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The resonant-state expansion (RSE), a rigorous perturbative method developedin electrodynamics for non-dispersive optical systems is applied to media withan Ohm's law dispersion, in which the frequency dependent part of thepermittivity scales inversely with the frequency, corresponding to afrequency-independent conductivity. This dispersion has only a single pole atzero frequency, which is already present in the non-dispersive RSE, allowing tomaintain not only the linearity of the eigenvalue problem of the RSE but alsoits size. Media which can be described by this dispersion over the relevantfrequency range, such as optical glass or doped semiconductors, can be treatedin the RSE without additional complexity. Results are presented usinganalytically solvable homogeneous spheres, for doped silicon and BK7 glass,both for a perturbation of the system going from non-dispersive to dispersivemedia and the reverse, from dispersive to non-dispersive media.

Resonant-state expansion for a simple dispersive medium