Correlated phase screens for beams in extreme turbulence

Beam propagation through turbulence is commonly simulated by split-step Fourier methods with independent phase screens. This approach relies on the paraxial-Markov approximation, which has a wide range of validity. However, it is not justified in strongly turbulent media, where correlated phase screens are needed. Examples of extreme turbulence, considered in the paper, arise, for example, in beam propagation through a jet plume and in aero-optics applications. The goal of this paper is two-fold: first, it clarifies when the use of independent phase screens fails, meaning that it corrupts the estimated statistics of the wave field. Second, it describes an efficient method for sampling correlated phase screens, denoted by the acronym SCE-DFT. It uses the discrete fast Fourier transform and circulant embedding, with a particular spline-based smooth embedding, designed to improve the efficiency.