Reflectivity calculations in L3 photonic crystal slab cavities

Abstract

In this work, a detailed study is made of the reflectivity spectrumof L3 photonic crystal slab cavities. The scattering matrix method forpatterned multilayer photonic structures is implemented to study thecoupling between the scattering and bounded states in the crystal.Some modifications are made in the original treatment of the methodin order to describe arbitrary geometrical shapes of the incident lightspot and to calculate the reflectivity in a cross-polarized scheme. Thelineshape of the fundamental mode resonance is well fitted by theFano formula, evidencing an electromagnetic Fano interference phe-nomenon in the reflection process. It is found that the lineshape ofthe Fano resonance can be accurately controlled and reversed by thepolarization of the incident field, and the continuum contribution inthe Fano phenomenon can be enhanced increasing the incident spotsize. Good agreement is obtained between the theoretical and experimental results. The outline of the work is as follows: Chapter one presents a gen-eral state of the art in the photonic crystal area. Then, in chapter two, the fundamental concepts of the solid state physics and electromagnetism in inhomogeneous and periodic media are described. In chapter three a revision is made of the standard plane wave expansionmethod applied to two dimensional photonic crystals. In chapter fourthe scattering matrix treatment of patterned multilayer structures isformulated in a general form, to study the diffractive properties ofphotonic structures. Chapter five presents the implementation of thescattering matrix method to photonic crystal slabs and in chapter sixthe principal results of this work are presented and discussed. Finally,chapter seven contains the principal conclusions and perspectives.