FDTD simulations with negative, non-infinite real part of epsilon are known to be unstable. Even if you use a single optical frequency, you will run into trouble, as the switching on of the source already gives rise to band of frequencies. The solution is to use Drude-Lorentz susceptiblities to model your materials. If you use only a single wavelength, this becomes easy, as a single term to get the correct value. If you need it to work over a broad range of frequencies, you generally need more terms.
The reason that the Drude-Lorentz expression can be expected to work, whereas a constant negative real part of epsilon does not is that the former obeys the Kramers-Kronig relations and the latter does not! best, Dries ________________________________________ From: meep-discuss [meep-discuss-boun...@ab-initio.mit.edu] on behalf of Weiner John [johwei...@gmail.com] Sent: Thursday, June 19, 2014 2:07 PM To: meep-discuss@ab-initio.mit.edu Subject: [Meep-discuss] real metal material Dear meep users and experts: I am really stuck, and I need your help. I am trying to implement a real metal material such a silver (Ag) or gold (Au): these are materials with a negative real relative permittivity and a positive imaginary permittivity. According to “Materials in Meep” it should be possible to characterize the leading (frequency independent) term of the complex permittivity by specifying the real epsilon (for metals this is a negative number) and the D-conductivity. The D-conductivity is expressed in terms of the imaginary part of epsilon (see the first equation on the “Materials in Meep” page). If one knows the real part and the imaginary part of the permittivity at a given wavelength of interest, then one knows the D-conductivity at that wavelength, and one should be able to use meep to simulate the electromagnetic fields in and around an object characterized by that material. So far so good…it works as advertised for positive real permittivities, but generates NaN fields if negative real permittivities are invoked. A frequency-dependent Drude or Lorentz expression always has as the leading term the same frequency-independent expression as described above. So if the D-conductivity approach at fixed wavelength (or frequency) does not work, then there is no reason to expect the Drude-Lorentz expressions to work either. The use of the “metal” material, which is a perfect electrical conductor (PEC), does produce meaningful fields in meep. The PEC is characterized by epsilon -> negative infinity without loss (imaginary permittivity = 0). Since “metal” works, one would think that a large negative real epsilon and reasonably small loss term would work as well and would show slight field penetration into these materials (skin depth), etc. If someone has a little piece of meep code that they could show me as an example of a real metal, I would be most grateful. I just don’t see any way forward from here. Best regards, John WEINER 22 Ave. de la Sibelle 75014 Paris _______________________________________________ meep-discuss mailing list meep-discuss@ab-initio.mit.edu http://ab-initio.mit.edu/cgi-bin/mailman/listinfo/meep-discuss _______________________________________________ meep-discuss mailing list meep-discuss@ab-initio.mit.edu http://ab-initio.mit.edu/cgi-bin/mailman/listinfo/meep-discuss
