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IEEE Journal of Quantum Electronics

Optical bistability based on self-focusing: An approximate analysis

John E. Bjorkholm, P. W. E. Smith, W. Tomlinson

Published Dec 1, 1982• 26 citations
Publisher

Abstract

Calculations are presented which describe approximately the behavior of optically bistable devices based on the self-focusing of light. A simple heuristic calculation and a more complicated calculation which incorporates saturation of the material nonlinearity are presented. Both give a good qualitative description of situations in which a single hysteresis loop is observed. More complicated types of behavior, some of which have been observed, are predicted by the calculations which incorporate saturation. The results provide useful guides for the design of such devices.

DOI
10.1109/jqe.1982.1071480

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Calculations are presented which describe approximately the behavior of optically bistable devices based on the self-focusing of light. A simple heuristic calculation and a more complicated calculation which incorporates saturation of the material nonlinearity are presented. Both give a good qualitative description of situations in which a single hysteresis loop is observed. More complicated types of behavior, some of which have been observed, are predicted by the calculations which incorporate saturation. The results provide useful guides for the design of such devices.
Two years ago, the first proposal and demonstration of self-focusing optical bistability was published.1 In this paper it was shown that a self-focused beam in a nonlinear medium would exhibit hysteresis if the beam were reflected back on itself. The effect was demonstrated using a dye laser beam and Na vapor as the nonlinear medium. The optical hysteresis observed is in good qualitative agreement with a recently - published analysis of this system.2 By taking account of the saturation of the nonlinearity, more complex behavior has been predicted.2 This behavior is due to oscillations of the spot size as the self-focused beam propagates through the nonlinear medium. In this paper we report on our experimental studies of optical multistability due to these spot size oscillations.
We experimentally demonstrate a fundamentally new type of intrinsic optical bistability that requires no resonant optical cavity. Operation is based on mutual self-focusing of counterpropagating laser beams in a nonlinear medium. We propose and experimentally demonstrate a fundamentally new type of optical bistability. 1 The operation of this new class of devices is based on self-focusing of light; the feedback required for bistability is provided by an apertured retroreflector. These devices exhibit intrinsic bistability (the feedback is optical) and are related to nonlinear waveguide devices proposed earlier. 2 Self-focusing occurs when a light beam having a nonuniform spatial profile (such as a Gaussian laser beam) and sufficient intensity propagates through a nonlinear medium having an intensity-dependent index of refraction. 3 Previously proposed devices that exhibited
We propose and report the first experimental demonstration of a new type of active optical bistable device composed of an optical cavity and a lasing medium with a pumping source of either optical or nonopticai means. The basic principle underlying the operation of the optical bistable laser (OBL) is based on the stable-unstable cavity configuration transition of an active optical resonator. Generally speaking, a laser system showing both pump- and laser-induced tensing (focusing or defocusing) effects may display such a hysteresis loop in its input-output characteristics. Optical bistability (OB) based on self-focusing of light in a medium having a nonlinear refractive index has recently been shown experimentally.1
When the output parameter of an optical device could be a multivalued function of the input parameter, this device can be working in an optical bistable status. The most typical optical bistable device is a Fabry–Perot cavity containing a nonlinear optical medium, the refractive index of which depends on the light intensity. Upon the action of an intense input optical beam, the transmitted (or reflected) intensity of this device may exhibit a nonlinear response to the incident light intensity variation and, especially under appropriate working conditions, the characteristic output/input curve may manifest a single (or multiple) hysteresis loop(s). Such type of optical bistable device can be used as an optical differential amplifier, optical switch, optical limiter, optical clipper, optical discriminator, or an optical memory element, depending on the chosen nonlinear medium and operation conditions.
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.