Localization of Superradiance near a Photonic Band Gap

We describe collective spontaneous emission of $N$ two-level atoms placed within a photonic band-gap material. When the atomic resonance frequency lies at the band edge, superradiant emission remains localized in the vicinity of the atoms. This leads to a steady state with spontaneously broken symmetry in which the atomic system acquires a macroscopic polarization. The superradiant decay rate is proportional to ${N}^{2/3}$ and ${N}^{2}$ for isotropic and anisotropic 3D band gaps, respectively. The corresponding peak intensity of superradiance is proportional to ${N}^{5/3}$ and ${N}^{3}$, respectively.

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