Highly efficient noniterative full-vectorial beam propagation method based on the alternating-direction implicit scheme

A novel alternating-direction implicit method is developed for the full-vectorial wave equation. The cross-coupling terms are split off from the full-vectorial propagation operator, and their inversions are performed separately by a noniterative method at each step. The present method shows good performance in efficiency by comparison with the iterative method. It can be proved that the algorithm is of second-order accuracy along the propagating direction. To examine the accuracy of the present algorithm, it is compared with previously presented formulas, and the results show that it maintains high accuracy.