Plasmon model of an asymmetric nanosphere pair

Abstract

This study focuses on the effects of symmetry breaking to the localized surface plasmon resonance (LSPR) energy of coupled nanospheres in the strongly interacting regime. First, the fundamental roles of size asymmetry and material type asymmetry are investigated separately. Then, the symmetry breaking in both particle sizes and material types are studied. The LSPR energies are obtained within the quasistatic approximation by solving the Laplace equation in bispherical coordinate system. By applying the matrix calculation, the general condition for surface mode resonance is derived in terms of nonlinear eigenvalue problem. This allows us to interpret the LSPR coupling in the asymmetric nanosphere pair as the coupling between two images of symmetric nanosphere pairs of the constituent particles. The LSPR energies of the nanosphere pairs are calculated and the excited mode order analysis for the excited mode identifying in optical measurement is established. The results show that in the case of symmetry breaking due to material type, the lowest LSPR energy has bonding mode character and is bounded by the lowest LSPR energy of the bonding symmetric pair image states. The second lowest LSPR energy has bonding (antibonding) mode character at small (large) separation distance and changes its mode character at a particular separation distance defined as mode switching point. In the case of symmetry breaking due to particle sizes, the lowest LSPR energy has bonding mode character. The energy increases as the size ratio increases and has the lowest LSPR energy of the single sphere as the upper bound. The curvature of the second lowest LSPR energy curve decreases as the size ratio increases and has the lowest LSPR energy of the single sphere as the lower bound. In the case asymmetry in both of material type and particle sizes, the lowest LSPR energy is unbounded and the value of mode switching points decrease with increasing size ratio.