As we have discussed in Chapter 1, the presence of an object with a refractive index different from that of the surrounding host medium changes the electromagnetic field that would otherwise exist in an unbounded homogeneous space. The difference between the total field in the presence of the object and the total field that would exist in the absence of the object can be thought of as the field scattered by the object. In other words, the total electromagnetic field in the presence of the object is mathematically represented as the vector sum of the incident and scattered fields.

The spatial distribution of the scattered field depends on specific characteristics of the incident field as well as on such properties of the scatterer as its size relative to the wavelength and its morphology, composition, and orientation. Therefore, in practice one usually must solve the scattering problem anew every time some or all of these input parameters change. It is appropriate, however, to consider first the general mathematical description of electromagnetic scattering without making any detailed assumptions about the scattering object, except that it is composed of linear, isotropic, and nonmagnetic materials. Hence the goal of this chapter is to establish a basic theoretical framework underlying specific problems discussed in the following chapters. Consistent with this objective and with the discussion in Section 1.1, we will assume that the scattering object is stationary and will consider only monochromatic fields whose dependence on time is completely described by the time-harmonic factor exp(—iωt).