A finite element beam propagation method for strongly guiding and longitudinally varying optical waveguides

A unified finite element beam propagation method is described for both TE and TM waves propagating in strongly guiding and longitudinally varying optical waveguides with magnetooptic materials. In order to avoid nonphysical reflections from the computational window edges, the transparent boundary condition is introduced for both polarizations. In order to show the validity and usefulness of this approach, numerical examples are presented for a directional coupler composed of two parallel identical waveguides, an S-bend, a Y-branching optical isolator, and a 4-ports optical circulator. The present algorithm is, to our knowledge, the first beam propagation method for modeling nonreciprocal magnetooptic components.