We solve Maxwell’s macroscopic equations under the assumption that the sources of
the electromagnetic fields are fully specified throughout space and time. Charge, current,
polarization, and magnetization are thus assumed to have predetermined distributions as
functions of the space-time coordinates (r, t). In this type of analysis, any action by the fields
on the sources will be irrelevant, in the same way that the action on the sources by any other
force-be it mechanical, chemical, nuclear, or gravitational-need not be taken into
consideration. It is true, of course, that one or more of the above forces could be responsible for
the presumed behavior of the sources. However, insofar as the fields are concerned, since the
spatio-temporal profiles of the sources are already specified, knowledge of the forces would not
provide any additional information. In this chapter, we use Fourier transformation to express
each source as a superposition of plane-waves. Maxwell’s equations then associate each planewave
with other plane-waves representing the electromagnetic fields. Inverse Fourier
transformation then enables us to express the electric and magnetic fields as functions of the
space-time coordinates.
