Surface plasmon modes of a nanoegg above a substrate

An analytical approach describing the surface plasmon modes of a nanoegg (a nanoshell with a nonconcentric core) above a substrate is presented. The bispherical coordinate system is used for mathematical convenience. A general dispersion relation for the coupled modes as function of geometrical characteristics of the system is obtained. In the special case (in the limit of a very large separation between the nanoegg and substrate) dispersion relation of the plasmon modes of an isolated nanoegg is derived. It is shown that the coupled plasmon modes exhibit excellent numerical convergence.