  The resonant state expansion (RSE), a rigorous perturbative method in
electrodynamics, is applied to two-dimensional open optical systems. The
analytically solvable homogeneous dielectric cylinder is used as unperturbed
system, and its Green's function is shown to contain a cut in the complex
frequency plane, which is included in the RSE basis. The complex
eigenfrequencies of modes are calculated using the RSE for a selection of
perturbations which mix unperturbed modes of different orbital momentum, such
as half-cylinder, thin-film and thin-wire perturbation, demonstrating the
accuracy and convergency of the method. The resonant states for the thin-wire
perturbation are shown to reproduce an approximative analytical solution.
