  The single-mode approximation of the resonant state expansion has proven to
give accurate first-order approximations of resonance shifts and linewidth
changes when modifying the material properties inside open optical resonators.
Here, we extend this first-order perturbation theory to modifications of the
material properties in the surrounding medium. As a side product of our
derivations, we retrieve the already known analytical normalization condition
for resonant states. We apply our theory to two example systems: A metallic
nanosphere and a one-dimensional photonic crystal slab.
