Surface plasmon wavevector calculations

[jsc01]

I am trying to calculate the wavevector of a surface plasmon. The magnitude of the wavevector is given by:

k = $\frac{ω}{c}$$\sqrt{\frac{ε_1ε_2}{ε_1+ε_2}}$

where ε1 is the dielectric constant for air and ε2 is the dielectric constant for the metal. However, according to the Drude model, the dielectric constant for a metal is not a constant but is a complex function of wavelength (frequency). I am looking to make this calculation for incident radiation in the mid-infrared (λ = 10 microns or so) where ωτ >> 1. Would using

ε(ω) = 1 - $\frac{ω_p^2}{ω^2}$

work well in this region (where $ω_p$ is the plasma frequency)?

 

[Valerie Park]

Or is there another approach that would be better?Yes, using the Drude model with the expression for the dielectric constant given above will work well in the mid-infrared region. The expression for the wavevector of a surface plasmon will then be: k = \frac{ω}{c}\sqrt{\frac{ε_1(1 - \frac{ω_p^2}{ω^2})\cdot ε_2}{ε_1+ε_2(1 - \frac{ω_p^2}{ω^2})}}