The formal theory developed in Chapter 2 assumed the Stokes parameters to be additive. The sufficient condition for additivity is that the radiation fluxes in the atmosphere shall have no phase coherence. Thermal emission from independently excited molecules is necessarily incoherent with respect to phase. Atmospheric scattering centers are widely and randomly spaced, and they can be treated as independent and incoherent scatterers. The situation differs, however, when we consider details of the scattering process within a single particle, and in order to derive the extinction coefficient and the scattering matrix (see § 2.1.3) we must make use of a theoretical framework that involves the phase explicitly. The problem of the interaction between an electromagnetic wave and a dielectric particle can be precisely formulated using Maxwell’s equations. For a plane wave and a spherical particle, Mie’s theory provides a complete solution (see §7.6). But the general problem is complicated and our understanding is rendered more difficult by preconceptions based on the approximations of elementary optics. This chapter provides a brief survey of the important results and the underlying concepts. The geometry of the problem is illustrated in Fig. 7.1. An isolated particle is irradiated by an incident, plane electromagnetic wave. The plane wave preserves its character only if it propagates through a homogeneous medium; the presence of the scattering particle, with electric and magnetic properties differing from those of the surrounding medium, distorts the wave front. The disturbance has two aspects: first, the plane wave is diminished in amplitude; second, at distances from the particle that are large compared with the wavelength and particle size, there is an additional, outward-traveling spherical wave. The energy carried by this spherical wave is the scattered energy; the total energy lost by the plane wave corresponds to extinction; the difference is the absorption. The properties of the spherical wave in one particular direction (the line of sight) will be considered. This direction can be specified by the scattering angle 6 (see Fig. 7.1) in a plane containing both the incident and scattered wave normals (the plane of reference), and the azimuth angle ϕ) between the plane of reference and a plane fixed in space.
Calculation of single-layer dielectric coatings for antireflection
in a given range of angles of incidence
