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The classical optical theorem that describes the extinction of electromagnetic radiation by an arbitrary particle is reformulated by use of the diffusion properties of the mutual spectral densities. This reformulation yields three novel coherency tensors: an extinction-loss coherency tensor, a scattering-loss coherency tensor, and an absorption-loss coherency tensor. The first tensor is used to establish the polarimetric optical theorem and to derive the extinction-loss matrix. The second tensor is used to derive the scattering-loss matrix. The third tensor is used to develop the absorption-loss matrix and the absorption cross sections. Furthermore, the derived extinction- and scattering-loss matrices are found to be similar to the extinction coefficient and phase matrices of the vector radiative transfer equations.

The problem of electromagnetic wave interaction with a stratified dielectric medium is solved in the framework of molecular optics, leading to a new derivation for the refraction and reflection laws at stratified media interfaces. In addition, the solution confirms the Lorentz–Lorenz refractive index formula characterizing the transverse propagation modes and the characteristic frequencies associated with the longitudinal mode. The analytic results presented in this study support the existence of another longitudinal mode propagating with the vacuum wave number within the medium, and they provide a new concept for the Ewald–Oseen extinction theorem. Other new results of this study are that (1) the relation between Fresnel horizontal and vertical reflection coefficients and the relation between the corresponding transmission coefficients are revealed and (2) a new concept is presented for the Brewster angle, and (3) the concept is introduced of multiple reflections in formulating the reflection coefficient at the interface between two different dielectric materials.