Reflection/Absorption in Drude Metals

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One result of the Drude model of metals is that metals cannot sustain an electromagnetic wave for frequencies lower than the plasma frequency - since the wavevector is imaginary the wave will be evanescent and won't propagate. The books I've read say however, that this means the metal will perfectly reflect an incoming wave. None of the books mention absorption of the radiation at this point however. Is absorption not a consideration because there is an evanescent wave then? In real life there should always be some absorption happening though, so how would we reconcile the reflection/absorption processes?
 
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In the Drude model, absorption only happens in the immediate vicinity of the plasma frequency.
In real life metals, absorption will reduce the reflectivity of the metal, as is the case e.g. in copper or gold where interband transitions from the d-band to the conduction band are present below the plasma frequency.
 
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