Theoretical design of photonic crystal devices for integrated optical circuits

Abstract

In this thesis we investigate novel photonic crystal devices that can be used as building blocks of all-optical circuits. We contrast the behavior of light in photonic crystal systems and in their traditional counterparts. We exhibit that bends in photonic crystals are able to transmit light with over 90% efficiency for large bandwidths and with 100% efficiency for specific frequencies. In contrast to traditional waveguides, bound states in photonic crystal waveguides can also exist in constrictions and above the cutoff frequency. We discuss how to lower reflections encountered when photonic crystal waveguides are terminated, both in an experimental setup as well as in numerical simulations. We show that light can be very efficiently coupled into and out of photonic crystal waveguides using tapered dielectric waveguides. In time-domain simulations of photonic crystal waveguides, spurious reflections from cell edges can be eliminated by terminating the waveguide with a Bragg reflector waveguide. We demonstrate novel lasing action in two-dimensional photonic crystal slabs with gain media, where lasing occurs at saddle points in the band structure, in contrast to one-dimensional photonic crystals. We also design a photonic crystal slab with organic gain media that has a TE-like pseudogap. We demonstrate that such a slab can support a high-Q defect mode, enabling low threshold lasing, and we discuss how the quality factor depends on the design parameters. We also propose to use two dimensional photonic crystal slabs as directionally efficient free-space couplers. We draft methods to calculate the coupling constant both numerically and analytically, using a finite-difference time-domain method and the volume current method with a Green's function approach, respectively.