Transverse magnetic defect modes in two-dimensional triangular lattice photonic crystals

Abstract

Summary form only given. We used the finite-difference time-domain method to solve Maxwell equations. More specifically, we applied the non-dissipative Yee's algorithm with a duality relation between the spatial representations of the electric and magnetic fields that represents both the differential and integral forms of Maxwell equations. The computational domain consists of 19 photonic lattice cells in the periodic structure for /spl epsi/ in the x and y direction and 8 mesh cells in the z direction. Each photonic lattice cell has been divided into 40/spl times/40 computational mesh cells, but due to duality of the discretization mesh, effectively we determined each field on only 20/spl times/20 points inside a photonic lattice cell. Periodic boundary conditions were used in all three directions. We observed the spatial distribution of the magnetic and electric fields and the movement of the mode resonance through the photonic band gap as the defect radius is changed. In addition, we determined the dependence of the localization (the field energy confined at the defect cell) on frequency (defect radius). We also found well localized defect modes.A defect in the form of an air hole with a modified radius was introduced in the center of a triangular lattice.