Surface plasmon resonances of silver triangle nanoplates: graphic assignments of resonance modes and linear fittings of resonance peaks

The extinction spectra of five silver equilateral triangle plates with a fixed thickness of 10 nm and side lengths of 50, 100, 150, 200 ,and 250 nm, respectively, have been simulated by the discrete dipole approximation (DDA) method in which a geometric object of interest is meshed and represented by a lattice of spatial dipoles. Irradiated by an incident plane wave with a given propagation direction and polarization state, each triangle nanoplate presents three surface plasmon resonance (SPR) peaks in the range of 300 to 1200 nm. At a given peak, every complex spatial oscillatory vector derived by DDA (corresponding to a certain dipole in the meshed target) is orthogonally resolved into three basic oscillations. Each basic component can be subsequently expressed by two parameters, amplitude (P) and phase angle (varphi). The distributions of six such physical parameters of all the dipoles in the selected cross plane of the target are illustrated colorfully in plots as a graphic characterization and assignment of the SPR modes. The graphic method is applied to reveal the local fine features of SPR modes. And it provides direct evidence for classifying SPR peaks which belong to different triangle nanoplates and appear at different wavelengths. Three SPR modes are recognized graphically and the wavelengths of SPR peaks are found to have linear relationships with the side lengths of the triangle nanoplates.