  We evaluate the exact dipole coupling strength between a single emitter and
the radiation field within an optical cavity, taking into account the effects
of multilayer dielectric mirrors. Our model allows one to freely vary the
resonance frequency of the cavity, the frequency of light or atomic transition
addressing it and the design wavelength of the dielectric mirror. The coupling
strength is derived for an open system with unbound frequency modes. For very
short cavities, the effective length used to determine their mode volume and
the lengths defining their resonances are different, and also found to diverge
appreciably from their geometric length, with the radiation field being
strongest within the dielectric mirror itself. Only for cavities much longer
than their resonant wavelength does the mode volume asymptotically approach
that normally assumed from their geometric length.
