Waveguides in finite-height two-dimensional photonic crystals

We present a three-dimensional (3-D) finite-difference time-domain (FDTD) analysis of the transmission and the waveguiding properties of dielectric structures of finite height. A two-dimensional (2-D) photonic-crystal geometry is used for lateral confinement, and traditional waveguiding by dielectric mismatch is used for vertical confinement. We investigate different types of waveguide in photonic crystals with a finite height. We examine the dependence of the guiding properties on the lengths of the holes that constitute the photonic crystal and the widths of the layers of the waveguide. The role of the filling ratio of the holes and the dielectric constants of the upper and the lower layers for the guiding properties is presented. Also, a comparison between the 3-D and the 2-D FDTD results is given.