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Chin. Phys. B, 2012, Vol. 21(2): 024210    DOI: 10.1088/1674-1056/21/2/024210
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A scaling law of high-order harmonic generation

Wu Yan(吴艳)a), Ye Hui-Liang(叶会亮)a), Shao Chu-Yin(邵初寅)b), and Zhang Jing-Tao(张敬涛)a)
a. State Key Laboratory of High Field Laser Physics, Shanghai Institute of Optics and Fine Mechanics, Chinese Academy of Sciences, Shanghai 201800, China;
b. Changshu Institute of Technology, Changshu 215500, China
Abstract  Using a nonperturbative quantum electrodynamics theory of high-order harmonic generation (HHG), a scaling law of HHG is established. The scaling law states that when the atomic binding energy Eb, the wavelength $\lambda$ and the intensity I of the laser field change simultaneously to kEb, $\lambda$/k, and k3I, respectively. The characteristics of the HHG spectrum remain unchanged, while the harmonic yield is enhanced k3 times. That HHG obeys the same scaling law with above-threshold ionization is a solid proof of the fact that the two physical processes have similar physical mechanisms. The variation of integrated harmonic yields is also discussed.
Keywords:  high-order harmonic generation      scaling law      harmonic yield      nonperturbative quantum electrodynamics  
Received:  28 June 2011      Revised:  29 August 2011      Accepted manuscript online: 
PACS:  42.65.Ky (Frequency conversion; harmonic generation, including higher-order harmonic generation)  
  32.80.Fb (Photoionization of atoms and ions)  
  32.80.Rm (Multiphoton ionization and excitation to highly excited states)  
Fund: Project supported by the National Natural Science Foundation of China (Grant Nos. 10774153 and 61078080) and the National Basic Research Program of China (Grant Nos. 2010CB923203 and 2011CB808103).
Corresponding Authors:  Zhang Jing-Tao,     E-mail:

Cite this article: 

Wu Yan(吴艳), Ye Hui-Liang(叶会亮), Shao Chu-Yin(邵初寅), and Zhang Jing-Tao(张敬涛) A scaling law of high-order harmonic generation 2012 Chin. Phys. B 21 024210

[1] Guo D S, Zhang J T, Xu Z Z, Li X F, Fu P M and Freeman R R 2003 Phys. Rev. A 68 043404
[2] Larsson J, Mével E, Zerne R, L'Huillier A, Wahlström C G and Svanberg S 1995 J. Phys. B 28 L53
[3] Kim D S, Park J J, Lee K H, Park J and Nam C H 2009 Jpn. J. Appl. Phys. 48 026506
[4] Teubner U and Gibbon P 2009 Rev. Mod. Phys. 81 445
[5] Ganeev R A 2007 J. Phys. B 40 213(R)
[6] Wu J, Zhai Z and Liu X S 2010 Chin. Phys. B 19 093201
[7] Smirnova O, Mairesse Y, Patchkovskii S, Dudovich N, Villeneuve D, Corkum P and Ivanov M Y 2009 Nature 460 972
[8] Baker S, Robinson J S, Lein M, Chirilva C C, Torres R, Bandulet H C, Comtois D, Kieffer J C, Villeneuve D M, Tisch J W G and Marangos J P 2008 Phys. Rev. Lett. 101 053901
[9] Lin Z Z, Zhuang J and Ning X J 2010 Chin. Phys. B 19 113204
[10] Zhang C L, Qi Y Y, Liu X S and Ding P Z 2009 Acta Phys. Sin. 58 3078 (in Chinese)
[11] Blaga C I, Catoire F, Colosimo P, Paulus G G, Muller H G, Agostini P and DiMauro L F 2009 it Nat. Phys. 5 335
[12] Catoire F, Blaga C I, Sistrunk E, Muller H G, Agostini P and DiMauro L F 2009 Laser Phys. 19 1574
[13] Quan W, Lin Z, Wu M, Kang H, Liu H, Liu X, Chen J, Liu J, He X T, Chen S G, Xiong H, Guo L, Xu H, Fu Y, Cheng Y and Xu Z Z 2009 Phys. Rev. Lett. 103 093001
[14] Liu C, Nakajima T, Sakka T and Ohgaki H 2008 Phys. Rev. A 77 043411
[15] Doumy G, Wheeler J, Roedig C, Chirla R, Agostini P and DiMauro L F 2009 Phys. Rev. Lett. 102 093002
[16] Shiner A D, Trallero-Herrero C, Kajumba N, Bandulet H C, Comtois D, Leare F, Gigue M, Kieffer J C, Corkum P B and Villeneuve D M 2009 Phys. Rev. Lett. 103 073902
[17] Gibson E A, Paul A, Wagner N, Tobey R, Gaudiosi D, Backus S, Christov I P, Aquila A, Gullikson E M, Attwood D T, Murnane M M and Kapteyn H C 2003 Science 302 95
[18] Yakovlev V S, Ivanov M and Krausz F 2007 Opt. Express 15 15351
[19] Tate J, Auguste T, Muller H G, Salieres P, Agostini P and DiMauro L F 2007 Phys. Rev. Lett. 98 013901
[20] Pérez-Hernández J A, Ramos J, Roso L and Plaja L 2010 Laser Phys. 20 1044
[21] Frolov M V, Manakov N L and Starace A F 2008 Phys. Rev. Lett. 100 173001
[22] Chen J, Zeng B, Liu X, Cheng Y and Xu Z 2009 New J. Phys. 11 113021
[23] Gao L H, Li X F, Guo D S and Fu P M 1999 Chin. Phys. Lett. 16 502
[24] Gao L H, Li X F, Fu P M, Freeman R R and Guo D S 2000 Phys. Rev. A 61 063407
[25] Guo D S, Aberg T and Crasemann B 1989 Phys. Rev. A 40 4997
[26] Wang Y, Zhang J T, Ren X H and Xu Z Z 2009 Chin. Phys. B 18 4815
[27] Shan B and Chang Z 2001 Phys. Rev. A 65 011804(R)
[28] Itatani J, Levesque J, Zeidler D, Niikura H, P閜in H, Kieffer J C, Corkum P B and Villeneuve D M 2004 Nature 432 867
[29] Fu P M, Wang B B, Li X F and Gao L H 2001 Phys. Rev. A 64 063401
[30] Zhang X M, Zhang J T, Bai L H, Gong Q H and Xu Z Z 2005 Opt. Express 13 8708
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