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.)

 

[mark726]

Hi there,

First of all, you are correct in using the dielectric function to estimate the transmission of light through the gold film. To address your concerns about the imaginary part being much larger than the real part, this is expected for metals at optical frequencies. In fact, the imaginary part of the dielectric function represents the absorption of light by the material.

To account for this absorption in your calculation, you can use the Beer-Lambert law, which relates the intensity of light transmitted through a material to the material's absorbance and thickness. In this case, the absorbance can be calculated from the imaginary part of the dielectric function and the thickness of the gold film. This will give you an estimate of the amount of light that is absorbed by the gold film.

I hope this helps! Let me know if you have any further questions.