Long Distance Propagation of Wave Beams in Paraxial Regime

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Abstract
This paper concerns the propagation of high frequency wave beams in highly turbulent atmospheres. Using a paraxial model of wave propagation, we show in the long-distance weak-coupling regime that the wavefields are approximately described by a complex Gaussian field whose scintillation index is unity. This provides a model of the speckle formation observed in many practical settings. The main step of the derivation consists in showing that closed-form moment equations in the Itô–Schrödinger regime are still approximately satisfied in the paraxial regime. This is done via Duhamel expansions, under the assumption that the random medium has Gaussian statistics. The rest of the proof is then an extension of results derived in [G. Bal and A. Nair, Complex Gaussianity of Long-Distance Random Wave Processes, preprint, arXiv:2402.17107, 2024].
Funding Information
  • National Science Foundation (DMS-230641)

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