Robust plasmonic Fano resonance in π-shaped nanostructure Supporting Information Zhendong Yan, 1 Ping Gu,1 Wenjing Bao, 2 Wei Du,1 Zhuo Chen, 1,* Xinhua Xia,2 and Zhenlin Wang1,* 1 School of Physics and National Laboratory of Solid State Microstructures School of Chemistry and Chemical Engineering, Nanjing University, Nanjing 210093, China *Corresponding authors: (Z.C.) zchen@nju.edu.cn (Z.L.W.) zlwang@nju.edu.cn 2 Contents Fig. S1 The magnetic diople modes of L-shape and the two π-shaped nanostructures Fig. S2 The magnified SEM image of Au PODT array and the calculation of scattering, absorption and extinction of an individual PODT Fig. S3 Experimental and calculated transmittance spectra of a single triangle array upon exposure to the dielectric media with different index of refraction Fig. S1 The magnetic diople modes of L-shape and the two π-shaped nanostructures Fig. S1 The magnetic diople modes of L-shape and the two π-shaped nanostructures under normal incident excitation with the polarization state shown the top-left. The schematic of the three types of nanoparticles and the corresponding magnetic field (H), surface current distributions and vertical component (Hz) of magnetic field are shown in left, middle and right columns. The corresponding geometrical parameters are given as the same as shown in Fig. 1 and Fig. 3 in the main text Fig. S2 The magnified SEM image of Au PODT array and the calculation of scattering, absorption and extinction of an individual PODT Fig. S2: a The magnified SEM image of Au PODT array. The distance (d) between bases of the PODT nanostructures is around 80 nm, which means the plasmonic coupling between the PODT nanostructure bases is very weak. b The calculated spectra of scattering, absorption and extinction for an individual Au PODT under normally incident light with y polarization. The arrows labeled as p3 and p4 correspond to the two plasmonic modes of the corresponding PODT array. c The simulated absorption spectrum of an individual Au PODT and the transmittance spectrum of the corresponding PODT array with y polarization. The results plotted in c show that both a single PODT and the PODT array have almost identical plasmon modes under the y-polarization excitation, which means that the influence of the plasmonic coupling between the PODT nanostructure bases is very weak and could be neglected Fig. S3 Experimental and calculated transmittance spectra of a single triangle (ST) array upon exposure to dielectric matrix with different values of refractive index (n) Fig. S3: a Experimental and b calculated transmittance spectra for the Au ST sample exposed to dielectric matrix with different refractive index under a normal incidence of y-polarized light. c Linear plot of the localized surface plasmon resonance (LSPR) wavelength shifts of the Au π-shape sample as shown in Fig. 3b in the main text and Au ST vs refractive index of the embedding medium. The obtained FoM is 3.5 for Au π-shaped sample and 0.9 for ST