Spectral Domain Optical Theorem and Radiative Transfer in Random Media With Large-Scale Fluctuations

A spectral domain optical theorem (SDOT) is derived for multiple scattering in random media. The spectral domain Dyson and Bethe-Salpeter equations (BSEs) are employed along with the energy flux conservation principle to arrive at the result. To demonstrate an application, the SDOT is used to derive the radiative transport equation (RTE) in random media with large-scale fluctuations (LSFs). In particular, the parameter regime is established for RTE in random media with LSF. This was enabled by imposing two conditions. One is based on estimating the error involved in approximating the mass operator by its leading term. The second is based on the quasi-homogeneity requirement of the coherence function. By expanding the Wigner distribution as a perturbation series, it is found that the convergence of this series requires that the scale size of fluctuation is much smaller than the spatial range where radiative transport manifests. To illustrate another application of SDOT, an outline of a scheme is provided for measuring the attenuation rate of waves propagating in random media.