Photonic crystals : from theory to practice

Abstract

In this thesis, we explore the design, computation, and analysis of photonic crystals, with a special emphasis on structures and devices that make a connection with practically realizable systems. First, we analyze the properties of photonic-crystal slabs: 2d periodic dielectric structures that have a band gap for propagation in a plane and that use index-guiding to confine light in the third dimension. Such structures are more amenable to fabrication than photonic crystals with full 3d band-gaps, but retain or approximate many of the latter's desirable properties. We show how traditional band-structure analysis can be adapted to slab systems in the context of several representative structures, and describe the unique features that arise in this framework compared to ordinary photonic crystals. We study the possibility of lossless linear waveguides in such systems, and highlight their differences with both conventional waveguides and waveguides in true photonic crystals. Finally, we consider the creation of high-Q cavities in slabs, for which the lack of a complete gap entails unavoidable radiation losses. Two mechanisms for minimizing such losses are described and demonstrated: mode delocalization and the novel far-field multipole cancellation. Next, we present a 3d periodic dielectric structure with a large, complete photonic bandgap. The structure is distinguished by a sequence of planar layers, identical except for a horizontal offset, and repeating every three layers to form an fcc lattice.

(cont.) The high symmetry of the layers means that complex devices could be formed by modifying only a single layer, and their similarity to common 2d photonic crystals allows the direct application of results and experience from those simpler systems. Third, we present and demonstrate general criteria for crossing perpendicular waveguides without crosstalk, based on a priori principles of symmetry and resonance. Finally, we describe a fully-vectorial, 3d algorithm to compute the definite-frequency eigenstates of Maxwell's equations in arbitrary periodic dielectric structures, including systems with anisotropy (birefringence) or magnetic materials, using preconditioned block-iterative eigensolvers in a planewave basis. Many different numerical techniques are compared and characterized. Our implementation is freely available on the Web.