The Zones

Suppose the source lives inside a region of maximum size $d \ll \lambda$ where $\lambda = 2\pi c/\omega$. By that I mean that a sphere of radius $d$ (about the origin) completely contains all charge-current distributions. Then we can define three zones of approximation:

1. The near (static) zone $d « r « \lambda$
2. The intermediate (induction) zone $d « r \sim \lambda$
3. The far (radiation) zone $d « \lambda « r$

The field has very different properties in these zones. We will briefly discuss each of them.

• (Atomic and Molecular) sources all live inside their own near zone at optical frequencies. If the atoms are in a liquid or solid, there is a near field interaction (implicitly alluded to in chapter 4 and 7) that may be important in determining optical dispersion and other observable phenomena. Only for microwave frequencies and less does the near zone become relevant on a macroscopic scale. For rf waves it becomes extremely relevant, as it may extend a hundred meters or more.

• The induction zone is an annoying region where most of the simple approximations fail. It is distinguished by not being either of the other two zones. The wave changes character completely inside this zone. Because condensed matter theory invariably has objects interacting within this zone it is important there, although it can only be crudely treated. Without doing an obnoxious amount of work, that is.

• The far zone is where we all live, most of the time, with respect to the major sources of EM radiation. Our detectors are many wavelengths away from the atoms. Our radios are many wavelengths away from the transmitters. And, generally, the sources are smaller, if not much smaller, than a wavelength^11.4. In the far zone, the emitted EM fields are characteristically transverse and fall off in amplitude as $1/r$ or faster, and often far enough away they look locally like plane waves! This is typical of radiation fields from compact sources. We will spend most of our time considering solutions in the far zone.