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I am doing study on electromagnetism and Drude model is applied recently in my simulation. I am quite confused about the exact meaning of the terms in the expression of the dielectric constant in Drude model.

I have tried with the case of gold and here is what I got from my calculations:

One the one hand, the $\omega$ within in the denominator should be interpreted as the angular frequency with rad/s as the unit. On the other hand, the plasma frequency in the numerate and the damping coefficient in the denominator should be interpreted as the frequency with unit Hz.

By interpreted I mean just substitute in the value of the quantity while it is with that particular unit

But can the angular frequency just be added with frequency given their different units?

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  • $\begingroup$ Both frequency and angular frequency are measure in Hz. You have to be told if the variables are angular or not, although there is a very very strong convention that $\omega$ is angular frequency, and a somewhat strong convention that $f$ is frequency. Often it doesn't matter, as the expression is the ratio of frequencies. (Assuming the author didn't do something stupid.) But you can't add variables if one is $f$ and the other $\omega$. $\endgroup$
    – garyp
    May 8, 2020 at 12:52
  • $\begingroup$ @garyp It is killing me. I have substitute the value of $\omega$ when it is in rad/s and the values of $\omega_p$ and $\Gamma$ when they are in 1/s to get the right dielectric constant of for example gold, which is well established. $\endgroup$
    – cxz
    May 8, 2020 at 13:41
  • $\begingroup$ @garyp the expressions are in this link,horiba.com/fileadmin/uploads/Scientific/Downloads/… $\endgroup$
    – cxz
    May 8, 2020 at 13:42
  • $\begingroup$ Please can you write out the calculation you are doing using mathjax and include all the numerical values and the units. $\endgroup$
    – boyfarrell
    May 8, 2020 at 19:11

1 Answer 1

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You cannot add them if they have different units, you are correct.

They are related simply by a factor of $2\pi$,

$$ \omega = 2\pi\nu$$

where $\nu$ is in Hz and $\omega$ is rads/s.

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