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Applied Physics Letters

Theory of bistability in nonlinear distributed feedback structures

Herbert G. Winful, John H. Marburger, E. Garmire

Published Sep 1, 1979• 494 citations
Publisher

Abstract

We show that optical bistability can occur in a distributed feedback structure with an intensity-dependent refractive index. Analytical expressions for the transmissivity are obtained and a comparison with Fabry-Perot-type devices is presented.
DOI
10.1063/1.91131

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In order to study optical bistability in a non-linear distributed feedback structure (NLDFB), we have generalized previous work. A mono-mode rectangular waveguide is chosen as the basic configuration for the device, although other guides could be considered. The grating, providing the passive feedback mechanism, has a geometry that can be arbitrarily chosen. Linear absorption is taken into account and the non-linearity is taken to be of the Kerr type. The effect of these three perturbations is treated using the Coupled Mode Theory and the Slowly Varying Envelope Approximation, including the radiation modes. Expressions for the coupling constants due to the three fundamental perturbations are derived and we show that new terms arise due to the interplay between the latter. Our model shows that an extra term, causing a shift of the Braggfrequency occurs in the equations. The analytical expressions are integrated numerically with the proper boundary conditions. Overall reflection and transmission properties of the device are displayed as a function of the intensity, the period of the grating, its length and several other device parameters.
It is shown that, when two coherent waves are obliquely incident to a one-dimensional nonlinear optical superlattice containing Kerr-form dielectric nonlinearity, an incident-dependent two-dimensional nonlinear optical superlattice can be constructed. This structure can be bistable. There exist two types of optical bistable mechanism, i.e., the index-modulation mechanism and distributed feedback mechanism. Owing to the index-modulation mechanism, the threshold for the bistability is lower than that of a more traditional one-dimensional distributed feedback structure.