Three-dimensional noniterative full-vectorial beam propagation method based on the alternating direction implicit method

The alternating direction implicit (ADI) method is adopted in the full-vectorial beam propagation formulation, which was discretized in the longitudinal direction via the standard Crank-Nicholson scheme. Through proper operator decomposition, operator inversions for the cross-coupling terms existing in the full-vectorial formulation are avoided and second-order accuracy along the propagation direction is achieved in the proposed algorithm. With the aid of the ADI method, our full-vectorial algorithm also has good performance in efficiency. This implicit scheme can theoretically be shown to be numerically unconditionally stable, Several numerical simulations have been performed and compared with those obtained by the finite difference mode-solving scheme based on the shifted inverse power method (SIPM) in order to examine the accuracy of our algorithm.