ABSTRACT
This chapter considers the Yee-mesh-based FD algorithm for formulating the eigenvalue problem for waveguide mode solutions and incorporate into it the perfectly matched layer absorbing boundary conditions so that leaky waveguide modes. It presents the formulation of the finite-difference frequency-domain method for analysis of photonic band structures and calculated results of two-dimensional PC band diagrams. The chapter discusses the application of the FDFD method to modal analysis of planar PC waveguides. Since the photonic crystal (PC) concept was proposed, there has been a growing interest in the development of PC or electromagnetic crystal materials. They are characterized by an amazing ability to control the flow of light or electromagnetic waves within a frequency band called the photonic bandgap (PBG). Many research efforts have been devoted to utilizing the PBG material into waveguides in microwave and optical frequencies, and several PC waveguides have been fabricated.
