Implementation of Bérenger layers as boundary conditions for the beam propagation method: applications to integrated waveguides

Abstract

In order to numerically solve the wave equation in integrated optics devices, the implementation of appropriate boundary conditions should be a key issue. In this work, we formulate the perfectly matched layer boundary condition, introduced by Bérenger [J. Comput. Phys. 114 (1994) 185], for operation in the scalar bidimensional finite difference beam propagation method (FD-BPM). With this boundary condition, a high absorption of outgoing waves along the propagation direction is achieved. To test the operation of Bérenger layers, two numerical experiments have been performed: the propagation of a Gaussian beam in vacuum and the propagation of a guided mode in a slab waveguide.