Spontaneous emission near the band edge of a three-dimensional photonic crystal: a fractional calculus approach

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题名:	Spontaneous emission near the band edge of a three-dimensional photonic crystal: a fractional calculus approach
作者:	Cheng, SC (Cheng, Szu-Cheng) Wu, JN (Wu, Jing-Nuo) Tsai, MR (Tsai, Ming-Rung) Hsieh, WF (Hsieh, Wen-Feng)
贡献者:	物理系
关键词:	MACROSCOPIC MANIFESTATION QUANTUM ELECTRODYNAMICS LIGHT-EMISSION;GAP RANDOMNESS TECHNOLOGY
日期:	2009-01
上传时间:	2011-12-09 14:58:02 (UTC+8)
摘要:	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.
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