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将Guo-Åberg-Crasemann形式散射理论推广到高次谐波产生过程, 获得了高次谐波产生概率公式. 利用这一公式, 计算了不同惰性气体原子的高次谐波谱. 理论分析和数值计算显示高次谐波有新的截断定律qcħω = (9 -4√2) Up + (2√2-1) Ip ≈ 3.34 Up + 1.83 Ip, 其中, Up 为电子的有质动能, Ip 为原子电离能, ħω 为激光光子能量, qc 为高次谐波的截断阶数. 这一截断定律与近期Popmintchev等 (Popmintchev et al. 2012 Science 336 1287) 的实验观测符合得很好.Based on the scattering theory of Guo-Åberg-Crasemann (GAC), which has no artificial assumptions, high harmonic generation (HHG) is studied by using first-principles. The HHG spectra of different rare atoms are also calculated. Using the properties of ordinary Bessel functions and the Einstein photoelectric law in the strong-field case, we reveal a new cutoff law qcħω = (9 -4√2) Up + (2√2-1) Ip ≈ 3.34 Up + 1.83 Ip of HHG based on a mathematical deduction method and a graphical method, which accords well with the Popmintchev’s experimental result published on Science in 2012. This cutoff law also agrees well with our own calculation using the HHG transition rate formula derived from the GAC scattering theory. Thus, we have four pieces of independent evidence for the same cutoff law of HHG. The cutoff orders predicted by this theory are higher due to the absorption of the extra photons. These photons only participate in the photon-mode up-conversion and do nothing in the photoionization process.
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Keywords:
- high harmonic generation /
- cutoff law /
- Bessel function /
- law of photoelectricity
[1] Lewenstein M, Balcou Ph, Yu M, Ivannov, L’Huillier A, Corkum P B 1994 Phys. Rev. A 49 2117
[2] Corkum P B 1993 Phys. Rev. Lett. 71 1994
[3] Guo D S, Drake G W 1992 Phys. Rev. A 45 6622
[4] Guo D S 1996 Phys. Rev. A 53 4311
[5] Li X F, Zhang J T, Xu Z Z, Fu P M, Guo D S, Freeman R R 2004 Phys. Rev. Lett. 92 233603
[6] Guo D S, Freeman R R, Wu Y S 1998 Phys. Rev. A 58 521
[7] Guo D S 1990 Phys. Rev. A 42 4302
[8] Zhang J T, Zhang W, Xu Z Z, Li X F, Fu P M, Guo D S, Freeman R R 2002 J. Phys. B: At. Mol. Opt. Phys. 35 4809
[9] Bai L H, Zhang J T, Xu Z Z, Guo D S 2006 Phys. Rev. Lett. 97 193002
[10] Guo D S, Zhang J T, Xu Z Z, Li X F, Fu P M, Freeman R R 2003 Phys. Rev. A 68 043404
[11] Zhang J T, Bai L H, Gong S Q, Xu Z Z, Guo D S 2007 Opt. Express 15 7261
[12] Guo D S 2013 Front. Phys. 8 39
[13] Gao L H, Li X F, Fu P M, Freeman R R, Guo D S 2000 Phys. Rev. A 61 063407
[14] Gao J, Shen F, Eden J G 2000 Phys. Rev. A 61 043812
[15] Guo D S, Åberg T 1988 J. Phys. A: Math. Gen. 21 4577
[16] Guo D S, Åberg T, Crasemann B 1989 Phys. Rev. A 40 4997
[17] Yu C, Zhang J T, Sun Z W, Sun Z R, Guo D S 2014 Front. Phys. DOI: 10.1007/s11467-014-0429-x
[18] Guo D S, Yu C, Zhang J T, Gao J, Sun Z W, Sun Z R 2015 Front. Phys. 10 215
[19] Krause L J, Schäfer K J, Kulander K C 1993 Phys. Rev. Lett. 68 3535
[20] Popmintchev T, Chen M C, Popminchev D, Arpin P, Brown S, Alisauskas S, Andriukaitis G, Balciunas T, Mucke O D, Pugzlys A, Baltuska A, Shim B, Schrauth S E, Gaeta A, Hernandez-Garcia C, Plaja L, Becker A, Jaron-Becker A, Murnane M M, Kapteyn H C 2012 Science 336 1287
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[1] Lewenstein M, Balcou Ph, Yu M, Ivannov, L’Huillier A, Corkum P B 1994 Phys. Rev. A 49 2117
[2] Corkum P B 1993 Phys. Rev. Lett. 71 1994
[3] Guo D S, Drake G W 1992 Phys. Rev. A 45 6622
[4] Guo D S 1996 Phys. Rev. A 53 4311
[5] Li X F, Zhang J T, Xu Z Z, Fu P M, Guo D S, Freeman R R 2004 Phys. Rev. Lett. 92 233603
[6] Guo D S, Freeman R R, Wu Y S 1998 Phys. Rev. A 58 521
[7] Guo D S 1990 Phys. Rev. A 42 4302
[8] Zhang J T, Zhang W, Xu Z Z, Li X F, Fu P M, Guo D S, Freeman R R 2002 J. Phys. B: At. Mol. Opt. Phys. 35 4809
[9] Bai L H, Zhang J T, Xu Z Z, Guo D S 2006 Phys. Rev. Lett. 97 193002
[10] Guo D S, Zhang J T, Xu Z Z, Li X F, Fu P M, Freeman R R 2003 Phys. Rev. A 68 043404
[11] Zhang J T, Bai L H, Gong S Q, Xu Z Z, Guo D S 2007 Opt. Express 15 7261
[12] Guo D S 2013 Front. Phys. 8 39
[13] Gao L H, Li X F, Fu P M, Freeman R R, Guo D S 2000 Phys. Rev. A 61 063407
[14] Gao J, Shen F, Eden J G 2000 Phys. Rev. A 61 043812
[15] Guo D S, Åberg T 1988 J. Phys. A: Math. Gen. 21 4577
[16] Guo D S, Åberg T, Crasemann B 1989 Phys. Rev. A 40 4997
[17] Yu C, Zhang J T, Sun Z W, Sun Z R, Guo D S 2014 Front. Phys. DOI: 10.1007/s11467-014-0429-x
[18] Guo D S, Yu C, Zhang J T, Gao J, Sun Z W, Sun Z R 2015 Front. Phys. 10 215
[19] Krause L J, Schäfer K J, Kulander K C 1993 Phys. Rev. Lett. 68 3535
[20] Popmintchev T, Chen M C, Popminchev D, Arpin P, Brown S, Alisauskas S, Andriukaitis G, Balciunas T, Mucke O D, Pugzlys A, Baltuska A, Shim B, Schrauth S E, Gaeta A, Hernandez-Garcia C, Plaja L, Becker A, Jaron-Becker A, Murnane M M, Kapteyn H C 2012 Science 336 1287
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