General Relationship Between e and

We must reemphasize that the real and imaginary parts of the complex dielectric function (and the complex refractive index) are not independent. Arbitrary choices of c and (or n and k) do not necessarily correspond to 

We are now in a position to better understand and, we hope, appreciate, the sometimes mysterious Kramers-Kronig relations. 

we note that the consequence of no absorption (e = 0) at all frequencies is that the integral in (9.44) vanishes and e = 1. Optically, such a material does not exist there is no way that it can be distinguished from a vacuum by optical means. The Kramers-Kronig relations also tell us that it is a contradiction to assert that either the real or imaginary parts of the dielectric function can be independent of frequency the frequency dependence of the one implies the frequency dependence of the other. These consequences of the Kramers-Kronig relations are almost trivial, but it is disturbing how often they are blithely ignored. 

The high- and low-frequency behavior of c can be inferred from (9.44) regardless of the nature and number of absorption features in c . As to becomes arbitrarily large, all contributions to the integral go to zero and 

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