Quantization of electromagnetic fields in cavities and spontaneous emission

A quantization procedure was developed with three-dimensional boundary conditions from the theoretical aspect. This procedure was applied to three different boundary conditions in the rectangular coordinate system. Three kinds of cavities were considered. In each case, certain normal modes were introduced to carry out canonical quantizations of the fields in the cavities. The multipolar expansion of the interaction between an atom and the fields in the cavities has been obtained. In addition, the spontaneous emission by an atom in the cavities was studied employing the field-theoretic methods. The transition rates per second in the three types of cavities were obtained, showing an intriguing side-mirror effect.