  The resonant-state expansion (RSE) Born approximation, a rigorous
perturbative method developed for electrodynamic and quantum mechanical open
systems, is further developed to treat waveguides with a Sellmeier dispersion.
For media that can be described by these types of dispersion over the relevant
frequency range, such as optical glass, I show that the perturbed RSE problem
can be solved by diagonalizing a second-order eigenvalue problem. In the case
of a single resonance at zero frequency, this is simplified to a generalized
eigenvalue problem. Results are presented using analytically solvable planar
waveguides and parameters of borosilicate BK7 glass, for a perturbation in the
waveguide width. The efficiency of using either an exact dispersion over all
frequencies or an approximate dispersion over a narrow frequency range is
compared. I included a derivation of the RSE Born approximation for waveguides
to make use of the resonances calculated by the RSE, an RSE extension of the
well-known Born approximation.
