Split step non-paraxial finite difference method for 3D scalar wave propagation

We describe a simple and efficient wide-angle, split-step finite-difference based explicit transfer matrix method to solve the 3D scalar wave equation. The formulation is completely analytic and does not involve any numerical matrix inversion or diagonalization. It also does not use the ADI scheme. The PML boundary condition can be easily implemented with only a marginal increase in computational effort.