標題: | Spontaneous emission near the band edge of a three-dimensional photonic crystal: a fractional calculus approach |
作者: | Cheng, Szu-Cheng Wu, Jing-Nuo Tsai, Ming-Rung Hsieh, Wen-Feng 光電工程學系 Department of Photonics |
公開日期: | 7-一月-2009 |
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. |
URI: | http://dx.doi.org/10.1088/0953-8984/21/1/015503 http://hdl.handle.net/11536/7753 |
ISSN: | 0953-8984 |
DOI: | 10.1088/0953-8984/21/1/015503 |
期刊: | JOURNAL OF PHYSICS-CONDENSED MATTER |
Volume: | 21 |
Issue: | 1 |
結束頁: | |
顯示於類別: | 期刊論文 |