Transmission through thin gold film

[G01]

Homework Statement

Estimate the transmission of light with $\lambda=1\mu m$ that is transmitted through 20nm thick gold film at 77k where

The DC conductivity:

$$\sigma_{DC}=2*10^8 \Omega^{-1} m^{-1})$$

The carrier density:

$$n=5.9*10^28 m^{-3})$$

and the plasmon frequency:

$$\frac{\omega_p}{2\pi}=2.18*10^{15} Hz$$Use n to estimate absorption.

Homework Equations

$$\epsilon(\omega)=1-\frac{\omega_p^2}{\omega^2} + \frac{i\sigma_{DC}}{\epsilon_0\omega}$$

The Attempt at a Solution

OK. So, I know I should do this problem by computing the dielectric function at the given frequency and then finding the reflection coefficient from that. However, when I do this, I get the imaginary part being much much bigger than the real part.

This mean the imaginary part of N, the index of refraction, is equal to the real part of N, and thus, R becoms equal to one. I know this isn't the case.

The second problem:

I confused on how to account for the absorption in the dielectric function. Any hints would be greatly appreciated. Thanks!

(I hope this is enough info. I'm pressed for time, so if you need any more info, please ask, and I'll try my best to provide.)