Two-Frequency Radiative Transfer and Asymptotic Solution

Abstract

Two-frequency radiative transfer (2f-RT) theory is developed for classical waves in random media. Depending on the ratio of the wavelength to the scale of medium fluctuation 2f-RT equation is either a Boltzmann-like integral equation with a complex-valued kernel or a Fokker-Planck-like differential equation with complex-valued coefficients in the phase space. The 2f-RT equation is used to estimate three physical parameters: the spatial spread, the coherence length and the coherence bandwidth (Thouless frequency). A closed form solution is given for the boundary layer behavior of geometrical radiative transfer and shows highly nontrivial dependence of mutual coherence on the spatial displacement and frequency difference. It is shown that the paraxial form of 2f-RT arises naturally in anisotropic media which fluctuate slowly in the longitudinal direction.

Typos corrected

References in corpus (6)

• Multiple scattering of classical waves: from microscopy to mesoscopy and diffusion
• Green function Retrieval and Time-reversal in a Disordered World
• Spatial field correlation, the building block of mesoscopic fluctuations
• Self-Averaging Scaling Limits of Two-Frequency Wigner Distribution for Random Paraxial Waves
• Radiative Transfer Limits of Two-Frequency Wigner Distribution for Random Parabolic Waves
• Space-frequency correlation of classical waves in disordered media: high-frequency and small scale asymptotics

Cited by in corpus (4)

• Self-Averaging Scaling Limits of Two-Frequency Wigner Distribution for Random Paraxial Waves
• Two-Frequency Radiative Transfer. II: Maxwell Equations in Random Dielectrics
• Mutual Coherence of Polarized Light in Disordered Media: Two-Frequency Method Extended
• Space-frequency correlation of classical waves in disordered media: high-frequency and small scale asymptotics