The condition of a propagating surface plasmon wave in a metal film is that the refractive indexes of the metal and surrounding medium are opposite and equal (please correct me!) but this requires that the refractive index of, normally, the metal is negative.

A common example given is that of a gold thin film and the well known Johnson and Christy graph showing the real part of gold refractive index in the optical regime and towards IR too being negative.

When you look up a value for the refractive index of gold, in the same regime, it is positive - between 1 and 3.

How can these two facts be true simultaneously?

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    $\begingroup$ Are you comparing the refractive index of a thin film to the refractive index of something that is bulk? I would imagine, in general, this is always going to vary because of things like surface plasmons and other zoo of nanoscale effects. $\endgroup$ – John M Sep 8 '16 at 21:41
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    $\begingroup$ Are you confusing $\epsilon$ and (n,k) values? $\endgroup$ – Jon Custer Sep 9 '16 at 3:06

The condition for propagating surface plasmon waves is not that the refractive indices n of the metal and the surrounding medium have opposite signs! The condition is that the real parts of the complex relative permittivities Re(𝜀) have opposite signs. This is usually achieved by the metal having a negative Re(𝜀) in the considered frequency range due to the plasma effects of free electrons. The refractive index n of metals and all simple dielectrics is always positive, even if the real part of the permittivity is negative.(See, e.g., Wikipedia "Refractive Index", where the equations relating n and the extinction coefficient 𝜅 to the complex relative permittivity are shown.) So the fact that you find a positive n for gold in the literature is no contradiction to the negative Re(𝜀).

  • $\begingroup$ thank you for your answer, could you also comment on what the intuition should be here - relating to how only the opposite permittivites support the SPP? $\endgroup$ – Mark Corrigan Sep 10 '16 at 16:25
  • $\begingroup$ @ Mark Corrigan - you have to look at the derivation of the dispersion relations from Maxwells equations using the boundary conditions and assuming sinusoidal waves in the adjacent media. The dispersion relations show that solutions that are surface (or better interface) waves which propagate along the interface and decay exponentially laterally in both media only exist when the real parts of the permittivities have opposite signs. (Wikipedia under "Surface plasmon polaritons" gives dispersion relations with references regarding the their derivation.) $\endgroup$ – freecharly Sep 14 '16 at 22:26

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