The dielectric permittivities of plasmonic materials are defined by a Drude model, where the high-frequency permittivity limit is involved. What is the physcial meaning of this limit? Thank you.
You can take a look to the following link below.
http://ocw.mit.edu/courses/mechanical-engineering/2-58j-radiative-transfer-spring-2006/readings/chap6_solid_prop.pdf
For very high frequencies above electronic absorption the value of the permittivity is one. Going down in frequency, every absorption leads to an increase of the permittivity. Below the frequency range of the electronic absorptions all these contributions due to these absorptions can be summed up in a constant which is the "high-frequency permittivity limit" often called epsilon infinity. See attachment....
Thank you, Thomas Mayerhöfer. That's exactly what I want! While, the relationship between dielectric function and wavenumber in the picture attached is for dielectric material, instead of noble metal, am I right?
You are right, above the plasma frequency a metal behaves completely different from a dielectric, but below the behavior is comparable and so is the origin of the "high-frequency permittivity limit". I have attached the dielectric function of gold for comparison (notice the negative sign of the real part in the lower graph)
Do you mean the "Chi" like in the electric susceptibility? This is simply eps - 1, which does not make much of a difference (sorry, no pun intended... ;-) for lower wavenumbers....
Thomas Mayerhöfer Thank you for this explanation! Is this "high-frequency permittivity limit " a fixed number for every metal? I want this number for Gold and Silver.
For Gold:
https://aip.scitation.org/doi/full/10.1063/1.2360270?crawler=true
http://adsabs.harvard.edu/abs/2007JChPh.127r9901E
Gold and Silver:
Article An Analytic Model for the Dielectric Function of Au, Ag, and...
hello.
I work on Si and I want the permittivity at high frequencies of Si.
may you help me?
Taraneh Dehghan can you specify what exactly you mean by "high frequency"? Are we talking about the UV/Vis spectral range? Take a look at https://refractiveindex.info/?shelf=main&book=Si&page=Aspnes
As you probably know, you can calculate the real part of the permittivity by n2-k2 and the imaginary part by 2nk.
Thomas Mayerhöfer، thanks so much for your explanation. but it is routine to report an exact number in articles as infinit epsilon that most of the time is not equal to one.could you please explain about it? do you know how to find that?
Dear Atefe Marasi , I wish I could point you to a corresponding article (or book chapter), but there seems to be none. First, I have to correct one thing in this thread, namely eps_infinity is not the high-frequency limit, but the zero frequency limit of the UV-Vis contribution to the real part. What I can offer you is the first draft (just completed today!) to a new section for the script to my lecture series, which I attached to this answer. Please let me know if you find mistakes or if you want something explained in more details. The old version of the manuscript can be found under Preprint Wave optics in Infrared Spectroscopy
Dear Thomas Mayerhöfer,
Thanks a lot for your complete answer. Your lecture is exactly what I need.
Thank you very much.
best regards
Arefe Marasi
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