QUANTIZATION OF ELECTROMAGNETIC-FIELDS IN CAVITIES AND SPONTANEOUS EMISSION

The normal modes of electromagnetic fields satisfying three different boundary conditions are constructed systematically. For each of these cases, cavity quantization of the electromagnetic fields is carried ou t explicitly. It is possible, using normal modes, to perform a unitary transformation of the minimal-coupling Hamiltonian of an atom inside the cavity to a multipolar form. It is shown that the boundary conditi on plays an important role in the transition rates for the spontaneous emission by the atom. Some explicit calculations are carried out for several different boundary conditions. These results become consistent with those for free space in the large-box limit.