Way *above* the highest resonant frequency the dielectric constant takes
on a simple form (factoring out
and doing the sum to the
lowest surviving order in
. As before, we start out
with:

(9.131) |

where

(9.132) |

The wave number in this limit is given by:

(9.133) |

In certain physical situations (such as a plasma or the ionosphere) all the
electrons are essentially ``free'' (in a degenerate ``gas'' surrounding the
positive charges) and resonant damping is neglible. In that case this
relation can hold for frequencies well below (but well above the
static limit, since plasmas are low frequency ``conductors''). Waves incident
on a plasma are reflected and the fields inside fall off exponentially away
from the surface. Note that

(9.134) |

The reflectivity of metals is caused by essentially the same mechanism. At
high frequencies, the dielectric constant of a metal has the form

(9.135) |

Metals reflect according to this rule (with a very small field penetration length of ``skin depth'') as long as the dielectric constant is negative; in the ultraviolet it becomes positive and metals can become transparent. Just one of many problems involved in making high ultraviolet, x-ray and gamma ray lasers -- it is so hard to make a mirror!