The split-step Fourier method is commonly used to simulate the propagation of radiation in a turbulent atmosphere using two-dimensional phase screens that have the desired spatial spectral content given by the atmospheric power spectrum. Using existing methodologies, isotropy of the structure function can never be achieved, mainly along the axis of propagation, for several reasons. In this paper, we introduce the sparse spectrum harmonic augmentation method that will address the lack of isotropy along the propagation axis, the limited achievable frequencies, and the limited time development possible using known approaches. Following the methodology described will produce phase screens that are transversely endless, perfectly correlated along the propagation axis, and contain the desired spectral content, including the low frequencies that even though they contain most of the energy, are usually neglected. The methodology presented can be used for many aspects of wave propagation in random media, such as atmospheric propagation, underwater acoustics, radio wave propagation in the ionosphere, and more.
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