Cylindrical photonic crystals

Abstract

In this thesis, we explore the properties of cylindrical photonic crystal waveguides in which light is confined laterally by the band gap of a cylindrically-layered photonic crystal. We show in particular that axially-uniform photonic band gap waveguides can exhibit novel behavior not encountered in their traditional index-guiding counterparts. Although the effects discussed in each chapter range from hollow-core transmission to zero and negative group velocity propagation and to high-Q cavity confinement, they are all a result of the photonic band gap guiding mechanism. The reflective cladding of the photonic crystal waveguide is unique in that it allows one to confine light in a low index of refraction region, and to work with guided modes whose dispersion relations lie above the light line of air, in a region where the longitudinal wave vector of the guided mode can approach zero. Chapter 2 discusses hollow-core photonic band gap fibers that can transmit light with minimal losses by confining almost all of the electromagnetic energy to a hollow core and preventing it from entering the lossy dielectric cladding. These fibers have many similarities with hollow metallic waveguides, including the fact that they support a non-degenerate low-loss annular-shaped mode. We also account for the main differences between metal waveguides and photonic band gap fibers with a simple model based on a single parameter, the phase shift upon reflection from the photonic crystal cladding. In Chapter 3 we combine the best properties of all-dielectric and metallic waveguides to create an all-dielectric coaxial waveguide that supports a guided mode with properties similar to those of the transverse electromagnetic mode of a coaxial cable.

(cont.) In Chapter 4, we introduce a mode-repulsion mechanism that can lead to anomalous dispersion relations, including extremely flattened dispersion relations, backward waves, and nonzero group velocity at zero longitudinal wave vector. The mechanism can be found in any axially-uniform reflective-cladding waveguide and originates in a mirror symmetry that exists only at zero longitudinal wave vector. In Chapter 5 we combine the anomalous dispersion relations discussed above with tunable waveguides to obtain new approaches for the time reversal (phase conjugation) and the time delay of light pulses. Chapter 6 discusses a new mechanism for small-modal-volume high-Q cavities based on a zero group velocity waveguide mode. In a short piece of a uniform waveguide having a specially designed cross section, light is confined longitudinally by small group velocity propagation and transversely by a reflective cladding. The quality factor Q is greatly enhanced by the small group velocity for a set of cavity lengths that are determined by the dispersion relation of the initial waveguide mode. In Chapter 7, we present a surprising result concerning the strength of band gap confinement in a two-dimensional photonic crystal. We show that a saddle-point van Hove singularity in a band adjacent to a photonic crystal band gap can lead to photonic crystal structures that defy the conventional wisdom according to which the strongest band-gap confinement is found at frequencies near the midgap.