Stable Discrete Mixed Fourier Transform (DMFT) in Split-Step Parabolic Equation (SSPE) for Long-range Electromagnetic Propagation Modeling Over Ocean Surfaces

A split-step parabolic equation (SSPE) with a stable discrete mixed Fourier transform (DMFT) is introduced for the modeling of long-range electromagnetic propagation over ocean surfaces. Our DMFT approach utilizes the difference equation with a mixed coefficient, and the initial coefficients of the general solutions are determined using the endpoints of normalized fields. Numerical computations based on realistic atmospheric environments are conducted to ensure that the two-way DMFT-SSPE remains stable and efficient even for small discretization steps and a large number of sample points.