  Using the resonant-state expansion for leaky optical modes of a planar Bragg
microcavity, we investigate the influence of disorder on its fundamental cavity
mode. We model the disorder by randomly varying the thickness of the Bragg-pair
slabs (composing the mirrors) and the cavity, and calculate the resonant energy
and linewidth of each disordered microcavity exactly, comparing the results
with the resonant-state expansion for a large basis set and within its first
and second orders of perturbation theory. We show that random shifts of
interfaces cause a growth of the inhomogeneous broadening of the fundamental
mode that is proportional to the magnitude of disorder. Simultaneously, the
quality factor of the microcavity decreases inversely proportional to the
square of the magnitude of disorder. We also find that first-order perturbation
theory works very accurately up to a reasonably large disorder magnitude,
especially for calculating the resonance energy, which allows us to derive
qualitatively the scaling of the microcavity properties with disorder strength.
