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Opt. Soc. Am. A"],"published-print":{"date-parts":[[2026,7,1]]},"abstract":"<jats:p>Beam propagation through turbulence is commonly simulated by split-step\n\t\t\t\tFourier methods with independent phase screens. This approach relies on\n\t\t\t\tthe paraxial-Markov approximation, which has a wide range of validity.\n\t\t\t\tHowever, it is not justified in strongly turbulent media, where correlated\n\t\t\t\tphase screens are needed. Examples of extreme turbulence, considered in\n\t\t\t\tthe paper, arise, for example, in beam propagation through a jet plume and\n\t\t\t\tin aero-optics applications. The goal of this paper is two-fold: first, it\n\t\t\t\tclarifies when the use of independent phase screens fails, meaning that it\n\t\t\t\tcorrupts the estimated statistics of the wave field. Second, it describes\n\t\t\t\tan efficient method for sampling correlated phase screens, denoted by the\n\t\t\t\tacronym SCE-DFT. 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