The search for new device concepts for applications in optical and millimeter-wave communications has recently led to the possibility of utilizing the nonlinear electronic properties of optical and high-temperature superconducting (HTS) materials. However, analysis of these devices is considerably complicated by the very fact that the material constitutive relations are nonlinear, and a rigorous solution of the problem in general requires a numerical approach. Toward this aim, we propose in this thesis an efficient hybrid Finite-Difference Time-Domain (FDTD) method for analyzing nonlinear wave propagation in two-dimensional optical and millimeter-wave devices. By employing different numerical schemes to solve for the electromagnetic fields separately in the regions of linear and nonlinear materials, the computation time of the overall method can be reduced without compromising the accuracy of the solution. In particular, for TE-polarized wave, the hybrid method combines the computational simplicity of the conventional explicit FDTD scheme with the superior stability property of a partially-implicit discretization to provide efficient and stable solutions to the scalar wave equation. For the case of TM polarization, a full-wave analysis using the leap-frog scheme with subgridding capability is integrated into the explicit scalar solution. In addition, in order to extend the FDTD method to nonlinear HTS media, a method of analysis based on the nonlinear London theory of superconductivity is proposed. The formulation directly incorporates the nonlinear Meissner effect into the analysis to give an approach that is expedient to FDTD solution and yields considerable saving in computation time over the traditional technique base don the Ginzburg-Landau theory. The result is an efficient and accurate algorithm for analyzing nonlinear propagation in HTS waveguides.

The hybrid FDTD method introduced provides a powerful tool for analyzing a large class of two-dimensional nonlinear devices. We demonstrate its application to a number proposed novel devices for optical and millimeter-wave signal processing. Examples include nonlinear periodic optical waveguides for wavelength and power discrimination, nonlinear HTS transmission lines for impulse generation vis shock-wave formation, and nonlinear resonating structures for frequency mixing and harmonic generation with high conversion efficiencies. Numerical results obtained for these devices serve to demonstrate the potential applications of material nonlinearity in millimeter-wave and optical integrated circuits.