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When an atom or a molecule interacts with an intense laser field, a coherent high-order harmonic emission is observed at a frequency that is an integer multiple magnitude of the initial frequency of the incident laser field. The harmonic emission has the characteristic of high emission efficiency at relatively high orders, and it also has a wide expansion in the frequency domain. Thus, the high-order harmonic generation can be utilized to generate coherent EUV or soft X-ray light sources as well as ultrashort at to second laser pulses. It is promising that the attosecond laser pulse will be an important tool for detecting and controlling the electron dynamics in atom and molecule systems. The mechanisms of high-order harmonics especially the high energy part of the harmonic spectrum can be explained by the well-known three-step model. The three-step model assumes that the electron in the bound state firstly are ionized by the potential barrier formed by the laser electric field and the atomic potential, then the ionized electrons oscillate in the laser field, and finally the electron with high kinetic energy gained in the laser field has the possibility to return back to the parent ion and recombines with the ground state of the system with a high energy photon emitted. As for harmonics with low orders, especially those with single photon energy near the ionization threshold, the Coulomb potential of the atom has significant influences on them. However,the effect of the Coulomb potential of the atom are not included in the three-step model, so the mechanism of near-threshold harmonics (NTH) cannot be clearly interpreted with the three-step model alone. In this circumstance, the study of the mechanism of near-threshold harmonic emission attracted people's attention in general. One important application of NTH is that it can be utilized to generate optical comb with EUV frequencies. Theoretically, Xiong et al. studied the mechanism of below-threshold harmonic (BTH) emission and found that the mechanism of this part of harmonics include the effect of the quantum-path interference and the Coulomb potential. He et al. analyzed the emission of BTH in various laser intensity regions and found that the harmonic spectrum exhibits a periodic structure as a function of the harmonic frequency when the incident laser intensity is about 1013 W/cm2. Utilizing the quantum-path and time-frequency analyses of the harmonic emission, He et al. indicated that this periodic structure can be attributed to the interference effect between two specific quantum paths. Li et al. adopted the synchrosqueezing scheme to study the near-and below-threshold harmonic emission of Cs atoms in an intense mid-infrared laser field and they showed that the multiphoton and the multiple rescattering trajectories have an effect on the NTH and BTH generation processes. Shafir et al. found that the ionic potential plays an critical role in NTH emission. Under the interaction between the atom and the intense laser field, electron in the ground state not only can be ionized but also be pumped into excited state, and these excitation processes also affect the harmonic emission. We studied the harmonic emission process near the ionization threshold by solving the time-dependent Schrdinger equation of an atom interacting with a strong laser field. Utilizing the obtained wavefunction, we systematically studied the high-order harmonic emission with the variation of the incident laser intensity. Meanwhile, through solving the TDSE with the momentum-space method, the excited-state population is precisely calculated and achieved. We show that the ninth harmonic exhibits a periodic oscillation structure with the intensity of the incident laser field increasing, and we reveals that there is a synchronous variation between the harmonic intensity and the relatively high bound state population.Within a certain range of laser intensity, the increase of the total population of the excited states corresponds to the low efficiency of harmonic emission, and this competition relationship is quite clear. Therefore, when the wavelength of the driving laser pulse is fixed, we can optimize the driving laser intensity to achieve the near-threshold harmonic emission with high efficiency.
[1] Li X F, L'Huillier A, Ferry M, Lompre L A, Mainfray 1989Phys. Rev. A 39 5751
[2] L'Huillier A, Lompre L A, Mainfray G, Manus C 1992Adv. At. Mol. Opt. Phys. Suppl 1 139
[3] Yang Y J, Chen G, Chen J G, Zhu Q R 2004Chin. Phys. Lett. 21 652
[4] Kohler M C, Pfeifer T, Hatsagortsyan K Z, Keitel C H 2012Adv. At. Mol. Opt. Phys. 61 159
[5] Paul P M, Toma E S, Breger P 2001Science 292 1689
[6] Meckel M, Comtois D, Zeidler D, Staudte A, Pavicic D 2008Science 320 1478
[7] Wang J, Chen G, Guo F M, Li S Y, Chen J G, Yang Y J 2013Chin. Phys. B 22 033203
[8] Blaga C I, Xu J L, Dichiara A D, Sistrunk E, Zhang K, Agostini P, Miller T A, DiMauro L F, Lin C D 2012Nature 483 194
[9] Krausz F, Ivanov M 2009Rev. Mod. Phys. 81 163
[10] Wei S S, Li S Y, Guo F M, Yang Y J, Wang B B 2013Phys. Rev. A 87 063418
[11] Corkum P B, Krausz F 2007Nat. Phys. 3 381
[12] Corkum P B 1993Phys. Rev. Lett. 71 1994
[13] Li P C, Sheu Y L, Laughlin C, Chu S I 2015Nat. Commun. 6 7178
[14] Xiong W H, Geng J W, Tang J Y, Peng L Y, Gong Q H 2014Phys. Rev. Lett. 112 233001
[15] He L X, Lan P F, Zhai C Y, Li Y, Wang Z, Zhang Q B, Lu P X 2015Phys. Rev. A 91 023428
[16] Chini M, Wang X W, Cheng Y, Wang H, Wu Y, Cunningham E, Li P C, Haslar J, Telnov D A, Chu S I, Chang Z H 2014Nat. Photon. 8 437
[17] Yost D C, Schibli T R, Ye J, Tate J L, Hostetter J, Gaarde M B, Schafer K J 2009Nat. Phys. 5 815
[18] Brizuela F, Heyl C M, Rudawski P, Kroon D, Rading L, Dahlstrom J M, Maurisson J, Johnsson P, Arnold C L, L'Huillier A 2013Sci. Rep. 3 1410
[19] Shafir D, Fabre B, Higuet J, Soifer H, Dagan M, Descamps D, Mevel E, Petit S, Wörner H J, Pons B, Dudovich N, Mairesse Y 2012Phys. Rev. Lett. 108 203001
[20] Tian Y Y, Wang C C, Li S Y, Guo F M, Ding D J, Roeterdink W G, Chen J G, Zeng S L, Liu X S, Yang Y J 2015Chin. Phys. B 24 043202
[21] Tong X M, Chu S I 1997Chem. Phys. 217 119
[22] Zhou Z Y, Chu S I 2011Phys. Rev. A 83 013405
[23] Tian Y Y, Li S Y, Wei S S, Guo F M, Zeng S L, Chen J G, Yang Y J 2014Chin. Phys. B 23 053202
[24] Wang C C, Tian Y Y, Luo S Z, Roeterdink W G, Yang Y J, Ding D J, Okunishi M, Prumper G, Shimada K, Ueda K, Zhu R H 2014Phys. Rev. A 90 023405
[25] Landau R H 1983Phys. Rev. C 27 2191
[26] Raekwon Y, Tabakin F 1978Phys. Rev. C 18 932
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[1] Li X F, L'Huillier A, Ferry M, Lompre L A, Mainfray 1989Phys. Rev. A 39 5751
[2] L'Huillier A, Lompre L A, Mainfray G, Manus C 1992Adv. At. Mol. Opt. Phys. Suppl 1 139
[3] Yang Y J, Chen G, Chen J G, Zhu Q R 2004Chin. Phys. Lett. 21 652
[4] Kohler M C, Pfeifer T, Hatsagortsyan K Z, Keitel C H 2012Adv. At. Mol. Opt. Phys. 61 159
[5] Paul P M, Toma E S, Breger P 2001Science 292 1689
[6] Meckel M, Comtois D, Zeidler D, Staudte A, Pavicic D 2008Science 320 1478
[7] Wang J, Chen G, Guo F M, Li S Y, Chen J G, Yang Y J 2013Chin. Phys. B 22 033203
[8] Blaga C I, Xu J L, Dichiara A D, Sistrunk E, Zhang K, Agostini P, Miller T A, DiMauro L F, Lin C D 2012Nature 483 194
[9] Krausz F, Ivanov M 2009Rev. Mod. Phys. 81 163
[10] Wei S S, Li S Y, Guo F M, Yang Y J, Wang B B 2013Phys. Rev. A 87 063418
[11] Corkum P B, Krausz F 2007Nat. Phys. 3 381
[12] Corkum P B 1993Phys. Rev. Lett. 71 1994
[13] Li P C, Sheu Y L, Laughlin C, Chu S I 2015Nat. Commun. 6 7178
[14] Xiong W H, Geng J W, Tang J Y, Peng L Y, Gong Q H 2014Phys. Rev. Lett. 112 233001
[15] He L X, Lan P F, Zhai C Y, Li Y, Wang Z, Zhang Q B, Lu P X 2015Phys. Rev. A 91 023428
[16] Chini M, Wang X W, Cheng Y, Wang H, Wu Y, Cunningham E, Li P C, Haslar J, Telnov D A, Chu S I, Chang Z H 2014Nat. Photon. 8 437
[17] Yost D C, Schibli T R, Ye J, Tate J L, Hostetter J, Gaarde M B, Schafer K J 2009Nat. Phys. 5 815
[18] Brizuela F, Heyl C M, Rudawski P, Kroon D, Rading L, Dahlstrom J M, Maurisson J, Johnsson P, Arnold C L, L'Huillier A 2013Sci. Rep. 3 1410
[19] Shafir D, Fabre B, Higuet J, Soifer H, Dagan M, Descamps D, Mevel E, Petit S, Wörner H J, Pons B, Dudovich N, Mairesse Y 2012Phys. Rev. Lett. 108 203001
[20] Tian Y Y, Wang C C, Li S Y, Guo F M, Ding D J, Roeterdink W G, Chen J G, Zeng S L, Liu X S, Yang Y J 2015Chin. Phys. B 24 043202
[21] Tong X M, Chu S I 1997Chem. Phys. 217 119
[22] Zhou Z Y, Chu S I 2011Phys. Rev. A 83 013405
[23] Tian Y Y, Li S Y, Wei S S, Guo F M, Zeng S L, Chen J G, Yang Y J 2014Chin. Phys. B 23 053202
[24] Wang C C, Tian Y Y, Luo S Z, Roeterdink W G, Yang Y J, Ding D J, Okunishi M, Prumper G, Shimada K, Ueda K, Zhu R H 2014Phys. Rev. A 90 023405
[25] Landau R H 1983Phys. Rev. C 27 2191
[26] Raekwon Y, Tabakin F 1978Phys. Rev. C 18 932
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