Page 248 - Electrical Properties of Materials

230 Dielectric materials

S

Radio Microwave Visible
f

Fig. 10.7

Typical variation of and with

frequency. f
the crystal, and they will transfer maximum energy from an electromagnetic
wave at this frequency. Another case is the ‘viscous lag’ occurring between
the field and the polarized charge which is described by the Debye equations,
which we shall presently consider. A consequence of all this is that materials
that transmit light often absorb strongly in the ultraviolet and infrared regions,
for example most forms of glass. Radio reception indoors is comparatively
easy because (dry) bricks transmit wireless waves but absorb light; we can
listen in privacy. The Earth’s atmosphere is a most interesting dielectric. Of
the fairly complete spectrum radiated by the Sun, not many spectral bands
8
reach the Earth. Below 10 Hz the ionosphere absorbs or reflects; between 10 10
14
and 10 Hz there is molecular resonance absorption in H 2 O, CO ,O 2 , and
2
15
N 2 ; above 10 Hz there is a very high scattering rate by molecules and dust
15
14
particles. The visible light region (about 10 –10 Hz) has, of course, been
of greatest importance to the evolution of life on Earth. One wonders what we
would all be like if there had been just a little more dust around, and we had
10
8
had to rely on the 10 –10 Hz atmosphere window for our vision.
10.7 Anomalous dispersion
As shown in Fig. 10.7, there are wide frequency ranges within which ε remains

constant, but in the vicinity of certain resonances the change is very fast; the
dielectric constant declines as a function of frequency. This was already known
in the nineteenth century. They called it anomalous dispersion. What is anom-
alous about it? Well, let’s look at the group velocity. It was defined in eqn (2.26)
for electron waves but of course the definition applies to all kind of waves. It is

dω
v g = , (10.20)
dk