Approximate scalar finite-element beam-propagation method with perfectly matched layers for anisotropic optical waveguides

The perfectly matched layer boundary condition for arbitrary anisotropic media is incorporated into the approximate scalar beam propagation method, The procedure is based on a finite-element method for three-dimensional anisotropic optical waveguides with off-diagonal elements in a permittivity tenser. In order to treat a wide-angle beam propagation, the Fade approximant operator is employed, To show the validity and usefulness of this approach, numerical results are presented for Gaussian beam propagation in free space and Gaussian beam excitation on a three-dimensional anisotropic optical waveguide.