Full-Vectorial Bidirectional Beam Propagation Method for Nonradiative Dielectric Waveguides

We present a novel numerical analysis method called 1D full-vectorial finite element bidirectional beam propagation method (BiBPM) for the efficient design of nonradiative dielectric (NRD) waveguide components. The BiBPM is a field-based propagation operator method that does not require computing eigenpairs or diagonalizing characteristic matrixes. The dimension of the problem can be reduced in the case that the structure of the NRD guide does not vary in the perpendicular direction to its parallel perfect conductor plates. Moreover, since propagation operator methods eliminate the need to discretize in a homogeneous direction, a 3D problem can be converted into a 1D problem in specific situations. First, we analyze NRD guides with an offset and an air gap to verify the applicability of the transfer-matrix-based BiBPM to NRD guides. Given the instability of transfer matrix formulation, we also introduce the scattering-matrix-based BiBPM. Its validity is confirmed using numerical examples of an electromagnetic bandgap filter and a square resonator.