Volume 80, Number 1, October 2007
|Number of page(s)||6|
|Section||Electromagnetism, Optics, Acoustics, Heat Transfer, Classical Mechanics, and Fluid Dynamics|
|Published online||11 September 2007|
Space-frequency correlation of classical waves in disordered media: High-frequency and small-scale asymptotics
Department of Mathematics, University of California - Davis, CA 95616-8633, USA
Accepted: 13 August 2007
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-Plancklike 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.
PACS: 42.25.Dd – Wave propagation in random media / 42.68.Ay – Propagation, transmission, attenuation, and radiative transfer / 05.40.-a – Fluctuation phenomena, random processes, noise, and Brownian motion
© Europhysics Letters Association, 2007
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