A Wide-Angle Full-Vector Beam Propagation Method Based on an ADI Preconditioner

Wide-angle full-vector Beam Propagation Methods (BPMs) for three dimensional wave-guiding structures can be derived based on rational approximants of a square root operator or its exponential (i.e. the one-way propagator). While the less accurate BPM based on the slowly varying envelope approximation can be efficiently solved by the Alternating Direction Implicit (ADI) method, the wide-angle variants involve linear systems that are more difficult to handle. In this paper, we present an efficient solver for these linear systems based on a Krylov subspace method with an ADI preconditioner. The resulting wide-angle full-vector BPM is used to simulate the propagation of wave fields in a Y -branch and a taper.