  A Brillouin-Wigner perturbation theory is developed for open electromagnetic
systems which are characterised by discrete resonant states with complex
eigenenergies. Since these states are exponentially growing at large distances,
a modified normalisation is introduced that allows a simple spectral
representation of the Green's function. The perturbed modes are found by
solving a linear eigenvalue problem in matrix form. The method is illustrated
on exactly solvable one- and three-dimensional examples being, respectively, a
dielectric slab and a microsphere.
