Role of Symmetry in Coupled Localized Surface Plasmon Resonance of a Nanosphere Pair

We investigated localized surface mode resonance of two nanospheres immersed in a continuum dielectric medium within the framework of quasistatic approximation. We solved the Laplace equation in the bispherical coordinates subjected to the boundary conditions on both spheres. By using the matrix formulation, new method for surface mode resonance calculation is derived in terms of a nonlinear eigenvalue problem. This allows us to discuss the effects of symmetry breaking due to the difference in particle materials and particle sizes. We calculated the surface plasmon resonance (LSPR) energy for pairs of Drude metallic spheres. The solutions show that the LSPR coupling in an asymmetric pair can be interpreted as the coupling between symmetric pairs of its constituent particles. we also analyzed the LSPR excitation sequence to identify the modes of peaks from optical measurement. We found that the ambiguous dipole antibonding sigma mode of the asymmetric Au-Ag pair in the experimental work (Sheikholeslami et al., Nano Lett 10(7):2655–2660, 2010) must be the quadrupole bonding sigma mode.