Spontaneous emission from photonic crystals: Full vectorial calculations

Quantum electrodynamics of atom spontaneous emission from a three-dimension al photonic crystal is studied in a full vectorial framework. The electroma gnetic fields are quantized via solving the eigenproblem of photonic crysta ls with use of a plane-wave expansion method. It is found that the photon d ensity of states and local density of states (LDOS) with a full band gap va ry slowly near the edge of band gap, in significant contrast to the singula r character predicted by the previous isotropic model. Therefore, the spont aneous emission can be solved by conventional Weisskopf-Wigner approximate theory, which yields a pure exponentially decaying behavior with a rate pro portional to the LDOS.