Purcell effect in disordered one-dimensional photonic crystals

The rate of spontaneous emission of an emitter placed in a disordered one-dimensional photonic crystal is analyzed. It is shown that the spontaneous emission of a dipole placed in a disordered photonic crystal can either be enhanced (if the frequency corresponds to an optical eigenmode of the structure) or suppressed (if the frequency lies in the band gap or the position of the emitter corresponds to a node in the electric- field profile of the eigenmode). It is demonstrated that, for high levels of disorder, the photonic band gap is narrowed and the emission rate at the center of the band gap becomes significantly different from zero. Furthermore, for high levels of disorder, localized states featuring significantly enhanced spontaneous emission may appear within the photonic band gap.