Browsing by Author "Tsai, Ming-Rung"

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Fractional dynamics of the spontaneous emission of an atom in photonic crystals
(2008-08-01)
Cheng, Szu-Cheng
;
Tsai, Ming-Rung
;
Hsleh, Wen-Feng
;
光電工程學系
;
Department of Photonics
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.
Spontaneous emission near the band edge of a three-dimensional photonic crystal: a fractional calculus approach
(2009-01-07)
Cheng, Szu-Cheng
;
Wu, Jing-Nuo
;
Tsai, Ming-Rung
;
Hsieh, Wen-Feng
;
光電工程學系
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.