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High-order harmonic generation (HHG) from the interaction among intense laserfields and atoms and molecules has attracted much attention. It is of the paramount importance and is still a rapidly growing field due to its potential to produce coherent and bright light within the uv and soft X-ray region and to generate attosecond pulses. Generally speaking, a typical spectrum of HHG shows that for the first few harmonics decrease rapidly, then present by a broad plateau of almost constant conversion efficiency, and end up with a sharp cutoff. In a recent experiment, it is verified that the field enhancement induced around the bow-tie elements with a 20-nm gap allows the generation of extremeultraviolet light directly from the output of a single femtosecond oscillator of 100-kW peak power. With the development of the HHG in the vicinity of metallic nanostructure from atomic responses, the harmonic generation in the vicinity of metallic nanostructure from molecules has also been investigated. In this paper, HHG from H2+ in bowtie-shaped nanostructure is investigated by solving the one-dimensional time-dependent Schrdinger equation within the non-Born- Oppenheimer approximation by the splitting-operator fast-Fourier transform technique. We find that the spatial position of the inhomogeneous field inside the nanostructure has a great influence on the harmonic spectrum. When the spatial position of the inhomogeneous field is translated from 30 a.u. to -30 a.u., the cutoff of the HHG can be extended and the smoother supercontinuum harmonic spectrum is formed. The underlying physical mechanism can be well demonstrated by the time-frequency distribution, the three-step model, the ionization probability and electric field of the driving laser. The harmonic order as a function of the ionization time and emission time can be given by the semi-classial three-step model. The trajectory with an earlier ionization time but a later emission time as a long electronic trajectory, and the trajectory with a later ionization time but an earlier emission time as a short electronic trajectory. The interference between the long and the short trajectories will lead to a modulated structure of the supercontinuum. When the spatial position of the inhomogeneous field is translated from 0 a.u. to 30 a.u., the cutoff of the HHG can be shortened and there are short and long electronic trajectories contributing to each harmonics and bringing about more modulations. When the spatial position of the inhomogeneous field is translated from 0 a.u. to -30 a.u., the cutoff of the HHG can be extended and there is only a short electronic trajectory contributing to each harmonics and the smoother supercontinuum harmonic spectrum is formed. The effects of the carrier-envelope phase on HHG is also demonstrated. When the carrierenvelope phase is -0.2, the cutoff of the HHG is extended. When the carrier-envelope phase is -0.2, the cutoff of the HHG is shortened. But we find that with the change of the carrier-envelope phase, their overall trends are the same, that is, the cutoff of the HHG is extended when the spatial position of the inhomogeneous field is translated from 30 a.u. to -30 a.u..
[1] Corkum P B 1993 Phys. Rev. Lett. 71 1994
[2] Kim S, Jin J, Kim Y J, Park I Y, Kim Y, Kim S W 2008 Nature 453 757
[3] Husakou A, Im S J, Herrmann J 2011 Phys. Rev. A 83 043839
[4] Yavuz I 2013 Phys. Rev. A 87 053815
[5] Xue S, Du H C, Xia Y, Hu B T 2015 Chin. Phys. B 24 054210
[6] Zhong H Y, Guo J, Feng W, Li P C, Liu X S 2016 Phys. Lett. A 380 188
[7] Luo X Y, Ben S, Ge X L, Wang Q, Guo J, Liu X S 2015 Acta Phys. Sin. 64 193201 (in Chinese) [罗香怡, 贲帅, 葛鑫磊, 王群, 郭静, 刘学深 2015 物理学报 64 193201]
[8] Nguyen N T, Hoang V H, Le V H 2013 Phys. Rev. A 88 023824
[9] Kamta G L, Bandrauk A D 2005 Phys. Rev. Lett. 94 203003
[10] Jin C, Le A T, Lin C D 2011 Phys. Rev. A 83 053409
[11] Pan Y, Zhao S F, Zhou X X 2013 Phys. Rev. A 87 035805
[12] Chelkowski S, Foisy C, Bandrauk A D 1998 Phys. Rev. A 57 1176
[13] Han Y C, Madsen L B 2013 Phys. Rev. A 87 043404
[14] Guan X, Bartschat K, Schneider B I, Koesterke L 2013 Phys. Rev. A 88 043402
[15] Yuan K J, Bandrauk A D 2011 Phys. Rev. A 83 063422
[16] Zhang J, Ge X L, Wang T, Xu T T, Guo J, Liu X S 2015 Phys. Rev. A 92 013418
[17] Yavuz I, Tikman Y, Altun Z 2015 Phys. Rev. A 92 023413
[18] Bandrauk A D, Chelkowski S, Kawata I 2003 Phys. Rev. A 67 013407
[19] Lein M, Kreibich T, Gross E K U, Engel V 2002 Phys. Rev. A 65 033403
[20] Hermann M R, Fleck Jr J A 1988 Phys. Rev. A 38 6000
[21] Feit M D, Fleck Jr J A 1983 J. Chem. Phys. 78 301
[22] Antoine P, Piraux B, Maquet A 1995 Phys. Rev. A 51 R1750
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[1] Corkum P B 1993 Phys. Rev. Lett. 71 1994
[2] Kim S, Jin J, Kim Y J, Park I Y, Kim Y, Kim S W 2008 Nature 453 757
[3] Husakou A, Im S J, Herrmann J 2011 Phys. Rev. A 83 043839
[4] Yavuz I 2013 Phys. Rev. A 87 053815
[5] Xue S, Du H C, Xia Y, Hu B T 2015 Chin. Phys. B 24 054210
[6] Zhong H Y, Guo J, Feng W, Li P C, Liu X S 2016 Phys. Lett. A 380 188
[7] Luo X Y, Ben S, Ge X L, Wang Q, Guo J, Liu X S 2015 Acta Phys. Sin. 64 193201 (in Chinese) [罗香怡, 贲帅, 葛鑫磊, 王群, 郭静, 刘学深 2015 物理学报 64 193201]
[8] Nguyen N T, Hoang V H, Le V H 2013 Phys. Rev. A 88 023824
[9] Kamta G L, Bandrauk A D 2005 Phys. Rev. Lett. 94 203003
[10] Jin C, Le A T, Lin C D 2011 Phys. Rev. A 83 053409
[11] Pan Y, Zhao S F, Zhou X X 2013 Phys. Rev. A 87 035805
[12] Chelkowski S, Foisy C, Bandrauk A D 1998 Phys. Rev. A 57 1176
[13] Han Y C, Madsen L B 2013 Phys. Rev. A 87 043404
[14] Guan X, Bartschat K, Schneider B I, Koesterke L 2013 Phys. Rev. A 88 043402
[15] Yuan K J, Bandrauk A D 2011 Phys. Rev. A 83 063422
[16] Zhang J, Ge X L, Wang T, Xu T T, Guo J, Liu X S 2015 Phys. Rev. A 92 013418
[17] Yavuz I, Tikman Y, Altun Z 2015 Phys. Rev. A 92 023413
[18] Bandrauk A D, Chelkowski S, Kawata I 2003 Phys. Rev. A 67 013407
[19] Lein M, Kreibich T, Gross E K U, Engel V 2002 Phys. Rev. A 65 033403
[20] Hermann M R, Fleck Jr J A 1988 Phys. Rev. A 38 6000
[21] Feit M D, Fleck Jr J A 1983 J. Chem. Phys. 78 301
[22] Antoine P, Piraux B, Maquet A 1995 Phys. Rev. A 51 R1750
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