Introduction

The discussion in Section 4.10 on the scattering by gas molecules and by submicron particles illustrated the rules of superposition of radiation from several sources. Without much detail, the analysis there showed that the irradiance resulting from such superposition depends on the coherence properties of the sources: when the radiation emanating from several sources is coherent, the fields are additive; if incoherent, only the energies are additive. The distinction between these two modes of addition is important in view of the quadratic dependence (eqn. 4.42) between the irradiance and the electric field. Thus, the analysis of the superposition of radiation emitted by incoherent sources requires only the summation of the irradiance from all sources at a point. No consideration of the frequencies or the phases of the interacting fields is needed. On the other hand, the irradiance that results from the superposition of radiation from a multitude of sources that are coherent with each other depends on the spatial and temporal distribution of the interacting fields, on their phases, and on their frequencies. Thus, before such irradiance can be determined, the distribution of the combined fields must be found. The spatial and temporal distribution of the irradiance is then obtained from the field distribution using (4.42). Here we discuss the details of the superposition of coherent electromagnetic fields. Such detailed analysis can be simplified when considering the superposition of only two beams obtained by splitting one beam emitted by a single source.