The time-domain beam propagation based on finite element method for analyzing lightwave propagation in 2-dimensional anisotropic photonic crystal waveguide structure has been proposed in this thesis. The time-domain beam propagation analysis is a useful numerical tool for simulating lightwave propagation in photonic crystal waveguide structures. In addition, the finite element code for analyzing band structure in infinite photonic crystal structure has been developed in order to determine the guided operating frequency range of photonic crystal. The verification of the proposed time-domain beam propagation method has been carried out by comparing the computed results with the results of previous works in numerical examples. To demonstrate the usefulness of the proposed method, a novel 4 ports TE/TM polarization and wavelength splitter has been designed and computational simulated for operating at wavelength 1.49 um. and 1.5 um.
