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IEEE Convention of Electrical and Electronics Engineers in Israel

Photorefractive Saturable Absorptive and Dispersive Optical Bistability

Shimon Weiss, B. Fischer

Published Aug 24, 2005• 0 citations
Publisher

Abstract

It is shown that photorefractive wave-mixing gives saturable gain, saturable absorption and Kerr-like nonlinear phase retardation. An analogy between photorefractive two-beam coupling and two-level atom system is then drawn. We investigate optical bistability in a ring cavity, utilizing these phenomena, and compare our results with classical absorptive and dispersive optical bistability.

DOI
10.1109/eeis.1989.720180

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Nonlinear Optics•Dec 4, 2003•0 citations
It is shown that photorefractive wave-mixing gives saturable gain, saturable absorption and Kerr-like nonlinear phase retardation. An analogy between photorefractive two-beam coupling and two-level atom system is then drawn. We investigate optical bistability in a ring cavity, utilizing these phenomena, and compare our results with classical absorptive and dispersive optical bistability.
It is known that two-wave coupling in photorefractive crystal may result in an intensity-dependent phase shift as well as energy transfer between the two waves without phase crosstalk. In a sense, this kind of phase shift is similar to the intensity-dependent refractive-index effects in Kerr media. Consequently, optical bistability can be established in an optical cavity with a photorefractive crystal. We formulate the model and get the expected bistable transmission with numerical simulations. Several cases, including that of the codirectional coupling and the contradirectional coupling, are considered. The effects of the photorefractive crystal’s distribution absorption and the spatial phase shift between the index grating and the light interference pattern in the crystal on the nonlinear transmission characteristics have also been studied. It is interesting to note that the output of the pumping wave is dependent on the cavity intensity and thus shows bistable behavior with respect to the cavity input as well.
We report the observation of bistability in a unidirectional ring resonator that employs photorefractive barium titanate for gain and also for saturated loss. One photorefractive crystal provides gain via two-beam coupling in a conventional unidirectional ring configuration.1 A second crystal is arranged to couple light out of the resonator using two-beam coupling, thereby producing loss. The orientations of the two crystals are chosen so that the magnitude of the small signal loss is greater than the magnitude of the small signal gain. Thus the oscillation in the ring cannot build up from noise since there is no net gain. However, the pump intensity for the gain medium is made larger than that for the loss medium. This means that the loss saturates at a lower signal level. Hence, at large intensities, gain can exceed net loss so oscillation can occur.
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 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.