High-frequency Drude plasma cutoff (${\omega }_p^2=n{e}^2/(m{ϵ}_0)$)

The Drude model relative permittivity is $1-{\omega }_p^2/[\omega (\omega +i/\tau )]$. At frequencies large compared with the collision rate but below ${\omega }_p$, its leading real part is negative and the physical spatial wave-number branch has positive imaginary part. The field therefore decays into the conductor; close to the threshold the full complex response must be retained.