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