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In this paper, we numerically study the efficiencies of high-order harmonic generation (HHG) from CO2 molecule exposed to strong laser fields with different laser wavelengths and different orientation angles. Through calculating the HHG spectra in the directions parallel and perpendicular to the laser polarization, we show that the efficiency of perpendicular harmonics can be higher than or comparable to the parallel ones at the relatively small and intermediate orientation angles in some wavelength cases. At larger angles, the efficiency of perpendicular harmonics is generally lower than the parallel one. Further analyses show that the structure of the CO2 molecule plays an important role in the HHG efficiency and this role is also related to the laser wavelength. Specifically, we show that the relative yields of perpendicular harmonic versus parallel harmonic are closely associated with the parallel and perpendicular dipoles of the molecule. Due to the effect of two-center interference, the parallel or perpendicular dipoles of the molecule show some deep hollows in some energy regions, which depend on the molecular orientation, and so do the corresponding parallel and perpendicular harmonics. As the parallel harmonics are suppressed due to the interference effect strongly in some energy regions, the yields of the perpendicular harmonics, which are not subjected to the interference effect in the corresponding energy regions, can be higher than the parallel one. As a result, the integrated harmonic yield (i.e., the harmonic efficiency) in the perpendicular case can be higher than the parallel one, especially for the cases with short laser wavelengths and small orientation angles. In these cases, the interference effect induces the suppression of parallel harmonics in the whole HHG plateau. We therefore expect that the interference effect plays an important role in the HHG efficiency in these cases. For the case of long laser wavelength, the HHG plateau extends to high energy region and the main contributions to the integrated HHG yield can come from harmonics out of the interference-effect-dominating region. As a result, the interference effect plays a smaller role in determining the HHG efficiencies of parallel and perpendicular harmonics, in comparison with the case of short laser wavelength. For large orientation angles, the value of the perpendicular dipole is smaller than the parallel one in a wide energy region, and accordingly, the perpendicular harmonics are weaker than the parallel ones on the whole. As a rule, the parallel efficiency is usually higher than the perpendicular one. As the perpendicular harmonic can contribute importantly to the harmonic emission in some cases, our results suggest that for the complicated molecule, the perpendicular harmonics should be considered in the molecular orbital tomography experiments.
[1] Corkum P B 1993 Phys. Rev. Lett. 71 1994
[2] Antoine P, L’Huillier A, Lewenstein M 1996 Phys. Rev. Lett. 77 1234
[3] Zou P, Li R X, Zeng Z N, Xiong H, Liu P, Leng Y X, Fan P Z, Xu Z Z 2010 Chin. Phys. B 19 019501
[4] Zheng J, Sheng Z M, Zhang J 2005 Acta Phys. Sin. 54 2638(in Chinese) [郑君, 盛政明, 张杰 2005 物理学报 54 2638]
[5] Paul P M, Toma E S, Breger P 2001 Science 292 1689
[6] Hentschel M, Kienberger R 2001 Nature 414 509
[7] Chen J G, Yang Y J, Zeng S L, Liang H Q 2011 Phys. Rev. A 83 023401
[8] Zeng T T, Li P C, Zhou X X 2014 Acta Phys. Sin. 63 203201(in Chinese) [曾婷婷, 李鹏程, 周效信 2014 物理学报 63 203201]
[9] Christov I P, Zhou J, Peatross J, Rundquist A, Murnane M M, Kapteyn H C 1996 Phys. Rev. Lett. 77 1743
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[24] Shan B, Chang Z 2001 Phys. Rev. A 65 011804
[25] Yu S J, Zhang B, Li Y P, Yang S P, Chen Y J 2014 Phys. Rev. A 90 053844
[26] Zeng Z, Cheng Y, Song X, Li R, Xu Z 2007 Phys. Rev. Lett. 98 203901
[27] Zhao D, Li F L 2013 Chin. Phys. B 22 064215
[28] Feng L Q, Liu H 2015 Chin. Phys. B 24 034206
[29] Diao H H, Zheng Y H, Zhong Y, Zeng Z N, Ge X C, Li C, Li R X, Xu Z Z 2014 Chin. Phys. B 23 104210
[30] Ge X L, Du H, Wang Q, Guo J, Liu X S 2015 Chin. Phys. B 24 023201
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[32] Chen Y J, Zhang B 2011 Phys. Rev. A 84 053402
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[34] Itatani J, Zeidler D, Levesque J, Spanner M, Villeneuve D M, Corkum P B 2005 Phys. Rev. Lett. 94 123902
[35] Levesque J, Zeidler D, Marangos J P, Corkum P B, Villeneuve D M 2007 Phys. Rev. Lett. 98 183903
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[37] Torres R, Kajumba N, Underwood J G, Robinson J S, Baker S, Tisch J W G, de Nalda R, Bryan W A, Velotta R, Altucci C, Turcu I C E, Marangos J P 2007 Phys. Rev. Lett. 98 203007
[38] Le V H, Le A T, Xie R H, Lin C D 2007 Phys. Rev. A 76 013414
[39] Chen Y J, Hu B 2009 J. Chem. Phys. 131 244109
[40] Itatani J, Levesque J, Zeidler D, Hiromichi N, Pepin H, Kieffer J C, Corkum P B, Villeneuve D M 2004 Nature 432 867
[41] Chen Y J, Liu J 2008 Phys. Rev. A 77 013410
[42] Chen Y J, Chen J, Liu J 2006 Phys. Rev. A 74 063405
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[1] Corkum P B 1993 Phys. Rev. Lett. 71 1994
[2] Antoine P, L’Huillier A, Lewenstein M 1996 Phys. Rev. Lett. 77 1234
[3] Zou P, Li R X, Zeng Z N, Xiong H, Liu P, Leng Y X, Fan P Z, Xu Z Z 2010 Chin. Phys. B 19 019501
[4] Zheng J, Sheng Z M, Zhang J 2005 Acta Phys. Sin. 54 2638(in Chinese) [郑君, 盛政明, 张杰 2005 物理学报 54 2638]
[5] Paul P M, Toma E S, Breger P 2001 Science 292 1689
[6] Hentschel M, Kienberger R 2001 Nature 414 509
[7] Chen J G, Yang Y J, Zeng S L, Liang H Q 2011 Phys. Rev. A 83 023401
[8] Zeng T T, Li P C, Zhou X X 2014 Acta Phys. Sin. 63 203201(in Chinese) [曾婷婷, 李鹏程, 周效信 2014 物理学报 63 203201]
[9] Christov I P, Zhou J, Peatross J, Rundquist A, Murnane M M, Kapteyn H C 1996 Phys. Rev. Lett. 77 1743
[10] Ditmire T, Kulander K, Crane J, Nguyen H, Perry M 1996 J. Opt. Soc. Am. B 13 406
[11] Tate J, Auguste T, Muller H G, Salières P, Agostini P, DiMauro L F 2007 Phys. Rev. Lett. 98 013901
[12] Schiessl K, Ishikawa K L, Persson E, Burgdörer J 2007 Phys. Rev. Lett. 99 253903
[13] Frolov M V, Manakov N L, Starace A F 2008 Phys. Rev. Lett. 100 173001
[14] Yakovlev V, Ivanov M, Krausz F 2007 Opt. Express 15 15351
[15] Lan P F, Eiji J T, Katsumi M 2010 Phys. Rev. A 81 061802
[16] Liu C D, Zeng Z N, Wei P F, Liu P, Li R X, Xu Z Z 2010 Phys. Rev. A 81 033426
[17] Falcao-Filho E L, Gkortsas V M, Gordon A, Katner F X 2009 Opt. Express 17 11217
[18] Pérez-Hernández J A, Roso L, Plaja L 2009 Opt. Express 17 9891
[19] Jin C, Le A T, Lin C D 2011 Phys. Rev. A 83 023411
[20] Austin D R, Biegert J 2012 Phys. Rev. A 86 023813
[21] Auguste T, Catoire F, Agostini P, DiMauro L F, Chirila C C, Yakovlev V S, Salières P 2012 New J. Phys. 14 103014
[22] Le A T, Wei H, Jin C, Tuoc V N, Morishita T, Lin C D 2014 Phys. Rev. Lett. 113 033001
[23] Cui X, Li S Y, Guo F M, Tian Y Y, Chen J G, Zeng S L, Yang Y J 2015 Acta Phys. Sin. 64 043201(in Chinese) [崔鑫, 李苏宇, 郭福明, 田原野, 陈基根, 曾思良, 杨玉军 2015 物理学报 64 043201]
[24] Shan B, Chang Z 2001 Phys. Rev. A 65 011804
[25] Yu S J, Zhang B, Li Y P, Yang S P, Chen Y J 2014 Phys. Rev. A 90 053844
[26] Zeng Z, Cheng Y, Song X, Li R, Xu Z 2007 Phys. Rev. Lett. 98 203901
[27] Zhao D, Li F L 2013 Chin. Phys. B 22 064215
[28] Feng L Q, Liu H 2015 Chin. Phys. B 24 034206
[29] Diao H H, Zheng Y H, Zhong Y, Zeng Z N, Ge X C, Li C, Li R X, Xu Z Z 2014 Chin. Phys. B 23 104210
[30] Ge X L, Du H, Wang Q, Guo J, Liu X S 2015 Chin. Phys. B 24 023201
[31] Shiner A D, Trallero-Herrero C, Kajumba N, Bandulet H C, Comtois D, Légaré F, Giguère M, Kieffer J C, Corkum P B, Villeneuve D M 2009 Phys. Rev. Lett. 103 073902
[32] Chen Y J, Zhang B 2011 Phys. Rev. A 84 053402
[33] Zhang B, Chen Y J, Jiang X Q, Sun X D 2013 Phys. Rev. A 88 053428
[34] Itatani J, Zeidler D, Levesque J, Spanner M, Villeneuve D M, Corkum P B 2005 Phys. Rev. Lett. 94 123902
[35] Levesque J, Zeidler D, Marangos J P, Corkum P B, Villeneuve D M 2007 Phys. Rev. Lett. 98 183903
[36] Patchkovskii S, Zhao Z, Brabec T, Villeneuve D M 2006 Phys. Rev. Lett. 97 123003
[37] Torres R, Kajumba N, Underwood J G, Robinson J S, Baker S, Tisch J W G, de Nalda R, Bryan W A, Velotta R, Altucci C, Turcu I C E, Marangos J P 2007 Phys. Rev. Lett. 98 203007
[38] Le V H, Le A T, Xie R H, Lin C D 2007 Phys. Rev. A 76 013414
[39] Chen Y J, Hu B 2009 J. Chem. Phys. 131 244109
[40] Itatani J, Levesque J, Zeidler D, Hiromichi N, Pepin H, Kieffer J C, Corkum P B, Villeneuve D M 2004 Nature 432 867
[41] Chen Y J, Liu J 2008 Phys. Rev. A 77 013410
[42] Chen Y J, Chen J, Liu J 2006 Phys. Rev. A 74 063405
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