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Journal of the Optical Society of America B

Optical bistability with the waveguide mode

Victor J. Montemayor, Robert T. Deck

Published Jun 1, 1985• 44 citations
Publisher

Abstract

We present an exact plane-wave treatment of the triple-boundary waveguide geometry for the study of optical bistability. It is found that the switching intensity required to observe the desired switching behavior is lower by at least a factor of 25 from that previously reported, thus making this geometry a prime candidate for experimental investigation. A comparison with the results of an approximate theory is also presented, showing that the approximate theory closely describes the behavior of the system as predicted by the exact theory.

DOI
10.1364/josab.2.001010

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We present an exact plane-wave treatment of the triple-boundary waveguide geometry for the study of optical bistability. It is found that the switching intensity required to observe the desired switching behavior is lower by at least a factor of 25 from that previously reported, thus making this geometry a prime candidate for experimental investigation. A comparison with the results of an approximate theory is also presented, showing that the approximate theory closely describes the behavior of the system as predicted by the exact theory.
We develop an approximate analytical theory for the reflection of a finite-width square-wave light beam at a nonlinear interface and make use of the results to assess the effect of the finiteness of the incident beam on the bistability of the signal reflected from a triple boundary interface under conditions for excitation of a waveguide mode. The nonlinearity of the interface is assumed to result from a substrate medium that has a Kerr-type quadratic dependence on the local electric-field amplitude. Our results indicate that the finiteness of the width of the incident beam substantially reduces the magnitude of the reflectance jump at the bistable switching point in comparison with that predicted by an exact plane-wave theory. Nevertheless, we conclude that a bistable reflectivity should still exist for the geometry that we consider at the switching intensity predicted by the plane-wave theory.
We have derived nonlinear coupled mode equations appropriate for periodic channel waveguides. These equations contain the three different nonlinear coefficients which were not taken into account in the previous analysis provided by Stegeman et al.. [IEEE. J. Quantum Electron. 18 (1982) 1610.] It has been shown that such nonlinear coefficients lower the switching power for optical bistability generated in the periodic channel waveguides. Dependence of the switching power on the waveguide size, waveguide structure and the grating parameters has been numerically obtained for ridge polydiacetylene (PDA-C4UC4) waveguides.
This paper gives a detailed description of the plane-wave Gaussian models of optical bistability and of the experimental investigations of the single-mode instability induced on a beam of sodium atoms in a cavity by an external driving field. Our goal is to provide a careful comparison of the theoretical and experimental results. We focus on the shape of the instability domain, the nature and behavior of the spontaneous output oscillations produced by the instability, and their frequency dependence on the control parameters. We carry out this comparison using both the plane-wave and Gaussian models. Our analysis shows that the latter is in good quantitative agreement with the experimental results. We investigate in detail the main assumption of the Gaussian model, namely, that the internal cavity field retains the same radial profile as the input field.