A combined method of the beam propagation method (BPM) and the mode expansion propagation method (MEPM) is proposed for the analysis of reflections of both transverse electric (TE) and transverse magnetic (TM) polarized waves in waveguiding structures containing longitudinal discontinuities. BPM based on the finite-element method (FEM) is applied to slowly varying regions and MEPM is applied only to regions including abrupt discontinuities. FEM is also utilized for evaluating the eigenmodes necessary for the MEPM analysis. To show the validity and usefulness of the present approach, numerical examples for a semiconductor laser facet with antireflection coating and an optical directional coupler are presented.
Kohtaro Hayashi, Masanori Koshiba, Yasuhide Tsuji, Susumu Yoneta, and Ryosaku Kaji, "Combination of Beam Propagation Method and Mode Expansion Propagation Method for Bidirectional Optical Beam Propagation Analysis," J. Lightwave Technol. 16, 2040- (1998)