Fractional dynamics of the spontaneous emission of an atom in photonic crystals

Abstract

We studied the spontaneous emission of an atom in a photonic crystal with an isotropic band structure. We show that a fractal phenomenon induces the long-time memory of the spontaneous emission in the photonic crystal. The natural mathematics of describing the fractal phenomenon is fractional calculus. From fractional calculus, we show that no multiple-valued problem and no fractionalized steady-state inversion was encountered in the previous study [J. Opt. 13: Quantum Semiclass. Opt. 5, R43 (2003)] when the atomic transition frequency was within the allowed band.