Surface plasmon polaritons and negative refraction in fishnet metamaterial

Surface plasmon polaritons (SPP), supporting sub-wavelength confinement of light [1], enable a great potential for nanophotonic applications. SPP modes of flat interfaces, such as insulator-metal-insulator (IMI), and MIM geometries have been well investigated, however, more complicated structures used in metamaterial design need further exploration. In this work we characterize electromagnetic response of a fishnet metamaterial in analogy with the SPP modes of an IMIMI structure and associate its lowest order internal SPP mode to the so-called negative refractive response of the fishnet. The sample, fabricated using nano-imprint lithography, is comprised of 40-20-40 nm sandwich of Ag-SiO2-Ag layers on a glass substrate, and perforated by a P = 200 nm period square array of holes. Inset of Fig. 1b schematically shows the experimental setup. The wave-vector of the incident polarized light kⁱ is defined by the angle of incidence relative to the z-axis (θ). In order to measure inplane dispersion of the fishnet Bloch SPPs, k|| is swept along the Γ-X direction of the1st Brillouin zone, by varying θ. Figure 1 shows the measured band-structure of the fishnet, mapped by varying θ from 0° to 80° with 2° increments. SPP modes of the corresponding IMIMI geometry folded to the first Brillouin zone of the fishnet lattice are superimposed as dotted lines. Where, eSPP1(m, n) and eSPP2(m, n), represent the external SPP modes at the substrate and air interfaces, respectively, while iSPP1(m, n) shows the internal SPP resonances confined in the SiO2 spacer region. The calculated values of average electric field magnitudes <|E|> at cross sections between the holes (orange areas in the inset of Fig. 1) show a strong correlation between resonant field enhancement and features in the transmittance spectra. The modes labelled as iSPP1(−1,0), iSPP1(1,0) and iSPP1(−1,±1) show a significant field enhancement within the gap region, while, eSPP1, and eSPP2 have their peaks at the substrate and air side respectively, confirming the relation of Bloch SPPs with matching folded IMIMI SPPs. The significantly increased confinement and field enhancement is the specific of fishnet gap plasmon inherited from the MIM SPPs [2], and absent in the conventional EOT [3]. Of particular interest is the lowest frequency negative dispersion mode, iSPP1(−1,0), which has the highest field enhancement accompanied by a strongly backward power flux <Sx>. This mode is usually associated with negative effective index of refraction at normal incidence. In conclusion, we have observed the geometrically designed dispersion of fishnet SPPs, and pointed out their distinct features. In particular, backward gap plasmons lead to negative refraction.