Resonant-state-expansion Born approximation for waveguides with dispersion

Abstract

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.