Space-frequency correlation of classical waves in disordered media: High-frequency and small-scale asymptotics

Published 11 September 2007 Europhysics Letters Association
, , Citation A. C. Fannjiang 2007 EPL 80 14005 DOI 10.1209/0295-5075/80/14005

0295-5075/80/1/14005

Abstract

Two-frequency radiative transfer (2f-RT) theory is developed for geometrical optics in random media. The space-frequency correlation is described by the two-frequency Wigner distribution (2f-WD) which satisfies a closed-form equation, the two-frequency Wigner-Moyal equation. In the RT regime it is proved rigorously that 2f-WD satisfies a Fokker-Planck–like equation with complex-valued coefficients. By dimensional analysis 2f-RT equation yields the scaling behavior of three physical parameters: the spatial spread, the coherence length and the coherence bandwidth. The sub-transport mean-free-path behavior is obtained in a closed form by analytically solving a paraxial 2f-RT equation.

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10.1209/0295-5075/80/14005