> > > Hi Aaron, > > > >> Dear meep users,By the 3D simulation using MEEP, the transmission > >> property at > >> wavelengths 500~1000nm of 2D periodic array of Au nanoholes has now > been > >> achieved, from which an obvious SP resonant wavelength is observed. To > >> theoretically verify the simulation results, the commonly used formula, > >> lambda(SP) = a / sqrt ( i^2 + j^2 ) * sqrt ( epsilon(Au) * > >> epsilon(dielectric) / > >> ( > >> > epsilon(Au) + epsilon(dielectric )?) ), is employed. (a is the array > >> periodicity.)Then, a question occurs: for the theoretical calculation, > >> how > >> should I set the permittivity of gold? As it is a variable value > >> depending > >> on > >> the wavelength, the permittivity of which wavelength is appropriate for > >> this > >> purpose??Any comments and suggestions are welcomed, and will be highly > >> appreciated. Thanks in advance. > >> > >> > >> If you only want to verify that you've matched the SP resonance > >> condition, > >> it's > >> probably good enough to use the permittivity at a single wavelength. > Of > >> course, > >> make sure that the theoretical value is the one meep is using. > >> > > > > Thank you for your reply. > > > > I know your meaning, and that's exactly what I want to do now. However, > the > > question is: which single wavelength is appropriate for such purpose? > > Because the permittivity of gold depends on the wavelength. I have tried > a > > series of calculations with different wavelengths from the aimed > spectrum > > (500~1000nm). The results for different wavelengths differ greatly. > > > > Looking forward to any further comments on this problem. > > > > Tony > > It's a bit of time that I do not use MEEP, but I have got a hunch that you > need to specify the dielectric function of gold in a range of frequencies > using a Drude-Lorentz expansion - people that understand the physics and > numerics better than I do could confirm or deny, but there is a problem > with causality if using a negative epsilon without dispersion (with or > without an imaginary part). > > I suggest you have a look at this > > http://ab-initio.mit.edu/wiki/index.php/Meep_Tutorial/Material_dispersion > > and this > > http://www.mail-archive.com/[email protected]/msg03871.html > > Doing a Google search I have furthermore found this: which I did not > check, so I cannot say it is completely correct, but looks helpful > > > http://www.torrkish.com/index.php/research/34-meep/46-lorentz-drude-expansion-in-meep > > > Giovanni >
Hi Giovanni, Thanks for your reply and the links. I am sorry that I didn't make it so clear to my question. As for the meep simulation with dispersive materials, I have no problems and it goes well. At this stage, I just want to theoretically calculate the SPR wavelength using the formula mentioned to verify the simulation results. According to the related literatures, the permittivity for a specific wavelength from the concerned spectrum is used. However, none gives the reason why that wavelength is chosen. I made a calcualtion with different wavelengths, the achieved SPR wavelength differs greatly. Now, I am totally confused. Tony Uni. Freiburg, Germany
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