Numerical studies of 2D photonic crystals: Waveguides, coupling between waveguides and filters

In photonic crystals, light propagation is forbidden in a certain wavelengt h range, the bandgap. In a two-dimensional crystal composed of parallel hig h-refractive index rods in a low-index background a line defect can be form ed by removing a row of these rods, which can act as a waveguide for freque ncies in the bandgap of the crystal. In order to get more insight into the main features of such waveguides we have studied a number of properties, us ing simulation tools based on the finite difference time domain method and a finite element Helmholtz solver. We show conceptually simple methods for determining the bandgap of the crystal as well as the dispersion of a waveg uide for wavelengths in this bandgap. For practical applications, it is als o important to know how much light can be coupled into the waveguide. There fore, the coupling of light from a dielectric slab waveguide into the photo nic crystal waveguide has been examined, showing that a coupling efficiency of up to 83% can be obtained between a silicon oxide slab and a waveguide in a crystal of silicon rods. Finally, calculations on an ultra-compact fil ter based on reflectively terminated side-branches of waveguides (similar t o tuned stubs in microwave engineering) are shown and discussed.