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 obtained. 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.