Volume 80, Number 1, October 2007
Article Number 14005
Number of page(s) 6
Section Electromagnetism, Optics, Acoustics, Heat Transfer, Classical Mechanics, and Fluid Dynamics
Published online 11 September 2007
EPL, 80 (2007) 14005
DOI: 10.1209/0295-5075/80/14005

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

A. C. Fannjiang

Department of Mathematics, University of California - Davis, CA 95616-8633, USA

received 26 March 2007; accepted in final form 13 August 2007; published October 2007
published online 11 September 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-Planck$\hbox{--} $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.

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