  The resonant state expansion (RSE), a novel perturbation theory of
Brillouin-Wigner type developed in electrodynamics [Muljarov, Langbein, and
Zimmermann, Europhys. Lett., 92, 50010(2010)], is applied to planar,
effectively one-dimensional optical systems, such as layered dielectric slabs
and Bragg reflector microcavities. It is demonstrated that the RSE converges
with a power law in the basis size. Algorithms for error estimation and their
reduction by extrapolation are presented and evaluated. Complex
eigenfrequencies, electro-magnetic fields, and the Green's function of a
selection of optical systems are calculated, as well as the observable
transmission spectra. In particular we find that for a Bragg-mirror
microcavity, which has sharp resonances in the spectrum, the transmission
calculated using the resonant state expansion reproduces the result of the
transfer/scattering matrix method.
