Optical properties of anisotropic photonic crystals

Abstract

A photonic crystal can be simply viewed as a lattice with a motif attached to each lattice point. If the re-orientation of the motif causes changes in the optical properties of the photonic crystal then the corresponding photonic crystal is an anisotropic photonic crystal. Anisotropic photonic crystals can be classified as materially and geometrically anisotropic photonic crystals. The study so far in the field of anisotropic photonic crystal was concentrated mainly in optimizing and tuning the photonic bandgaps. This thesis aims to provide a unified understanding of anisotropic photonic crystals using proper symmetrical tools. Apart from this, the thesis also examines the properties of anisotropic photonic crystals that remain unexplored. Basic equations and operators that describe light propagation in one, two, and three dimensional anisotropic photonic crystals are formulated. The decoupling of the two independent polarizations of light in the case of a materially anisotropic photonic crystal is analyzed in detail. The symmetrical properties of the defined operator are investigated in detail using group theory, and novel concepts such as orientational group and fundamental zone of orientation are introduced. We have revealed a standard solution method based on plane wave expansion technique in order to solve the basic equations. In addition, a powerful approximation technique that leads to analytical equations to the evolution of the states in a two-dimensional photonic crystal is proposed. Equal frequency surface of the anisotropic crystal is analyzed. We propose one-plane-wave and two-plane-waves approximation techniques for calculating equal frequency surfaces in the photonic crystals with a small spatial modulation. When the modulation is large, it is found that the equal frequency surfaces can be defined using a set of negative principal refractive indices. The properties of such anisotropic negative index states were analyzed in detail, and the tuning of negative principal refractive indices and the phenomena of accidental isotropy in the anisotropic states are reported. Equal frequency surfaces are also used in predicting conduction properties of light in the anisotropic photonic crystals. Controllable conduction devices such as tunable superprism and polarization splitters are proposed, based on two-dimensional anisotropic photonic crystals, with electrically re-orientable motif. We have shown both switching action and continuous tunability in these devices. Apart from the conduction properties, bandgap engineering in materially anisotropic one- and two-dimensional photonic crystals is also investigated. In particular, we have shown how polarization dependent partial and full bandgaps are being created in a materially anisotropic square lattice photonic crystal. With the use of anisotropic materials and the flexibility of arranging the principal axes, the requirement on filling ratio, refractive index and anisotropy to achieve the largest bandgap is greatly alleviated.