  The resonant state expansion (RSE), a rigorous perturbative method in
electrodynamics, is formulated for Transverse Electrodynamic modes of an
effectively $2$-dimensional system. The RSE is a perturbation theory based on
the Lippmann Schwinger Green's function equation and requires knowledge of the
Green's function of the unperturbed system constructed from Resonant-states. I
use the analytic Green's function for the magnetic field to normalize the modes
appearing in the corresponding spectral Green's function. This use of the
residue and cut of the analytic Green's function is a solution to the failure
of the flux volume integral method of normalization for continuum states, a
problem which is discussed in detail in this manuscript. In brief, the flux
volume integral fails for continuum states because they are not true resonance.
An analytic relation between normalized magnetic and electric modes is
developed as part of the solution to these difficulties.The complex
eigenfrequencies of modes are calculated using the RSE for the case of a
homogeneous perturbation.
