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Suppose we write (for a given frequency)

(9.108) 
Then

(9.109) 
and the intensity of the (plane) wave falls off like
. measures the damping of the plane wave in the medium.
Let's think a bit about :

(9.110) 
where:

(9.111) 
In most ``transparent'' materials,
and this
simplifies to
. Thus:

(9.112) 
Nowever, now has real and imaginary parts, so may
as well! In fact, using the expression for in terms of and
above, it is easy to see that:

(9.113) 
and

(9.114) 
As long as
(again, true most of the time in
trasparent materials) we can thus write:

(9.115) 
and

(9.116) 
This ratio can be interpreted as a quantity similar to , the
fractional decrease in intensity per wavelength travelled through the
medium (as opposed to the fractional decrease in intensity per period).
To find in some useful form, we have to examine the details of
, which we will proceed to do next.
When is in among the resonances, there is little we can do
besides work out the details of the behavior, since the properties of
the material can be dominated strongly by the local dynamics
associated with the nearest, strongest resonance. However, there are
two limits that are of particular interest to physicists where the
``resonant'' behavior can be either evaluated or washed away. They are
the low frequency behavior which determines the conduction
properties of a material far away from the electron resonances per se,
and the high frequency behavior which is ``universal''.
Next: Low Frequency Behavior
Up: Dispersion
Previous: Anomalous Dispersion, and Resonant
Contents
Robert G. Brown
20071228