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Self-Averaging Scaling Limits of Two-Frequency Wigner Distribution for Random Paraxial Waves

Albert C. Fannjiang
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Abstract

Two-frequency Wigner distribution is introduced to capture the asymptotic behavior of the space-frequency correlation of paraxial waves in the radiative transfer limits. The scaling limits give rises to deterministic transport-like equations. Depending on the ratio of the wavelength to the correlation length the limiting equation is either a Boltzmann-like integral equation or a Fokker-Planck-like differential equation in the phase space. The solutions to these equations have a probabilistic representation which can be simulated by Monte Carlo method. When the medium fluctuates more rapidly in the longitudinal direction, the corresponding Fokker-Planck-like equation can be solved exactly.

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Albert C. Fannjiang. 2006-09-23. Self-Averaging Scaling Limits of Two-Frequency Wigner Distribution for Random Paraxial Waves. https://doi.org/10.1088/1751-8113/40/19/007

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