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

Resonant-state expansion of dispersive open optical systems