Diffusion Limit of 1-D Small Mean Free Path of Radiative Transfer Equations in Bounded Domain

2018 ◽  
Vol 31 (2) ◽  
pp. 177-192
Author(s):  
Chen Xiao and Wang Shu
Keyword(s):  
Radiative Transfer ◽  
Free Path ◽  
Bounded Domain ◽  
Mean Free Path ◽  
Diffusion Limit ◽  
Transfer Equations ◽  
Radiative Transfer Equations

Polarized Radiative Transfer in Anisotropic Disordered Media With Short-Range Order

2017 ◽  
Author(s):  
B. X. Wang ◽  
C. Y. Zhao
Keyword(s):  
Radiative Transfer ◽  
Free Path ◽  
Short Range ◽  
Short Range Order ◽  
Mean Free Path ◽  
Range Order ◽  
Radiative Properties ◽  
Disordered Media ◽  
Structural Anisotropy ◽  
Fundamental Physical

The aim of this study is to present a general method to investigate radiative transfer in disordered media with a subwave-length, anisotropic short-range order and provide a fundamental understanding on the interplay between polarized radiative transfer and microstructural anisotropy as well short-range order. We show the anisotropy of short-range order, described by an anisotropic correlation length in Gaussian random permittivity model, induces a significant anisotropy of radiative properties. Here the photon scattering mean free path is derived using the Feynman diagrammatic expansion of self-energy, and the transport mean free path and phase function are calculated based on the diagrammatic representation of the irreducible vertex in the Bethe-Salpeter equation. We further consider the transport of polarized light in such media by directly solving Bethe-Salpeter equation (BSE) for photons, without the use of traditional vector radiative transfer equation (VRTE). The present method advantageously allows us to elegantly relate anisotropic structural parameters to polarized radiative transport properties and obtain more fundamental physical insights, because the approximations in all steps of our derivation are given explicitly with reasonable explanations from the exact ab-initio BSE. Moreover, through a polarization eigen-channel expansion technique for intensity tensor, we show that values of transport mean free path in different polarization eigen-channels are rather different, which are also strongly affected by structural anisotropy and short-range order. As a conclusion, this study depicts some fundamental physical features of polarized radiative transfer in disordered media, and is also valuable for potential applications of utilizing anisotropic short-range order in disordered media in manipulation of polarized radiative transfer.

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