Optical constants of noble metals: the Drude model for microwave modelling

I have a question regarding the optical constants of noble metals.

According to Johnson and Christy's paper Optical Constants of Noble Metals (Phys. Rev. B 6, 4370–4379 (1972), doi:10.1103/PhysRevB.6.4370), in the Drude free electron theory the equation for the dielectric permittivity is $$\epsilon(\omega)=1-\frac{\omega_p^2}{\omega(\omega+i/\tau)}=1-\frac{\omega_p^2}{\omega(\omega+i\gamma)},$$ where $\epsilon(\omega)$ is the dielectric constant at frequency $\omega$, $\omega_p$ the plasma frequency, and $\gamma=1/\tau$ the collision frequency.

In the nanohub photonics database the constants can be calculated from different theoretical and experimental models.

However, in CST Microwave Studio I need to give the epsilon infinity value, which really comes from modified drude model: $$ε=ε(\infty)-\frac{ω_p^2}{ω^2+iγω}.$$ How do I get the value of $\epsilon(\infty)$ for gold? Is there any reference by using which we can directly convert the free electron theory Drude model to the modified Drude model?

I am specifically searching for the values of $ε(\infty)$, $ω_p$, and $γ$ for gold in the 700nm to 1100 nm range (specifically 830nm).

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Welcome, you can use latex by putting formula between two $signs. Also I have added a link to the article you mentioned. – hwlau Dec 16 '12 at 21:21 add comment 2 Answers $$\epsilon_\infty=9.5$$ $$\omega_P=1.36\times 10^{16} \text{ rad/s}$$ $$\gamma=1.05\times 10^{14} \text{ rad/s}$$ - Two things. First, this doesn't seem to answer the question which was "How do I get the the value of... ?", and secondly we have the MathJax rendering engine active on the site which allows you to write LaTeX-alike markup for mathematics. I'll do this post for you. – dmckee Feb 27 at 0:46 Indeed the question is about the way to get an answer, not about the answer itself (pretty much always, otherwise it doesn't belong on SE) – Michiel Feb 27 at 7:07 @dmckee is right. This answer of values is part of the question. The focus of OP's question is$\epsilon(\infty)$. In other words: Whats the dielectric permittivity for low wavelenghts? In this regime below the cut-off plasma frequency$\omega_p$there is no transmission. I don't understand the relation to your$\lambda_{min}=700\,$nm (red) area of interest. Could you please explain? – Stefan Bischof Mar 21 at 15:18 add comment Unless I'm misinterpreting your question I think you're confused. The values do not change much with wavelength. Instead these values are supposed to provide a model for which the permittivity can be found over a range of wavelengths. So to answer your last question, the values that were posted by user21414 are correct for the range listed, as they are actually correct for the range 250-2000nm. However these values vary based on certain authors that have produced them e.t. Blaman, Zeman, Grady . Point is, there are many values that actually are accepted. The term you are looking for$\epsilon_ib(\omega)$is the value for the bound electrons within a material. This value must be accounted for in the drude model. Since most metals are mostly free electrons the value$\epsilon_ib(\omega)$, is a constant known as$\epsilon(\infty)$. This is the value that you were wondering about. The equation for it is: $$\epsilon_ib(\omega)=1+{\omega_1^2}/{(\omega_0^2-\omega^2-i\gamma\omega)}$$ This should give you the value for$\epsilon(\infty)\$ for all metals.

Also, if you had thoroughly read the Johnson & Christy paper you would know that the first model (first equation you listed) only relates to the second in that, the first model is inaccurate for real world applications.

To actually experimentally find these values you have to go back into Johnson & Christy's paper or one of the paper's to see how they experimentally achieved these values. However I don't think this was your question. I think your question was more concerned more how to find these values in tables and secondly where these values were derived from.

Also if you have access, I'd suggest getting a copy of Optical Metamaterials: Fundamentals and Applications by Wenshan Cai & Vladimir Shalaev, the second chapter of the book does an excellent job of describing this.

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Ok, +1 now you have enough reputation to post the link. –  DIMension10 Nov 15 at 3:23