Mixed finite element beam propagation method

Abstract

An efficient mixed finite element (FE) beam propagation method (BPM) for three-dimensional (3-D) simulations is developed for integrated optic devices. Wide angle propagation is allowed by applying Pade approximants to the finite element operator. Mixed finite elements prevent spurious modes and accurately model waveguide corners allowing the adequate description of polarization effects. Furthermore, the finite element matrices are Hermitian leading to a unitary propagation scheme if lossless waveguides surrounded by metallic walls are assumed. In contrast to finite difference schemes energy conservation holds explicitly.