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

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

2006-09-23

arxiv.org/abs/physics/0609200v4

J. Phys. A: Math. Theor. 40 (2007) 5025-5044

Physics

Optics

typos corrected

Scientific paper

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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