Abstract

One of the key issues in implementing a numerical scheme such as the finite-difference method to solve a partial differential equation such as the Helmholtz equation in infinite spatial domain is the numerical boundary condition. Several techniques have been used in the finite-difference beam propagation method. Popular approaches are the absorbing boundary condition (ABC) and the transparent boundary condition (TBC)^[1]. Recently, a novel boundary condition, the perfectly matched layer (PML) boundary condition, was proposed by Berenger^[2] for the finite-difference time-domain (FDTD) method for Maxwell’s equations. The effectiveness of the PML boundary condition was subsequently verified^[3]. In this paper, we will show that, the PML provides an attractive addition to the arsenal of tools as a highly effective numerical boundary condition for methods such as the finite-difference beam propagation methods and mode solvers.

© 1996 Optical Society of America