Chapter 2 - Maxwell's equations for single-scattering particles

Abstract

This chapter presents a concatenation of the basic tools necessary to compute all the relevant optical properties resulting from the scattering of electromagnetic waves by a particle of an arbitrary shape and refractive index. Included in this litany of tools is a brief review of Maxwell's equations, constitutive relations, and electromagnetic boundary conditions. The concepts of the scattering and absorption cross sections are presented through the use of the Poynting vector. In addition, the extinction cross section, according to the optical theorem, is unambiguously determined by the projection of the scattered electric field vector onto the incident electric field vector in the 0° forward scattering direction, normalized by the incident irradiance and a constant. The polarization of light can be expressed by decomposing the electric field vector into two orthogonal components perpendicular to the wave propagation direction. For a light scattering event, the electric field vectors of the incident and scattered waves are related by the 2×2 amplitude scattering matrix (also called the Jones matrix). The Stokes parameters are introduced to specify the intensity and the polarization state of a light beam. An amplitude scattering matrix can be converted to a 4×4 scattering phase matrix, which relates the Stokes parameters of the incident and scattered waves; however, for this to occur a necessary and sufficient condition must be fulfilled. Certain symmetry relations of a particle or a collection of particles, in particular, the mirror and reciprocal orientations of the original particle, can be utilized to simplify the scattering phase matrix.