title: Spontaneous emission near the band edge of a three-dimensional photonic crystal: a fractional calculus approach.
abstract: We suggest a better mathematical method, fractional calculus, for studying the behavior of the atom-field interaction in photonic crystals. By studying the spontaneous emission of an atom in a photonic crystal with a one-band isotropic model, we found that the long-time inducing memory of the spontaneous emission is a fractional phenomenon. This behavior could be well described by fractional calculus. The results show no steady photon-atom bound state for the atomic resonant transition frequency lying in the proximity of the allowed band edge which was encountered in a previous study (Woldeyohannes and John 2003 J. Opt. B: Quantum Semiclass. Opt. 5 R43). The correctness of this result is validated by the 'cut-off smoothing' density of photon states (DOS) with fractional calculus. By obtaining a rigorous solution without the multiple-valued problem for the system, we show that the method of fractional calculus has a logically concise property.
authors.affiliation: Department of Physics, Chinese Culture University, Taipei, Taiwan, Republic of China.
authors.forename: Szu-Cheng
authors.initials: SC
authors.lastname: Cheng
authors.forename: Jing-Nuo
authors.initials: JN
authors.lastname: Wu
authors.forename: Ming-Rung
authors.initials: MR
authors.lastname: Tsai
authors.forename: Wen-Feng
authors.initials: WF
authors.lastname: Hsieh