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Plasmonic nanoarrays which support collective surface lattice resonances(SLRs) have become an exciting frontier in plasmonics. Compared with thelocalized surface plasmon resonance (LSPR) in individual particles, thesecollective modes have appealing advantages such as angle-dependent dispersionsand much narrower linewidths. Here, we investigate systematically how thegeometry of the lattice affects the SLRs supported by metallic nanoparticles.We present a general theoretical framework from which the various SLR modes ofa given geometry can be straightforwardly obtained by a simple comparison ofthe diffractive order (DO) vectors and orientation of the nanoparticle dipolegiven by the polarization of the incident field. Our experimental measurementsshow that while square, hexagonal, rectangular, honeycomb and Lieb latticearrays have similar spectra near the $\Gamma$-point ($k=0$), they haveremarkably different SLR dispersions. Furthermore, their dispersions are highlydependent on the polarization. Numerical simulations are performed to elucidatethe field profiles of the different modes. Our findings extend the diversity ofSLRs in plasmonic nanoparticle arrays, and the theoretical framework provides asimple model for interpreting the SLRs features, and vice versa, for designingthe geometrical patterns.

Geometry dependence of surface lattice resonances in plasmonic nanoparticle arrays