Dear John, I believe your paragraph on setting the epsilon at one given frequency is correct: The real part can be set directly. The imaginary part of permittivity is introduced by setting conductivity. I use the same approach and the frequency-domain computations give results that can be directly compared to those coming from Fourier transform of time domain data and to the experimental data from our laboratory. There is a relatively good match.
HOWEVER, according to to my experience so far, the real part of permittivity may never be negative even in frequency-domain computation in MEEP. Whenever I defined the constant-part-of-permittivity to be negative, the FDTD/FDFD simulation always became unstable. You wrote that it "generates NaN fields if negative real permittivities are invoked", so this could be the case (except for the detail that NaN data always identified an instability in my time-domain computations. I never ever observed NaNs resulting from a frequency-domain computation in MEEP. Are you sure e.g. MEEP terminated correctly?) I can see two solutions: 1) use epsilon=1 and some high conductivity; this defines a lossy conductor. You will correctly simulate electromagnetic resonances up to infrared frequencies, but no plasmon-related effects. 2) Switch to a FDTD simulation with a long enough gaussian source, which takes more time thand FDFD, but enables realistic metal model. BTW if I am correct, there is a little misconception in your last paragraph: The PEC is characterized by epsilon just going to "complex infinity", not "minus infinity". If epsilon was huge real positive, it leads to huge permittivity --> PEC, if it was huge real negative, it is a lossless metal with tiny electron mass --> PEC, if it had huge positive imaginary part, it is a inductance-free conductor with tiny resistivity, again --> PEC. Complex infinity has no sign. Hope this helps, Filip Dominec IOP ASCR, Prague 2014-06-19 14:07 GMT+02:00, Weiner John <johwei...@gmail.com>: > 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
