Design and numerical modelling of integrated optical components

This thesis is devoted to the design and theoretical and numerical analysis of a number of photonic crystal (PC) components. In its first part we study the influence of the surface structure of two-dimensional (2D) PCs on their optical properties. We formulate an effective-medium model of such PCs, able to reproduce the commonly observed strong dependence of their effective parameters on the position of their truncation plane. We then develop an algorithm for the design of compact wide-angle antireflection gratings for 2D PCs and show them to improve significantly the transmission through a PC flat lens. In the second part of the manuscript we introduce a new approach to the design of resonant cavities to be used in compact magneto-optical circulators. In contrast to structures proposed previously, they are devoid of oppositely-polarised magnetic domains, which significantly facilitates their fabrication. We show that these cavities need not be embedded in PCs, but can be coupled directly with standard rib waveguides. Some numerical techniques developed in the course of this thesis are presented in the last part of the manuscript. We extend the multiple-scattering method to the case of gyrotropic materials and introduce a straightforward and extremely accurate method for the calculation of band structures of 2D PCs composed of circular cylinders, based on Fourier-Bessel expansions. Finally, we describe the implementation of the finite-element method for the calculation of eigenmodes of open, axisymmetric, three-dimensional cavities containing gyrotropic materials.