Matrix split-step resolution for propagation based on an exact spectral formulation

This paper introduces an alternative method to simulate wave propagation with a split-step resolution. It is based on an exact formulation of the propagation operator. In this method, inspired by the classical parabolic equation formulation, the transforms from the spectral to the spatial representations are performed by a matrix multiplication. Although the matrix method is, in its current version, slower than usual split-step Fourier, it brings a new angle of view to perform the propagation simulation. Note that in the present version of the algorithm, the roughness is theoretically taken into account by modifying the Fresnel coefficient on the overall angular spectrum, and without spectral estimation or ray tracing to obtain the grazing angle.