Resonant-state expansion for waveguides with a Sellmeier dispersion

Authors:
  • MDM. B. Doost
    M. B. Doost
  • WLW. Langbein
    W. Langbein
  • EME. A. Muljarov
    E. A. Muljarov
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Abstract
The resonant-state expansion (RSE), a rigorous perturbative method developed in electrodynamics for non-dispersive optical systems is further developed to treat wave guides with a Sellmeier dispersion. For media which can be described by these types of dispersion over the relevant frequency range, such as optical glass, the perturbed problem can be solved by diagonalising a second-order eigenvalue problem. In the case of a single resonance at zero frequency, this is simplified to a generalised eigenvalue problem. Results are presented using analytically solvable planar waveguides and parameters of 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. Included is the RSE Born Approximation for waveguides.