Resonant dipole-dipole interaction in a cavity

Resonant dipole-dipole interaction (RDDI) in a Fabry-P\'erot cavity is studied by the mode-expansion method. It is shown that the RDDI depends upon three factors: the length of the cavity, the positions of molecules, and the polarization of dipoles. It is also revealed by the mode-expansion calculation that, instead of contributions only from the propagating modes, the RDDI can also be assisted by the evanescent photons in the cavity. The expressions of energy transfer rate are obtained both for the two-level model and multilevel one in terms of observed spectral shape functions.