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研究了光子晶体能带带边频率受到阶跃调制和三角函数周期调制两种情况下原子自发辐射场强度随时间的演化特性以及频谱的特性.阶跃调制时，调制发生后原子辐射的局域场的频率以及非局域场的构成情况都只取决于原子的跃迁频率和此时的带边频率，且都与具有相同参数条件的静态情形下的相同.调制发生时刻对自发辐射场的稳态强度有影响.三角函数周期调制时，辐射场强度在足够长时间后随时间做有衰减的准周期振荡.调制频率决定了准周期振荡的频率，并对衰减率有影响.辐射场能量在一组相邻间隔近似等于调制频率的离散频率附近形成尖锐峰值，它们的中心频率值取决于带边频率的取值范围和原子的跃迁频率，调制初相位会影响初始一段时间的辐射场强度以及辐射谱上连续谱成分的强弱.The spontaneous emission field and spectrum of a two-level atom, located in an isotropic photonic crystal with dynamic band edges, are investigated by means of numeric calculation. The investigation is expected to help comprehend the characteristics of the atomic spontaneous emission in the dynamic photonic crystal, and provide a possible way to control dynamically the spontaneous emission in photonic crystal. The expression of the spontaneous radiation field is obtained without using the far-zone approximation and the Weisskopf-Wigner approximation, and expected to be applicable in other relevant researches. In the investigation, the spontaneous radiation field and spectrum are calculated when the band edge frequency is unmodulated, or modulated by a step function or triangle function. In the unmodulated situation, the radiation field intensity tends to a constant which is equal to the intensity of the localized field component. The radiation field pulse presents a wave packet behavior as propagation distance increases. The components of the radiation field correspond one-to-one to the peaks in the spontaneous radiation spectrum. When the band edge frequency is modulated by step function, the radiation field intensity tends to a steady-state value after the modulation has happened. And the steady-state intensity is affected by the time when the modulation happens. The components of the non-localized field and the frequency of the localized field after modulation depend on the atomic transition frequency and the band edge frequency, and are identical to those in the unmodulated situation with the same parameters. When the band edge frequency is modulated by a triangle function, the field intensity presents a decaying quasi-periodic oscillation after a long enough time. The modulation frequency determines the frequency of the oscillation, and influences the decay rate. The radiation energy becomes sharp peaks around a set of the discrete frequencies which are evenly spaced with the modulation frequency. The central frequency of these frequencies depends on the atomic transition frequency and the value range of the band edge frequency. The modulation initial phase affects the intensity of the radiation field emitted in an initial period of time.
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Keywords:
- photonic crystal /
- two-level atom /
- dynamic structured reservoirs /
- radiation field
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[1] Purcell E M 1946 Phys. Rev. 69 681
[2] Yablonovitch E 1987 Phys. Rev. Lett. 58 2059
[3] John S 1987 Phys. Rev. Lett. 58 2486
[4] Tarhan I I, Watson G H 1996 Phys. Rev. Lett. 76 315
[5] John S 1984 Phys. Rev. Lett. 53 2169
[6] John S, Wang J 1991 Phys. Rev. B 43 12772
[7] John S, Wang J 1990 Phys. Rev. Lett. 64 2418
[8] Zhu S Y, Chen H, Huang H 1997 Phys. Rev. Lett. 79 205
[9] John S, Quang T 1994 Phys. Rev. A 50 1764
[10] Quang T, Woldeyohannes M, John S 1997 Phys. Rev. Lett. 79 5238
[11] Yang Y P, Zhu S Y 2000 Phys. Rev. A 61 043809
[12] Xie S Y, Yang Y P, Wu X 2001 Eur. Phys. J. D 13 129
[13] Wang X H, Gu B Y 2005 Physics 34 18 (in Chinese) [王雪华, 顾本源2005物理34 18]
[14] Figotin A, Godin Y A, Vitebsky I 1998 Phys. Rev. B 57 2841
[15] Su J, Chen H M 2010 Acta Opt. Sin. 30 2710 (in Chinese) [苏坚, 陈鹤鸣2010光学学报30 2710]
[16] Zhang L F, Huang J P 2010 Chin. Phys. B 19 024213
[17] Han M G, Shin C G, Jeon S J, Shim H, Heo C J, Jin H, Kim J W, Lee S 2012 Adv. Mater. 24 6438
[18] Oh J M, Hoshina T, Takeda H, Tsurumi T 2013 Appl. Phys. Express 6 062001
[19] Ge J P, He L, Goebl J, Yin Y D 2009 J. Am. Chem. Soc. 131 3484
[20] Yu G J, Pu S L, Wang X, Ji H Z 2012 Acta Phys. Sin. 61 194703 (in Chinese) [于国君, 卜胜利, 王响, 纪红柱2012 61 194703]
[21] Sugiyama H, Sawada T, Yano H, Kanai T 2013 J. Mater. Chem. C 1 6103
[22] Liu Z D, Gao J J, Li B, Zhou J 2013 Opt. Mater. 35 1134
[23] Law C K, Zhu S Y, Zubariry M S 1995 Phys. Rev. A 52 4095
[24] Priyesh K V, Thayyullathil R B 2012 Commun. Theor. Phys. 57 468
[25] Pisipati U, Almakrami I M, Joshi A, Serna J D 2012 Am. J. Phys. 80 612
[26] Wang L, Xu J P, Gao Y F 2010 J. Phys. B: At. Mol. Opt. Phys. 43 095102
[27] Liao X, Cong H L, Jiang D L, Ren X Z 2010 Acta Phys. Sin. 59 5508 (in Chinese) [廖旭, 丛红璐, 姜道来, 任学藻2010 59 5508]
[28] Jia F, Xie S Y, Yang Y P 2009 Chin. Phys. B 18 3193
[29] Kofman A G, Kurizki G 2000 Phys. Rev. Lett. 87 270405
[30] Linington I E, Garraway B M 2006 J. Phys. B: At. Mol. Opt. Phys. 39 3383
[31] Linington I E, Garraway B M 2008 Phys. Rev. A 77 033831
[32] Xing R, Xie S Y, Xu J P, Yang Y P 2014 Acta Phys. Sin. 63 094205 (in Chinese) [邢容, 谢双媛, 许静平, 羊亚平2014 63 094205]
[33] Linz P 1985 Analytical and Numerical Methods for Volterra Equations (Philadelphia: Society for Industrial and Applied Mathematics) Chapter 7
[34] Scully M O, Zubairy M S 1997 Quantum Optics (Cambridge: Cambridge University Press) Chapter 6
[35] Yang Y P, Huang X S 2007 J. Mod. Opt. 54 1407
[36] Yang Y P, Zhu S Y 2000 Phys. Rev. A 62 013805
[37] Lambropoulos P, Nikolopoulos G M, Nielsen T R, Bay S 2000 Rep. Prog. Phys. 63 455
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