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Journal of the Optical Society of America B

Optical bistability and differential gain resulting from absorption increasing with excitation

David A. B. Miller

Published Dec 1, 1984• 106 citations
Publisher

Abstract

An extended theoretical discussion of a novel general method of obtaining optical bistability is given. The method uses absorption that increases as the material becomes more excited and requires no mirrors or other external feedback. Criteria for bistability and differential gain are derived for a simple case, and specific illustrative analytic results are given. Limiting relations are derived for the switching powers and the width of the bistable region. It is shown that this general class of bistability encompasses at least six previous independent and unrelated investigations of mirrorless bistability in specific physical systems. The common general requirements for this bistability are discussed together with its attributes.

DOI
10.1364/josab.1.000857

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Koch et al.1 have solved the transport equations for the light intensity and the excitation density for a system that exhibits increasing absorption2 optical bistability. Under pulse operation a kink in the excitation density is predicted, which moves discontinuously in the beam direction and causes a saw-tooth variation in the transmitted intensity. Herein is reported the first observation of these kinks which emphasize the local nature of increasing absorption optical bistabillty. Kinks illustrate well the intrinsic difference between increasing absorption optical bistability and optical bistability that depends on external feedback, where a longitudinal discontinuity cannot occur.

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An extended theoretical discussion of a novel general method of obtaining optical bistability is given. The method uses absorption that increases as the material becomes more excited and requires no mirrors or other external feedback. Criteria for bistability and differential gain are derived for a simple case, and specific illustrative analytic results are given. Limiting relations are derived for the switching powers and the width of the bistable region. It is shown that this general class of bistability encompasses at least six previous independent and unrelated investigations of mirrorless bistability in specific physical systems. The common general requirements for this bistability are discussed together with its attributes.
It is shown theoretically that optical bistability will exist in a material whose optical absorption is more than linearly proportional to the degree to which the material is excited. No cavity or external feedback is required. The underlying principle of this bistability appears to be a generalization of several previous independent discussions of mirrorless bistabilities in specific physical systems. This bistability and associated differential gain are demonstrated experimentally using a thermal nonlinearity in a GaAs/GaAlAs multiple-quantum-well semiconductor. Theory and experiment show good agreement.
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.
Abstract A new type of optical bistability is presented. Instead of a resonator the intrinsic feedback between the optical excitation of carriers and their recombination is used. Optical bistability appears, if the absorption coefficient increases with growing carrier density. Both propagation effects and carrier diffusion are considered. Analytical model calculations are carried out for an abrupt behaviour of the absorption coefficient. The results explain the hysteresis in the transmittivity of CdS, recently observed.
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.
Koch et al.1 have solved the transport equations for the light intensity and the excitation density for a system that exhibits increasing absorption2 optical bistability. Under pulse operation a kink in the excitation density is predicted, which moves discontinuously in the beam direction and causes a saw-tooth variation in the transmitted intensity. Herein is reported the first observation of these kinks which emphasize the local nature of increasing absorption optical bistabillty. Kinks illustrate well the intrinsic difference between increasing absorption optical bistability and optical bistability that depends on external feedback, where a longitudinal discontinuity cannot occur.