This thesis concerns two active areas of research in optical communications, namely photonic device modeling employing the vector boundary element method and the analysis of polarization mode dispersion effects with the multicanonical procedure.

Regarding the first thesis topic, we introduce a new vectorial boundary element method that is then applied to the modal analysis of dielectric waveguides with linear, isotropic, non-magnetic and piecewise homogeneous refractive indices. The procedure determines the distribution of all electro-magnetic field components from the longitudinal fields at the refractive index boundaries. Matrix elements are evaluated through series solutions while the electric field discontinuity at corners is accommodated through various techniques including a grid refinement technique, a high order finite difference formulation and an analytic approach. Our formalism, which treats open boundaries exactly, generates propagation constants and modal field distributions for several representative refractive index profiles with far higher accuracy than standard finite difference and finite element procedures.

In the latter part of this thesis, we instead study the polarization mode dispersion induced system impairments and mitigation techniques. We apply multicanonical technique in the analysis of polarization mode dispersion and determine experimentally, for the first time, the probability distribution functions of polarization mode dispersion as well as a general stochastic system through this technique. Our specific implementation relates to a fiber based polarization mode dispersion emulator and yields the probability distribution function of the differential group delay for probabilities to 10-6 with only 8,000 samples. Employing this technique, we further measure the distribution of bit error ratio of a fiber recirculation loop. Further, we demonstrate how the statistical error of multicanonical methods can be reduced through weighted least square fitting procedures. Our method generalizes previous modified multicanonical approaches. In addition, we introduce several techniques to improve the accuracy and dynamic range of the multicanonical method by employing e.g. a simple variance reduction technique and estimation of transition probability using interpolation method.

A further result of our multicanonical studies demonstrates that properties of functions of stochastic system parameters can be rapidly determined both numerically and experimentally within any desired region of the system observables through the biased multiiii canonical procedure, which drive the system into the region of interest using appropriate bias function. By applying this method to an analysis of the joint distribution function of the first and second order polarization mode dispersion, we measure probability densities as small as 10⁻¹⁰ with only 20,000 sampling events both numerically and experimentally. Finally, we employ a modified version of the multicanonical algorithm to evaluate the system penalties and outage probabilities of different PMD compensators. The procedure determines the optimal operating conditions for each compensator architecture far more efficiently than the standard Monte-Carlo algorithm.