Figure 1. Measured dispersion of the SLR modes.

(a) The angle-resolved transmission/luminescence spectra were collected by focusing the image of the backfocal plane of the objective to the entrance slit of the spectrometer. For transmission measurements, a white light source was used. For lasing measurements, the gain medium was pumped with a femtosecond pulsed laser. (b) A schematic of the sample, consisting of rectangular arrays of silver nanoparticles on a borosilicate substrate, a gain medium and a cover glass. (c) A scanning electron micrograph of a typical sample. The scale bar is 200 nm. (d) Measured extinction of a typical sample, showing the dispersion of the SLR, which results from the hybridization of the nanoparticle surface plasmon resonance with the diffracted 〈+1,0〉 and 〈−1,0〉 orders of the lattice (denoted by dashed lines; the crossing of the dashed lines is referred to as the Γ-point). The location of the dark mode is indicated by the black circle. The colour bar indicates the value of extinction (1-transmission). (e–f) Charge and field distributions of the bright and dark modes for the infinite lattice, obtained from Finite-Difference Time-Domain (FDTD) simulations with periodic boundary conditions. The character of these modes can be understood by considering an array of nanoparticles with period p_x=p_y mainly polarized along y direction and thus radiating predominantly along the −x and +x direction. Two counter-propagating radiation fields result to a standing wave which has either a node or an antinode at each particle location, corresponding to the dark or bright mode at k=0, respectively.