Reformulation of the ADI-BPM using a fundamental scheme

Abstract

A fundamental scheme, developed for implicit finite-difference time-domain methods, is utilized to reformulate the beam-propagation method based on the alternating-direction implicit scheme (ADI-BPM). A derivative-free formulation is performed in the right-hand sides of equations to be solved, leading to quite efficient implementation of the algorithm. Numerical results reveal that the computation time and memory requirements are reduced to ≅ 80%, providing the results equivalent to those of the conventional ADI-BPM.