M-Point Lasing in Hexagonal and Honeycomb Plasmonic Lattices

This paper reports the observation of band-edge states at the high-symmetry M-point in the first Brillouin zone of hexagonal and honeycomb plasmonic nanoparticle (NP) lattices. The surface lattice resonance at the M-point (SLRM) of a hexagonal lattice results from asymmetric out-of-plane dipole coupling between NPs. In contrast to the hexagonal lattice, honeycomb lattices support two SLR modes at the M-point because of their non-Bravais nature: (1) a blue-shifted SLRM1 from the coupling of two distinct out-of-plane dipole LSP resonances, and (2) a red-shifted SLRM2 from in-plane dipole–dipole coupling. By incorporating organic dye solutions as gain media with Ag NP lattices, we achieved M-point lasing from both hexagonal and honeycomb lattices. Understanding coupling mechanisms at high-symmetry points in NP lattices with the same geometry but different unit cells is important to assess the prospects of topological states in plasmonic systems.