Regular plasmonic nanostructures have made great progress in numerous applications, such as nano-lasers, sensing, solid-state lighting, and so on, in which a crucial performance? with lower loss or high quality (Q) factor plasmonic resonances is improved. Hybridization of mixed plasmon-photonic modes can be known as surface lattice resonances (SLRs) in nanoparticle arrays, which originated from the coupling of localized surface plasmon resonances (LSPRs) to in-plane diffraction orders——so-called Rayleigh anomalies (RAs)——in a homogeneous environment, leading to extremely narrow resonances. Single metallic nanoparticle, however, can support both dipolar and quadrupolar resonances by increasing the size of nanoparticle, and dipolar lattice plasmon modes (DLPMs) or quadrupolar lattice plasmon modes (QLPMs) can be achieved through shifting diffraction orders related to particle-particle spacing and refractive index concerning these LSPRs in arrays of metallic nanoparticles.
In this letter, we explored sharp QLPMs of the silver nanodisks arrays in the visible region by adjusting lattice periods in x and y directions or the size of nanodisks. In the first place, scattering cross-section and near-field electric field distribution of single silver nanodisk indicate the existence of dipolar and quadrupolar LSPRs, and thus the optical response of silver nanodisk arrays exhibits the peak-and-dip profile of DLPMs and QLPMs at different wavelengths. The difference is that the propagation direction of QLPMs is along the direction of the incident electric field, while that of the DLPMs is just the opposite. Therefore, we can enable these resonance modes to be selectively accessed and individually optimized by tuning lattice periods in the x- or y-direction. By changing the lattice period in the x-direction from 300 nm to 550 nm with a step of 50 nm, transmission dips intensity increase gradually, and when the periods in the two directions are equal, the transmission dip exhibits a narrow-band QLPM resonance with a linewidth of 0.4 nm, corresponding quality factor as high as Q=1815 under the x-polarized light. In particular, by varying periods in the y-direction, the QLPM resonance can also be manipulated ranging from an asymmetric Fano-like lineshape peak to a dip. Moreover, we also have proved that the size of silver nanodisks play also a crucial role in the realization of QLPMs. The acquisition of these results may provide a design strategy for high-quality factor resonances in nanolasers, sensing, and nonlinear optics.