Semi-analytic simulation of optical wave propagation through turbulence with arbitrary phase screen placement

Split-step wave-optical simulations are useful for studying optical propagation through random media like at- mospheric turbulence. The standard method involves alternating steps of paraxial vacuum propagation and turbulent phase accumulation. We present a semi-analytic approach to evaluating the Fresnel diffraction integral with a phase screen in the source plane, which is a key building block in split-step simulations. Compared to the standard angular-spectrum approach using the fast Fourier transform, the semi-analytic method provides relaxed sampling constraints and an arbitrary computational grid. Also, when a limited number of observation-plane points are evaluated or when many time steps are used, the semi-analytic method computes faster than the angular-spectrum method.