrium stationary state of broken symmetry. Resonant and nonresonant nonlinear optical response of pi-electron excitations in conjugated electronic structure provides the nonlinearity essential to the onset of bistability. Electronic correlation effects in reduced dimensions are responsible for nonresonant nonlinear optical responses. Saturable absorption studies of glassy polymer films consisting of quasi-two dimensional conjugated disc-like structure of silicon naphthalocyanine demonstrate that on-resonance the system behaves as an optical Bloch system with an intensity dependent refractive index of 1 times 10sp−4 cmsp2/kW. Based on the results of these studies, electronic absorptive optical bistability is observed on a nanosecond time scale in a nonlinear Fabry-Perot interferometer employing the saturable absorbing silicon naphthalocyanine film as the nonlinear optical medium.
One of the most interesting and applicable effects of nonlinear optics is optical bistability. This phenomenon is exhibited by certain resonant optical structures where it is possible to have two stable steady transmission states for the device, depending on the history of the input. Such a bistable device may be useful for optical computing elements as a result of its memory characteristics. Optical bistability behaviour is usually observed by inserting a nonlinear matter inside a Fabry–Perot interferometer. But in this study, it was shown that this can be achieved without the application of any optical resonator. Two laser beams were used to interact with the photorefractive media (doped PMMA polymer) which resulted in the bistability of the intensity of transmitted wave. Feedback was provided by a periodic grating created in the photorefractive polymer PMMA.