Development and application of full-wave time-domain numerical modeling techniques for the analysis of linear and nonlinear photonic micro/nanostructures

With the advent of mesoscale materials processing techniques, photonic devices can be realized with micron- or sub-micron dimensions. As the dimensions are reduced to the scale of the optical wavelength, electromagnetic wave interactions become more complex. First-principles computational modeling tools help to understand the underlying physics in such devices. Moreover, these tools provide an invaluable virtual lab environment where novel device concepts are explored and optimized before fabrication. This dissertation addresses the development and application of such numerical techniques for modeling electromagnetic interactions in photonic micro/nanostructures.; The numerical tools for modeling vertical-cavity surface-emitting lasers (VCSELs) are based on the finite-difference time-domain (FDTD) method implemented in cylindrical coordinates. Uniaxial perfectly matched layer absorbing boundary conditions are optimized for the cylindrical-coordinates FDTD using a global-error analysis. The computational efficiency is improved with an FFT/Padé interpolation technique that permits cold-cavity modal characteristics to be extracted from the early-time response, thereby reducing the overall computation time. A comprehensive analysis of simplified antiresonant reflecting optical waveguide VCSELs is conducted using this numerical technique. Design parameters are optimized for single-mode operation. Simulation results predict strong modal discrimination in favor of the fundamental mode for a large aperture and a large built-in index step.; Nonlinear frequency conversion processes are very sensitive to the phase velocities of interacting optical waves. Accurate modeling of such problems using FDTD requires extremely fine grid resolutions to minimize numerical dispersion errors. This dissertation proposes an alternative approach based on a pseudo-spectral time-domain (PSTD) method. Nonlinear PSTD schemes with second- and fourth-order time-stepping are developed. Benchmark simulations demonstrate significant improvements in computational efficiency and accuracy over FDTD. The nonlinear PSTD algorithms are further augmented to include linear material dispersion. One-dimensional PSTD modeling is used to analyze ultrashort pulse propagation in periodically poled LiNbO₃. Two-dimensional PSTD models are used to investigate angle-dependent frequency conversion processes in a tilted quasi-phase-matching grating. These models are also used to model second-harmonic generation in nonlinear photonic crystals. The circular and hexagonal poling patterns are optimized for a maximum frequency conversion efficiency.