Resonant state expansion applied to planar waveguides

The resonant state expansion, a recently developed method in electrodynamics, is generalized here to planar open optical systems with non-normal incidence of light. The method is illustrated and verified on exactly solvable examples, such as a dielectric slab and a Bragg reflector microcavity, for which explicit analytic formulas are developed. This comparison demonstrates the accuracy and convergence of the method. Interestingly, the spectral analysis of a dielectric slab in terms of resonant states reveals an influence of waveguide modes in the transmission. These modes, which on resonance do not couple to external light, surprisingly do couple to external light for off-resonant excitation.