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Before we go on, we should understand a few things:

is now complex! The imaginary part is
explicitly connected to the damping constant.
 Consequently we can now see how the index of refraction
n = cv = &mu#mu;&epsi#epsilon;&mu#mu;_0&epsi#epsilon;_0,
can be also be complex. A complex index of refraction describes
absorption (or amplification!) and arises from the damping
term in the electrons' EOM (or nonlinear, nonequilibrium effects in
lasers, which we will not consider here). This makes energy
conservation kind of sense. Energy absorbed by the electrons and dissipated via the ``frictional'' damping force is removed from the EM
field as it propagates through the medium. This (complex dispersion of
incident waves) is the basis for the ``optical'' description of
scattering which is useful to nuclear physicists.
 The term
has a form that you will see again and again and again in your studies. It
should be meditated upon, studied, dreamed about, mentally masticated and
enfolded into your beings until you understand it. It is a complex
equation with poles in the imaginary/real plane. It describes (very
generally speaking) resonances.
It is useful to convert this into a form which has manifest real and
imaginary parts, since we will have occasion to compute them in real
problems one day. A bit of algebra gives us:
 If
is ``small'' (
molecules/cc for a gas)
is small (just like in the static case) and the medium is nearly transparent
at most frequencies.
 if
is ``large'' (
molecules/cc for a liquid or
solid)
can be quite large in principle, and near a resonance can be
quite large and complex!
These points and more require a new language for their convenient
description. We will now pause a moment to develop one.
Next: Anomalous Dispersion, and Resonant
Up: Dispersion
Previous: Dynamic Case
Contents
Robert G. Brown
20170711