The definition of a purely monochromatic electromagnetic field given in Section 2.3 implies that the time dependence of the complex vectors ε (r,t) and H(r,t) is fully described by the complex-exponential factor exp(—iωt) with a fixed angular frequency ω. This can be a good model for beams generated by certain types of laser, but not for the majority of natural and artificial electromagnetic fields. In reality, the electromagnetic field is typically polychromatic, i.e., is a superposition of a (possibly very large) number of monochromatic fields with different angular frequencies distributed over a given range [ωmin, ωmax]. Furthermore, in many cases the amplitudes of the complex electric and magnetic fields representing the component with an angular frequency ω are not constant but rather fluctuate in time, albeit much more slowly than the factor exp(—iωt). Then the resulting polychromatic field is said to consist of quasi-monochromatic components. The range of angular frequencies [ωmin, ωmax] of monochromatic or quasi-monochromatic components can be relatively narrow for some artificial sources of light. However, it can also be very wide, the solar radiation and the light produced by incandescent lamps being prime examples.

Given the ubiquity of polychromatic electromagnetic fields in natural and artificial environments, it is essential to analyze how the results of Chapters 7 and 8 can be generalized to account for a mix of different angular frequencies and/or random fluctuations of the amplitudes of the constituent complex fields.