Resonant-state expansion of dispersive open optical systems

A resonant-state expansion (RSE) for open optical systems with a general frequency dispersion of the relative permittivity, described by a finite number of simple poles, is presented. As in the non-dispersive case, the RSE of dispersive systems converts Maxwell's wave equation into a linear matrix eigenvalue problem in the basis of unperturbed resonant states, in this way numerically exactly determining all relevant eigenmodes of the optical system. This dispersive RSE is verified by application to the analytically solvable system of a sphere in vacuum, with a dispersion of the dielectric constant described by the Drude and Drude-Lorentz models. We calculate the change of the optical modes when converting the sphere material from gold to non-dispersive silica and back to gold, and evaluate the accuracy using the exact solutions.