Superradiant mode and photonic band of a one-dimensional resonant Bragg reflector

Based on a most general framework of dispersion equation for EM waves in a periodic system which contains both the effects of resonant levels and Bragg reflection, we have derived the dispersion equations of polaritons in the 1D resonant Bragg reflector (lattice constant equal to one half of the resonant wavelength). This equation gives a gap mode in the middle of the lowest photonic gap, which does not exist in the dispersion derived from a transfer matrix in the absence of nonradiative damping. The evolution of the superradiant (SR) mode is discussed as a function of the layer number N of the Bragg reflector from the reflectance in frequency and time domains. The frequency dependence of radiative correction is shown to be essential to obtain the consistent picture of the SR mode (small N) and photonic band formation (large N) in the whole range of N.