Influence of interface on surface plasmon frequencies of metallic nanosphere

A semi-analytical approximate method of calculation of surface plasmon (SP) frequency of a metallic nanoparticle near an interface is developed. The method allows transformation of the problem to solution of coupled algebraic equations for arbitrary values of parameters-particle radius, distance between the sphere and interface, dielectric permittivities of the matrix and metal. The approach is based on the fact that it is possible to find the point inside the sphere, with respect to which the quadrupole moment of the charge distribution on the sphere surface vanishes. Frequencies of the longitudinal and transversal oscillations of the system, both in-phase and counter-phase, are calculated. Obtained SP frequency dependence on the particle-interface separation can be used in biosensorics.