Nonparaxial Split-Step Method With Local One-Dimensional Scheme 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 three-dimensional scalar wave equation. Its essence is to convert the three-dimensional scalar wave equation into two two-dimensional equations that can be solved without using slowly varying envelope or one-way propagation approximations. To validate the effectiveness, numerical results for the Gaussian beam propagation in vacuum and the eigen-mode propagation in tilted step-index channel waveguide are compared with other beam propagation algorithms. Results show that the method has high accuracy and numerical efficiency compared with other known split-step methods. The perfectly matched layer boundary condition can be implemented easily.