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.
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JOURNAL OF THE KOREAN PHYSICAL SOCIETY Volume: 53 Issue: 2 Special Issue: Part 1 Sp. Iss. SI Pages: 1241-1245 Part: Part 1 Sp. Iss. SI
