Non-Paraxial Split-Step Semi-Vectorial Finite-Difference Method for Three-Dimensional Wide-Angle Beam Propagation

A wide-angle, split-step finite-difference method with the classical local one-dimensional scheme is presented to analyze the 3-D semi-vectorial wave equation. The method requires only matrix multiplication for beam propagation. To validate the effectiveness, numerical results for the eigen-mode propagation in tilted step-index channel waveguides are studied, and results show that the method has high accuracy and numerical efficiency.