= Plasmonics
<Plasmonics> studies and uses the coupling of <electromagnetic waves> with collective electron motion, especially at material surfaces and in small metallic structures. A <surface plasmon polariton> propagates along an interface while its field decays away from it; a <localized surface plasmon resonance> confines an oscillating response near a finite structure. Such modes can concentrate fields on scales smaller than the free-space <wavelength>.
For an ideal flat interface between a lossless metal of relative <permittivity> $\varepsilon_m$ and a dielectric of relative <permittivity> $\varepsilon_d$, the bound transverse-magnetic mode has
$$
k_{\parallel}=\frac{\omega}{c}\sqrt{\frac{\varepsilon_m\varepsilon_d}{\varepsilon_m+\varepsilon_d}}.
$$
With $\varepsilon_d>0$ and $\varepsilon_m<-\varepsilon_d$, its parallel wave number exceeds that of a propagating wave in the dielectric. This explains why direct illumination of a perfectly flat interface needs additional momentum coupling. A grating or nearby optical field can supply that coupling. Real metals have loss: stronger confinement does not automatically imply long propagation distances.
A striking <experiment> used periodic arrays of tiny holes in metal films. In 1998, <T. W. Ebbesen> and colleagues reported transmission peaks at <wavelengths> much larger than individual hole diameters. One silver sample had 150-nanometre holes, 900-nanometre spacing and 200-nanometre film thickness. A spectrophotometer measured the transmitted beam, and angle-dependent spectra supported coupling to surface electronic excitations. Efficiency normalized to hole area could exceed one; this compares with the small open area, not with all incident power.<Extraordinary optical transmission through sub-wavelength hole arrays by T. W. Ebbesen and others>[Page 667 and Figures 1–3: fabrication, transmission geometry, area normalization and angle dependence]{ref}
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