Complex Gaussianity of Long-Distance Random Wave Processes

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Abstract
Interference of randomly scattered classical waves naturally leads to familiar speckle patterns, where the wave intensity follows an exponential distribution while the wave field itself is described by a circularly symmetric complex normal distribution. Using the Itô–Schrödinger paraxial model of wave beam propagation, we demonstrate how a deterministic incident beam transitions to such a fully developed speckle pattern over long distances in the so-called scintillation (weak-coupling) regime.
Funding Information
  • National Science Foundation (DMS-2306411)

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