Vector radiative transfer equation for arbitrary shape particles derived from Maxwell's electromagnetic theory

Abstract

Instead of using the phenomenological approximation of the classical radiative transfer theory, the macroscopic statistical Maxwell electromagnetic theory was successfully adopted to derive the transfer equation of coherent wave intensity (direct radiation intensity) with the Twersky approximation and far-field representation for the dyadic Green's function. We develop new equations to directly describe the transition operator of a multi-particle system, and to establish the infinite series relationships between the total transition operator and the transition operator of a single particle. By taking into consideration of the randomness of the scattering particle distribution, we could obtain the ensemble average of the total transition operator. Finally, we acquire the coherent wave (average wave) equation and the formal and concrete solutions of its vertical and horizontal polarization components, indicating that the coherent wave is a plane wave propagating along the direction of incident light, with an effective dyadic wave number. The transfer equation of the Stokes column vector of coherent strength is obtained using the coherent wave. The formal and concrete solutions to the coherent intensity are developed. The formal solution of the coherent intensity is the generalized vector Beer law. For non-spherical particles, the extinction coefficient matrix, which is the generalized vector optical theorem, is achieved in the matrix of non-diagonalization. Furthermore, this article reveals the influence of non-spherical characteristics of particles on polarization and clarifies the difference between the independent distribution scattering and single scattering. This paper also discusses the relationships and differences between classical transfer equation by the phenomenological approach and the transfer equation of direct radiation specific intensity by electromagnetic wave theory.