Simple boundary condition for terminating photonic crystal waveguides

Abstract

Many photonic crystal (PhC) devices are nonperiodic structures due to the introduced defects in an otherwise perfectly periodic PhC, and they are often connected by PhC waveguides that serve as input and output ports. Numerical simulation of a PhC device requires boundary conditions to terminate PhC waveguides that extend to infinity. The rigorous boundary condition for terminating a PhC waveguide is a nonlocal condition that connects the wave field on the entire surface (or line in two-dimensional problems) transverse to the waveguide axis, and it is relatively difficult to use, especially for realistic devices, such as those in PhC slabs. In this paper, a simple approximate boundary condition involving a few points in the waveguide axis direction is introduced. The new boundary condition is used with the Dirichlet-to-Neumann map method to take advantage of the lattice structures and identical unit cells in PhC devices. Comparisons with the rigorous nonlocal boundary condition indicate that the simple boundary condition gives accurate solutions if the computational domain is enlarged by a few lattice constants in each direction.