Extended Data Fig. 4: Basis decomposition for LSPRs of a AuNCat by group representation analysis.
a, Symmetry operations for the D2d symmetric structure of a AuNCat. D2d point group has one C2 main axis and two perpendicular C2 axes with two mirror planes. b, Structure of a AuNCat used in the group representation analysis. The direction of light propagation is perpendicular to the C2 main axis and parallel to one of mirror planes while the polarization direction of electric field is parallel to C2 main axis. The major and minor diameter are 100 nm and 47 nm, respectively, and the gap distance is 3 nm. c, Theoretical extinction (black line), scattering (red line), and absorption (blue line) cross-section of the AuNCat shown in b. Two LSPRs, SBM and GDM, are marked by green and violet triangles, and their resonance wavelengths are 761 nm and 603 nm, respectively. d, Decomposed basis modes of the LSPRs of the AuNCat corresponding to their own irreducible representations. The contribution of the B2 symmetric basis dominates inter alia in both resonances, which implies that the two LSPs can interfere according to their respective phases.
