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

• The article only applies the Twersky approximation and avoids Foldy's effective field approximation. Under the condition of the only independently distributed scattering, we use the new expression of far field approximation of the dyadic Green's function, obtain the effective dyadic dielectric constant and, provides a new method to calculate the effective dielectric constant of a complex media with a variety of different composition and various particle size. • A new integral equation i.e., T matrix method, of the electric field with multiple scattering in multiple particle system is established. The infinite series relationship between total transition operator and single scatterer transition operator is obtained, and the transfer equation of coherent field (average field) is derived. For the average field equation, the formal solution and the concrete solution are obtained. The results demonstrate that the coherent wave is a plane wave propagating along the incident light with the characteristics of the dyadic effective wave number. • The article showed that the rate of attenuation in coherent wave propagation is the extinction coefficient of the radiative transfer equation. The extinction coefficient matrix of particles with arbitrary orientation and shape is a non-diagonal matrix, It is reflected that the Stokes parameters of the scattered wave are not only related to the Stokes parameter of the incident wave, but also related to the polarization state of the incident light, that is, the non-spherical particle scattering has dichroism, and the most generalized vector optical theorem is derived. • The vector transfer equations of four Stokes parameters are directly obtained from the vertical and horizontal polarization electric fields of the coherent wave, which is the familiar transfer equation of direct radiation specific intensity, and the formal solution (i.e., generalized vector Beer's law) and specific solution of the coherence intensity are derived. 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. [ABSTRACT FROM AUTHOR]