Two Classes of Unconventional Photonic Crystals

This thesis concerns two classes of photonic crystal that differ from the usual solid-state dielectric photonic crystals studied in optical physics. The first class of unconventional photonic crystal consists of atoms bound in an optical lattice. This is a “resonant photonic crystal”, in which an underlying optical resonance modifies the usual band physics. I present a three-dimensional quantum mechanical model of exciton polaritons which describes this system. Amongst other things, the model explains the reason for the resonant enhancement of the photonic bandgap, which turns out to be related to the Purcell effect. An extension of this band theoretical approach is then used to study dark-state polaritons in Λ-type atomic media. The second class of unconventional photonic crystal consists of two dimensional photonic crystals that break time-reversal symmetry due to a magneto-optic effect. The band theory for such systems involves topological quantities known as “Chern numbers”, which give rise to the phenomenon of disorder-immune one-way edge modes. I describe a system in which timereversal symmetry is broken strongly enough for experimental observation of the one-way edge modes. In addition to numerical studies of this photonic crystal, I develop an analytical effective theory, based on the symmetry of the lattice, that accurately describes its bandstructure.