An Efficient Semivectorial Bidirectional Beam Propagation Method for 3-D Optical Waveguide Structures

An efficient semi-vectorial bidirectional beam propagation method (Bi-BPM) based on the complex Denman-Beavers iterative (C-DBI) scheme for three-dimensional (3-D) optical waveguide structures is constructed. Beside merely calculating the transition operators by the C-DBI scheme, like our previous paper, a new approximation for the bidirectional propagators by using the combination of Pade approximants and C-DBI scheme is proposed and developed. Such a treatment can be capable of correctly dealing with the evanescent waves generated in the transition processes, greatly improving the stability and accuracy of the Bi-BPM. Moreover, the efficiency of the present Bi-BPM can be also improved since the operators calculated by the C-DBI scheme can be simultaneously utilized for both processes of the Bi-BPM. In addition, the biconjugate gradient stabilized method is utilized to solve the resulting linear systems, further improving the efficiency. Numerical results from both single and multiple longitudinal discontinuity examples show that the present method can deal with evanescent waves properly with the accuracy comparable to that of the existing well-established methods.