Two-Dimentional Photonic Crystal Waveguides

In the recent years a new class of periodic high-index contrast dielectric structures, known as photonic bandgap structures, has been discovered. In these structures frequency intervals, known as photonic bandgaps, where propagation of electromagnetic waves is not allowed, exist due to the periodic dielectric function. This is analogous to semiconductors, where electronic bandgaps exist due to the periodic arrangement of atoms. As is also the case for semiconductor structures, photonic bandgap structures may become of even greater value when defects are introduced. In particular, point defects make possible a novel class of optical microcavities, whereas line defects make possible a novel class of waveguides. In this paper we will analyze two-dimensional photonic crystal waveguides based on photonic crystals with rods arranged on a triangular and a square lattice using a plane-wave expansion method and a finite-difference-time-domain (FDTD) method. Design parameters, i.e. dielectric constants, rod diameter and waveguide width, where these waveguides are single-moded and multi-moded will be given. We will also show our recent results regarding the energy-flow (the Poynting vector) in these waveguides for guided modes.