
This is highly idealized  there is no material that comes
even close! Still, there is a clear structure. Especially there seems to be a
correlation between the real and imaginary part of the curve. That is indeed
the case; one curve contains all the
information about the other. 


Real
dielectric functions usually are only interesting for a small part of the
spectrum. They may contain fine structures that reflect the fact that there may
be more than one mechanism working at the
same time, that the oscillating or relaxing particles may have to be treated by
quantum mechanical methods, that the
material is a mix of several components,
and so on. 


In the link a
real dielectric function for
a more complicated molecule is shown. While there is a lot of fine structure,
the basic resonance function and the accompanying peak for e'' is still clearly visible. 

It is a general property of complex
functions describing physical reality that under certain very general
conditions, the real and imaginary part are directly related. The relation is
called KramersKronig relation; it is a mathematical, not a physical property, that only demands two very
general conditions to be met: 


Since two functions with a time or frequency
dependence are to be correlated, one of the requirements is causality, the other one linearity. 


The KramersKronig relation can be most easily
thought of as a transformation from one
function to another by a black box; the functions being inputs and outputs.
Causality means that there is no output
before an input; linearity means that twice
the input produces twice the output. Otherwise, the transformation can be
anything. 

The KramersKronig relation can be
written as follows: For any complex function, e.g. e(w) = e'(w) + ie''(w), we have the
relations 


e'(w) = 
– 2 w
p 

¥
ó
õ
0 

w^{*}
· e''(w^{*})
w^{*2 }– w^{2} 
· dw* 
e''(w) = 
2 w
p


¥
ó
õ
0 

e'(w^{*})
w^{*2 }– w^{2} 
· dw^{*} 




The KramersKronig relation can be
very useful for experimental work. If you want to have the dielectric function
of some materials, you only have to measure one component, the other one can be
calculated. 


More about the
Kramers Kronig relation
can be found in the link. 








