UC San Diego

The efficiency of nonlinear processes are limited by two effects: the small absolute scale of the nonlinear coefficients and the phase-mismatch effect. Micrometer scale structures with designed physical parameters offer a means to compensate for these limitations. This dissertation examines several types of structures that can provide more efficiency for a nonlinear processes than the same processes carried out in bulk crystal. Many of the structures use resonance to build the internal electric fields, and therefore increase the nonlinear response. Since numerous reflected waves exist within a resonant cavity, simple analysis methods for nonlinear processes do not apply. The reflected beams within the cavity interfere with each other as well as interact with the nonlinearity in the medium. No method of analysis for nonlinear processes in a resonator offered the accuracy and general applicability needed for these designs, so a new method is presented here. The new method is general and flexible, so that effects such as loss, gain, multiple nonlinear processes, and multiple cavities can be included in the modeling. The resulting field solution satisfies all of the imposed conditions and modeled effects, and is therefore as accurate as the modeling equations. This method is then used to examine complicated structures that could not be accurately characterized before. Included are multi-cavity bistable devices and microcavities exhibiting modulation instability