= Thin-cavity enhancement of a normal electric dipole
{title2=$A_\perp/A_{\rm free}=3\pi c/(2\omega_0d)$}
For a normal transition dipole of magnitude $D$, the <Fermi's golden rule>, one-polarization mode density $\omega/(2\pi c^2d)$ and single-photon squared field $\hbar\omega/(2\epsilon_0V)$ give $A_\perp=D^2\omega_0^2/(2\epsilon_0\hbar c^2d)$. Dividing by the <free-space electric-dipole spontaneous emission rate> gives the title. The factor three relative to the scalar density-of-states ratio comes from the isotropic free-space polarization average. This ideal <weak coupling> formula assumes wide plates and unperturbed atomic structure, with atomic size much smaller than $d$.
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