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

Application Of The Nonlinear Eikonal Treatment To The Design Of Optical Bistable Devices.

Meir Orenstein, Jacob Katriel, Shammai Speiser

Published Jan 8, 1987• 1 citation
Publisher

Abstract

A recently presented eikonal treatment of nonlinear resonators and coupled resonators is generalized to enable the treatment of absorptive as well as dispersive optical bistability. The behavior of molecular media, incorporated in various types of resonators is emphasized.
DOI
10.1117/12.936944

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A recently developed nonlinear complex eikonal approximation which was previously employed to the study of dispersively nonlinear resonators is applied to absorptively nonlinear resonator configurations. The nonlinear absorption is introduced phenomenologically, encompassing a large variety of intensity-dependent absorption mechanisms. Conditions for obtaining optical bistability are derived. Dynamically increasing absorption was not considered, and optical bistability in free propagation was not obtained.
We already discussed the bistable behavior of a Fabry Perot resonator filled with molecular media as well as the characteristics of a spatial light modulator (SLM) based on the nonlinearity induced by excited state absorption. In the present paper we present two practical configurations. First we analyze a cavity-less bistable element which removes some of the realization problems related to high finess cavity. In this configuration the nonlinear medium is located in one arm of an optical interferometer. The scheme provides the required amount of positive feedback by the bistable mechanism -- but without a cavity. We applied the nonlinear eikonal approximation, a method which takes care of the detailed propagation effects, and obtained conditions for bistability, as well as optimizing the design parameters such as the output mirror reflectivity, etc.
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.