A pair of synthetic methods are presented for describing nonlinear optical phenomena in photonic devices of any size scale and with any degree of refractive-index contrast.;The first method is a general description of nonlinear phenomena in guided-wave devices. By retaining all of the cartesian components of the field implicit assumptions about device dimensions and refractive-index contrast are not made. The method is applied to the study of nonlinear optical phenomena in silicon-on-insulator (SOI) waveguides. Contributions are found to the nonlinear propagation parameters that do not appear in traditional descriptions of nonlinear fiber optics, and are found to become significant as a result of the high index contrast of the SOI material system when device dimensions enter the subwavelength regime. An experimental study of nonlinear polarization effects in SOI waveguides is presented and the theoretical model is used to explain them.;The second method is a general description of nonlinear phenomena in optical resonators. The method makes no assumptions about device dimensions, refractive-index contrast, or the specific cavity structure. It is applied to understanding two different phenomena in resonators and to designing two different devices based on these phenomena. The first phenomenon is the influence of a dynamic refractive-index change on the optical field in a resonator. The resulting frequency shift of the field is proposed as a possible mechanism for implementing a wavelength conversion device, and device design criteria and theoretical performance capabilities are presented. The second phenomenon is the influence of the cross-phase modulation interaction of two resonator modes that results from the Kerr effect. The resulting bistability is proposed as a possible mechanism for implementing a phase-switched optical memory device, and device design criteria and theoretical performance capabilities are presented.
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