Electromagnetic simulations of active and nonlinear photonic devices

Computational simulation has been an essential tool for modeling integrated photonic devices, and in providing design insights for improving their performance. Due to an extensive growth in the computational resources available to contemporary optical scientists, rigorous and comprehensive numerical algorithms, which in the past had been too computationally demanding to be of much practical use, are now easily implemented even on a desktop computer. Through the application of one such rigorous algorithm, the Finite-Difference Time-Domain (FDTD) method, this dissertation models two important components of integrated photonics: modelocked Vertical Cavity Surface Emitting Lasers (VCSELs) and nonlinear Photonic Crystals (PCs). Furthermore, an implementation of the plane wave expansion (PWE) numerical technique, which includes in a self-consistent way the changes in the refractive index caused by Kerr-nonlinear effects, is also presented. This technique is useful for computing photonic band structures in nonlinear PCs and for accurately determining wave propagation in PCs, in the regime where they are strongly dispersive.An approach based on the FDTD method, which is extended to incorporate active-dispersive material, is developed for simulating the dynamics of VCSELs. The material response is incorporated in our FDTD algorithm by the effective semiconductor Bloch equations, and its effects are accounted for through a resonant polarization term in the Maxwell's equations. Moreover, nonlinear gain saturation is incorporated through a gain suppression factor in the equation governing the dynamics of the resonant polarization. This approach is verified by modeling a lambda-cavity VCSEL, with a multiple quantum well (MQW) gain region the corresponding continuous-wave operation is obtained at the expected wavelength. The dynamics of ultrashort pulses generated by a monolithic passively modelocked one dimensional VCSEL with a MQW gain region and a single quantum well saturable absorber are studied and it is demonstrated that a stable modelocked pulse train can be generated. It is also demonstrated that with our FDTD approach sub-cycle temporal precision can be achieved. The need for this fine temporal resolution is established by investigating pulse propagation through the semiconductor saturable absorber. Fine features of the spatial profile of the modelocked pulses are also examined within this approach. (Abstract shortened by UMI.)...