Influence of the filling factor on the spectral properties of plasmonic crystals

Plasmonics crystals (PCs) comprised of finite-size triangular lattices of gold bumps deposited on a gold thin film are studied by means of a near-field optical microscope. The plasmonic crystals fabricated by electron-beam lithography are illuminated by an incident surface plasmon polariton excited in the Kretschmann-Raether configuration at the gold/air thin-film interface for incident free-space wavelengths in the range $740–820\mathrm{nm}$. Based on the measurement of the surface plasmon polariton (SPP) damping distance in the crystals, the existence of a band gap for an incident SPP traveling along the two symmetry axes $\Gamma M$ and $\Gamma K$ is demonstrated. By increasing the lateral size of the bumps, the influence of the filling factor on the PC spectral properties is investigated. We show that, for the two $\Gamma M$ and $\Gamma K$ axes, the central gap frequency depends only weakly on the filling factor, whereas we observed a neat band-gap broadening for increasing filling factors. The experimental results are found to be consistent with the PC band structures computed by means of the differential method. In particular, a good agreement between the experimental and theoretical central gap frequencies for the two $\Gamma M$ and $\Gamma K$ axes is obtained. Finally, we investigate the origin of the band gap in PCs by computing modal reflectivity (or in-plane reflectivity) of semi-infinitely extended crystals. From these calculations, we show that the SPP propagation through a PC is inhibited by distributed reflection and not by losses channels such as absorption or out-of-plane scattering.