强激光场中双原子分子的高次谐波产生
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摘要
近年来,原子或者分子在强激光场中的高次谐波产生是一个广为研究的主题。这是因为高次谐波具有广阔的应用前景。首先,利用高次谐波人们可以获得相干的、脉冲持续时间短的XUV和X射线源。其次,高次谐波是人们实现阿秒相干脉冲的首选光源。第三,利用高次谐波可以实现分子的轨道成像。第四,高次谐波的研究对强场物理的研究有着强大的推动作用。目前实验和理论的研究主要集中在分子的高次谐波产生。因为分子具有更多的自由度和多中心特征,分子的高次谐波谱展示了比原子更复杂的结构,研究分子在强场中的动力学行为理论上也遇到了更多的困难。
本文研究强激光场中双原子分子的高次谐波产生。通过解析分析和数值计算,本文深入细致的研究了强场中双原子分子高次谐波产生的机制,发展了理论模型,并对新奇的实验现象进行了解释。
在第二章,我们发展了一个解析的模型来描述双原子分子的高次谐波产生。这个模型强调了电荷共振态对于大的核间距的分子高次谐波产生的重要影响,而且通过考虑两能级近似中忽略的连续态的贡献,它有能力描述大的核间距的分子的谐波谱的双平台结构:一个由于电荷共振形成的分子平台;一个由于束缚态-连续态跃迁形成的原子平台。理论计算结果与数值的计算结果展示了好的一致。我们的理论还明确了电荷共振态在形成分子的高次谐波谱的精细结构中的重要作用。并且显示通过调节分子的核间距,可以有效的控制谐波释放。
在第三章,我们利用第二章的解析模型,研究大的核间距的双原子分子的高次谐波产生。我们发现大的核间距的双原子分子的谐波谱的平台区域显示了峰-谷结构。这些显著的的结构的位置对场强非常敏感。我们的分析揭示两中心干涉以及不同的电子轨道之间的干涉共同导致了某些波段的谐波被增强,某些波段的谐波被抑制,而且激光参数,例如强度,对这些干涉效应的影响非常大。
在第四章,基于第三章对分子高次谐波产生机制的研究,我们研究利用分子的高次谐波实现分子的轨道成像。我们的研究显示,由于两中心干涉,高次谐波产生过程中的分子的再碰撞电子波包与分子电离时的最高占据的轨道和轨道的电离能密切相关。作为一个结果,分子的再碰撞电子波包的谱振幅可能和它的参考原子的再碰撞电子波包的谱振幅在某些能量区域显示很大的差别。这个发现意味着关于N_2分子的轨道成像实验[Nature 432,867(2004)]可能无法推广到另外的分子,例如CO_2。
在第五章,基于第四章阐述的分子轨道成像实验的局限性,我们研究如何通过另外的方式从分子的高次谐波谱读取分子的结构信息。在这一章,我们数值地和解析地调查H_2~+在不同的核间距和激光强度下高次谐波谱产生的取向依赖。我们的计算显示不同取向的谐波谱在平台区域有明显的交叉点,而且这些交叉点的位置对激光强度有较弱的依赖。对这些交叉点的分析显示两中心干涉在高次谐波产生的电离和再结合过程中具有重要作用。我们展示在一个超快的时域内,可以利用这些交叉点读取分子的结构信息。
在第六章,基于第二章和第五章对简单的分子H_2~+的研究,我们研究复杂的分子的高次谐波产生。在这一章,利用一个考虑平移不变性的强场近似模型,我们研究了O_2和CO_2分子高次谐波产生的取向依赖。计算显示对于O_2,谐波产量在θ=50°的时候最强(θ是分子轴与外场之间的夹角);对于CO_2,在θ=50°和θ=60°的时候,低阶和高阶的谐波产量分别达到了最大。计算还显示,这两个分子的电离产量在θ=45°的时候达到了最大。关于CO_2的计算结果与目前的理论预测(θ=30°时谐波产量最强)存在较大的差别。我们发现两中心干涉和分子的价轨道在电离过程中的相互作用是导致CO_2分子的高次谐波这种不同寻常的取向依赖的重要原因。特别地,由于这种相互作用,谐波谱不同取向时的最先的交叉点包含了丰富的分子的轨道信息。
在第七章,基于第六章的研究,我们详细的研究高次谐波产生的电离过程。在这一章,考虑强场近似的平移不变性,我们引入了修正的分子的强场近似(MM-SFA)。我们的模型适用于中性的双原子分子和双原子分子的离子。利用这个模型,我们研究了H_2~+,O_2和CO_2分子在强场中的电离对取向的依赖。我们把我们的结果和通过标准的分子的强场近似(SM-SFA),分子的隧穿电离理论(MO-ADK)得到的结果进行了比较。MM-SFA得到的结果和数值模拟以及实验测量得到的结果符合得更好。MM-SFA还预测了当分子轴与外场的夹角是45°时,CO_2分子的电离率最大。这一结果意味着当CO_2分子的取向偏离了价轨道电子云最密集的轴的方向时,它的电离最强。这一结果是反直觉的,已经被目前的实验测量[Phys.Rev.Lett 98,243001(2007)]所证实。我们的分析显示导致这个新奇现象发生的是由于电离过程中的两中心干涉效应。
以上各章节的研究,给出了分子高次谐波产生的半经典图像。在第八章,我们研究分子高次谐波产生的完整的量子机制。通过数值地模拟高次谐波产生的再碰撞过程,我们展示了一个谐波释放的完整的量子图像。这个模拟精确地包含了库伦效应,基态衰减,以及更高的束缚态对高次谐波产生的贡献。它揭示了带着一个宽的范围的能量的再结合电子都对释放某一阶谐波具有重要的贡献,这与半经典的图像是不同的。另外,基于这个模拟,我们提出了分子的高次谐波产生过程中的两中心干涉现象的完整的量子机制,并且明确了第一激发态在这个过程中的重要作用。
The high-order harmonic generation(HHG) from atoms and molecules has been one of the most intensely studied aspects of strong-field physics,this is due to:1) it can be applied as a coherent ultrashort radiation source in the extreme ultraviolet(XUV) and soft x-ray regions;2) it is the preferred choice for shaping the attosecond pulse;3) it can be used to molecular orbital tomography;4) the study on the HHG greatly improves the theory of the strong field physics. Presently,the investigation of the HHG focuses on molecules.Due to the multi-center characteristics and greater freedom,molecules show more complicated structures in their HHG spectra than atoms and the dynamics of molecules in the external field is more difficult to investigate.
In this thesis,we investigate the high-order harmonic generation(HHG) from diatomic molecules. We study the mechanism of the HHG from diatomic molecules numerically and analytically.We address the new theory models that illuminate the molecular HHG.Further,we explain the present novel experimental phenomena on moleclar HHG.
In the second chapter,we develop an analytic theory for the harmonic generation of symmetric diatomic molecular ions beyond two-level model,emphasizing on the influence of the chargeresonance (CR) states that are strongly coupled to electromagnetic fields for the case of large internuclear distance.With taking into account the continuum states that are ignored in the two-level model and become important for the intense laser case,our model is capable to produce the spectrum for the whole range of harmonic orders that consists of a molecular plateau due to the CR transition and an atomic-like plateau for a long-wavelength excitation.Our analytic results are in good agreement with the numerical results from directly solving the Schr(o|¨)dinger equation. Our theory also identifies the crucial role of the CR states in the fine structure of the harmonic spectrum and shows that the harmonic generation in molecular system can be effectively controlled by adjusting the internuclear distance.
In the third chapter,using the strong field approximation(SFA) model developed in the above chapter,we investigate the high-order harmonic generation(HHG) from diatomic molecules with large internuclear distance.We find that the hump and dip structure emerges in the plateau region of the harmonic spectrum,and the location of this striking structure is sensitive to the laser intensity.Our model analysis reveals that two-center interference as well as the interference between different recombination electron trajectories are responsible for the unusual enhanced or suppressed harmonic yield at a certain order,and these interference effects are greatly influenced by the laser parameters such as intensity.
In the four chapter,based on the investigation in the third chapter,we investigate molecular orbital tomography using the HHG.The calculations show that the molecular recollision electronic wave packets(REWPs) in the HHG are closely related to the ionization potential as well as the particular orbital from which it ionized.As a result,the spectral amplitude of the molecular REWP could be largely different from its reference atom(i.e.,with the same ionization potential as the molecule under study) in some energy regions due to the interference between the atomic cores of the molecules.This finding implies that molecular orbital tomography experiment using HHG[Nature 432,867(2004)]that is applicable for N_2 can not be generalized to other molecules such as CO_2.
In the fifths chapter,based on the limitation of molecular orbital tomography illuminated in the four chapter,we investigate the new method for probing the molecular structure using the HHG.The calculations on the orientation dependence of high-order harmonic generation(HHG) from H_2~+ with different internuclear distances and laser intensities show,that harmonic spectra at different orientation angles have striking intersections in the plateau region,the locations of which are weakly dependent on the laser parameters.The model analysis on the formations of the intersections reveals that two-center interference has an important role in both the recombination and the ionization process of the molecular HHG.We demonstrate that molecular interior messages can be read from the intersections on an ultrafast time scale.
In the sixth chapter,based on the above investigation of the HHG from small molecules H_2~+, we investigate the HHG from larger molecules.In this chapter,using a strong field approximation model that considers the translation invariance,we investigate the orientation dependence of molecular high-order harmonic generation(ODM-HHG) of O_2 and CO_2.The calculations show that for O_2,the harmonic yields peak atθ=50°(θthe angle between the molecular axis and the laser polarization),and for CO_2,those peak atθ=50°andθ=60°for the low and the high order harmonics,respectively.While the ionization peaks of them are all arrived atθ=45°.The results for CO_2 are in significant disagreement with current theories.We demonstrate that it is the interplay of two-center interference and molecular orbital in the ionization step that has an important role in the unusual ODM-HHG of CO_2.Especially,due to the interplay,rich molecular information is printed on the intersections of harmonic spectra at differentθs.
In the seventh chapter,based on the investigation in the sixth chapter,we investigate the ionization process in the molecular HHG in detail.In the chapter,taking into account the translation iavariance in strong-field approximation(SFA),we introduce the modified molecular SFA (MM-SFA).The model developed here is applied to both neutral diatomic molecules and diatomic molecular ions.Using it we investigate the orientation dependence of molecular ionization for H_2~+, O_2 and CO_2.We compare the results obtained by it to that obtained by the standard molecular SFA(SM-SFA),the MO-ADK theory,etc.The predictions of the MM-SFA agree with the numerical simulations and the experimental measurements.Especially,the preference for ionization of CO_2 while aligned at 45°to the laser field revealed by the experimental measurement[Phys. Rev.Lett 98,243001(2007)]is reproduced by the theory,and can be attributed to the effect of two-center interference.
The above investigations give the semiclassical picture of the molecular HHG.In the eighth chapter,through the numerical simulation of the recollision process in the HHG,that accurately incorporates the Coulomb effects,the ground state depletion as well as the contribution of higher bound states to the HHG,we demonstrate a complete quantum picture of harmonic emission beyond the semiclassical one.The simulation reveals that the primary contribution to a certain harmonic comes from the electrons with a broad region of energy beyond the energy conservation. Moreover,based on the simulation,we address the quantum mechanism of two-center interference in the molecular HHG,and further,we identify the important role of the first excited state in that.
本文研究强激光场中双原子分子的高次谐波产生。通过解析分析和数值计算,本文深入细致的研究了强场中双原子分子高次谐波产生的机制,发展了理论模型,并对新奇的实验现象进行了解释。
在第二章,我们发展了一个解析的模型来描述双原子分子的高次谐波产生。这个模型强调了电荷共振态对于大的核间距的分子高次谐波产生的重要影响,而且通过考虑两能级近似中忽略的连续态的贡献,它有能力描述大的核间距的分子的谐波谱的双平台结构:一个由于电荷共振形成的分子平台;一个由于束缚态-连续态跃迁形成的原子平台。理论计算结果与数值的计算结果展示了好的一致。我们的理论还明确了电荷共振态在形成分子的高次谐波谱的精细结构中的重要作用。并且显示通过调节分子的核间距,可以有效的控制谐波释放。
在第三章,我们利用第二章的解析模型,研究大的核间距的双原子分子的高次谐波产生。我们发现大的核间距的双原子分子的谐波谱的平台区域显示了峰-谷结构。这些显著的的结构的位置对场强非常敏感。我们的分析揭示两中心干涉以及不同的电子轨道之间的干涉共同导致了某些波段的谐波被增强,某些波段的谐波被抑制,而且激光参数,例如强度,对这些干涉效应的影响非常大。
在第四章,基于第三章对分子高次谐波产生机制的研究,我们研究利用分子的高次谐波实现分子的轨道成像。我们的研究显示,由于两中心干涉,高次谐波产生过程中的分子的再碰撞电子波包与分子电离时的最高占据的轨道和轨道的电离能密切相关。作为一个结果,分子的再碰撞电子波包的谱振幅可能和它的参考原子的再碰撞电子波包的谱振幅在某些能量区域显示很大的差别。这个发现意味着关于N_2分子的轨道成像实验[Nature 432,867(2004)]可能无法推广到另外的分子,例如CO_2。
在第五章,基于第四章阐述的分子轨道成像实验的局限性,我们研究如何通过另外的方式从分子的高次谐波谱读取分子的结构信息。在这一章,我们数值地和解析地调查H_2~+在不同的核间距和激光强度下高次谐波谱产生的取向依赖。我们的计算显示不同取向的谐波谱在平台区域有明显的交叉点,而且这些交叉点的位置对激光强度有较弱的依赖。对这些交叉点的分析显示两中心干涉在高次谐波产生的电离和再结合过程中具有重要作用。我们展示在一个超快的时域内,可以利用这些交叉点读取分子的结构信息。
在第六章,基于第二章和第五章对简单的分子H_2~+的研究,我们研究复杂的分子的高次谐波产生。在这一章,利用一个考虑平移不变性的强场近似模型,我们研究了O_2和CO_2分子高次谐波产生的取向依赖。计算显示对于O_2,谐波产量在θ=50°的时候最强(θ是分子轴与外场之间的夹角);对于CO_2,在θ=50°和θ=60°的时候,低阶和高阶的谐波产量分别达到了最大。计算还显示,这两个分子的电离产量在θ=45°的时候达到了最大。关于CO_2的计算结果与目前的理论预测(θ=30°时谐波产量最强)存在较大的差别。我们发现两中心干涉和分子的价轨道在电离过程中的相互作用是导致CO_2分子的高次谐波这种不同寻常的取向依赖的重要原因。特别地,由于这种相互作用,谐波谱不同取向时的最先的交叉点包含了丰富的分子的轨道信息。
在第七章,基于第六章的研究,我们详细的研究高次谐波产生的电离过程。在这一章,考虑强场近似的平移不变性,我们引入了修正的分子的强场近似(MM-SFA)。我们的模型适用于中性的双原子分子和双原子分子的离子。利用这个模型,我们研究了H_2~+,O_2和CO_2分子在强场中的电离对取向的依赖。我们把我们的结果和通过标准的分子的强场近似(SM-SFA),分子的隧穿电离理论(MO-ADK)得到的结果进行了比较。MM-SFA得到的结果和数值模拟以及实验测量得到的结果符合得更好。MM-SFA还预测了当分子轴与外场的夹角是45°时,CO_2分子的电离率最大。这一结果意味着当CO_2分子的取向偏离了价轨道电子云最密集的轴的方向时,它的电离最强。这一结果是反直觉的,已经被目前的实验测量[Phys.Rev.Lett 98,243001(2007)]所证实。我们的分析显示导致这个新奇现象发生的是由于电离过程中的两中心干涉效应。
以上各章节的研究,给出了分子高次谐波产生的半经典图像。在第八章,我们研究分子高次谐波产生的完整的量子机制。通过数值地模拟高次谐波产生的再碰撞过程,我们展示了一个谐波释放的完整的量子图像。这个模拟精确地包含了库伦效应,基态衰减,以及更高的束缚态对高次谐波产生的贡献。它揭示了带着一个宽的范围的能量的再结合电子都对释放某一阶谐波具有重要的贡献,这与半经典的图像是不同的。另外,基于这个模拟,我们提出了分子的高次谐波产生过程中的两中心干涉现象的完整的量子机制,并且明确了第一激发态在这个过程中的重要作用。
The high-order harmonic generation(HHG) from atoms and molecules has been one of the most intensely studied aspects of strong-field physics,this is due to:1) it can be applied as a coherent ultrashort radiation source in the extreme ultraviolet(XUV) and soft x-ray regions;2) it is the preferred choice for shaping the attosecond pulse;3) it can be used to molecular orbital tomography;4) the study on the HHG greatly improves the theory of the strong field physics. Presently,the investigation of the HHG focuses on molecules.Due to the multi-center characteristics and greater freedom,molecules show more complicated structures in their HHG spectra than atoms and the dynamics of molecules in the external field is more difficult to investigate.
In this thesis,we investigate the high-order harmonic generation(HHG) from diatomic molecules. We study the mechanism of the HHG from diatomic molecules numerically and analytically.We address the new theory models that illuminate the molecular HHG.Further,we explain the present novel experimental phenomena on moleclar HHG.
In the second chapter,we develop an analytic theory for the harmonic generation of symmetric diatomic molecular ions beyond two-level model,emphasizing on the influence of the chargeresonance (CR) states that are strongly coupled to electromagnetic fields for the case of large internuclear distance.With taking into account the continuum states that are ignored in the two-level model and become important for the intense laser case,our model is capable to produce the spectrum for the whole range of harmonic orders that consists of a molecular plateau due to the CR transition and an atomic-like plateau for a long-wavelength excitation.Our analytic results are in good agreement with the numerical results from directly solving the Schr(o|¨)dinger equation. Our theory also identifies the crucial role of the CR states in the fine structure of the harmonic spectrum and shows that the harmonic generation in molecular system can be effectively controlled by adjusting the internuclear distance.
In the third chapter,using the strong field approximation(SFA) model developed in the above chapter,we investigate the high-order harmonic generation(HHG) from diatomic molecules with large internuclear distance.We find that the hump and dip structure emerges in the plateau region of the harmonic spectrum,and the location of this striking structure is sensitive to the laser intensity.Our model analysis reveals that two-center interference as well as the interference between different recombination electron trajectories are responsible for the unusual enhanced or suppressed harmonic yield at a certain order,and these interference effects are greatly influenced by the laser parameters such as intensity.
In the four chapter,based on the investigation in the third chapter,we investigate molecular orbital tomography using the HHG.The calculations show that the molecular recollision electronic wave packets(REWPs) in the HHG are closely related to the ionization potential as well as the particular orbital from which it ionized.As a result,the spectral amplitude of the molecular REWP could be largely different from its reference atom(i.e.,with the same ionization potential as the molecule under study) in some energy regions due to the interference between the atomic cores of the molecules.This finding implies that molecular orbital tomography experiment using HHG[Nature 432,867(2004)]that is applicable for N_2 can not be generalized to other molecules such as CO_2.
In the fifths chapter,based on the limitation of molecular orbital tomography illuminated in the four chapter,we investigate the new method for probing the molecular structure using the HHG.The calculations on the orientation dependence of high-order harmonic generation(HHG) from H_2~+ with different internuclear distances and laser intensities show,that harmonic spectra at different orientation angles have striking intersections in the plateau region,the locations of which are weakly dependent on the laser parameters.The model analysis on the formations of the intersections reveals that two-center interference has an important role in both the recombination and the ionization process of the molecular HHG.We demonstrate that molecular interior messages can be read from the intersections on an ultrafast time scale.
In the sixth chapter,based on the above investigation of the HHG from small molecules H_2~+, we investigate the HHG from larger molecules.In this chapter,using a strong field approximation model that considers the translation invariance,we investigate the orientation dependence of molecular high-order harmonic generation(ODM-HHG) of O_2 and CO_2.The calculations show that for O_2,the harmonic yields peak atθ=50°(θthe angle between the molecular axis and the laser polarization),and for CO_2,those peak atθ=50°andθ=60°for the low and the high order harmonics,respectively.While the ionization peaks of them are all arrived atθ=45°.The results for CO_2 are in significant disagreement with current theories.We demonstrate that it is the interplay of two-center interference and molecular orbital in the ionization step that has an important role in the unusual ODM-HHG of CO_2.Especially,due to the interplay,rich molecular information is printed on the intersections of harmonic spectra at differentθs.
In the seventh chapter,based on the investigation in the sixth chapter,we investigate the ionization process in the molecular HHG in detail.In the chapter,taking into account the translation iavariance in strong-field approximation(SFA),we introduce the modified molecular SFA (MM-SFA).The model developed here is applied to both neutral diatomic molecules and diatomic molecular ions.Using it we investigate the orientation dependence of molecular ionization for H_2~+, O_2 and CO_2.We compare the results obtained by it to that obtained by the standard molecular SFA(SM-SFA),the MO-ADK theory,etc.The predictions of the MM-SFA agree with the numerical simulations and the experimental measurements.Especially,the preference for ionization of CO_2 while aligned at 45°to the laser field revealed by the experimental measurement[Phys. Rev.Lett 98,243001(2007)]is reproduced by the theory,and can be attributed to the effect of two-center interference.
The above investigations give the semiclassical picture of the molecular HHG.In the eighth chapter,through the numerical simulation of the recollision process in the HHG,that accurately incorporates the Coulomb effects,the ground state depletion as well as the contribution of higher bound states to the HHG,we demonstrate a complete quantum picture of harmonic emission beyond the semiclassical one.The simulation reveals that the primary contribution to a certain harmonic comes from the electrons with a broad region of energy beyond the energy conservation. Moreover,based on the simulation,we address the quantum mechanism of two-center interference in the molecular HHG,and further,we identify the important role of the first excited state in that.
引文
[1]王迎松,徐至展,激光与光电子学进展,1999年第5期(总第401期).
[2]T.Kreibich,M.Lein,V.Engel,and E.K.U.Gross,Phys.Rev.Lett.87,103901(2001).
[3]R.Kopold,W.Becker,and M.Kleber,Phys.Rev.A 58,4022(1998).
[4]M.E.Sukharev,and V.P.Krainov,Phys.Rev.A 62,033404(2000).
[5]P.Dietrich,M.Yu.Ivanov,F.A.Ilkov,and P.B.Corkum,Phys.Rev.Lett.77,4150(1996)
[6]S.Chelkowski,A.Conjustean,T.Zuo,and A.D.Bandrauk,Phys.Rev.A 54,3235(1996).
[7]Taiwang Cheng,Jie Liu,and Shigang Chen,Phys.Rev.A 62,033402(2000).
[8]A.D.Bandrank,S.Chelkowski,H.Yu,and E.Constant,Phys.Rev.A 56,R2537(1997).
[9]H.Nikura et al.,Nature(London) 417,917(2002).
[10]A.D.Bandrauk,S.Chelkowski,and I.Kawata,Phys.Rev.A 67,013407(2003).
[11]M.Lein et al.,Phys.Rev.Lett 88,183903,(2002).
[12]G.Lagmago Kamta,and A.D.Bandrauk,Phys.Rev.A 70,011404(R)(2004);ibid 71,053407(2005).
[13]X.X.Zhou et al.,Phys.Rev.A 72,033412(2005).
[14]C.C.Chirila,and M.Lein,Phys.Rev.A 73,023410(2006).
[15]Xi Chu,and Shih-I Chu,Phys.Rev.A 63 023411(2001).
[16]X.M.Tong,and Shih-I Chu,Phys.Rev.A 61 021802(2000).
[17]K.Miyazaki,M.Kaku,G.Miyaji,A.Abdurrouf,and F.H.M.Faisal,Phys.Rev.Lett.95,243903(2005).
[18]A.D.Bandrauk,and Huizhong.Lu,Phys.Rev.A 68,043408(2003).
[19]Bingbing Wang,Taiwang Cheng,Xiaofeng Li,Panming Fu,Shigang Chen,and Jie Liu Phys.Rev.A 72,063412(2005)
[20]The spectrum due to CR states exhibits a shorter but higher plateau,termed as the molecular plateau;The second plateau corresponding to higher photon energy extends to 3.17U_p is named as the atomic-like plateau.Details refers to following cititaion[24]and our following discussions.
[21]C.Vozzi et al.,Phys.Rev.Lett.95,153902(2005),and references therein.
[22]G.Castiglia,P.P.Corso,R.Daniele,E.Fiordilino,F.Morales,and F.Persico,J.Mod.Opt.51(8)1163(2004)
[23]D.Zeidler,A.Staudte,A.B.Bardon,D.M.Villeneuve,R.D(o|¨)rner,and P.B.Corkum,Phys.Rev.Lett.95,203003(2005).
[24]Kanai.Tsuneto,Minemoto.Shinichirou,and Sakai.Hirofumi,Nature 435,470-473(2005).
[25]M.Yu.Ivanov,and P.B.Corkum,Phys.Rev.A 48,580(1993).
[26]R.S.Mulliken,J.Chem.Phys.7,20(1939).
[27]A.D.Bandrauk,and M.L.Sink,Chem.Phys.Lett.57,569(1978);J.Chem.Phys.74,1110(1981).
[28]T.Zuo,S.Chelkowski,and A.D.Bandrauk,Phys.Rev.A 48,3837(1993).
[29]T.Zuo,S.Chelkowski,and A.D.Bandrauk,Phys.Rev.A 49,3943(1994).
[30]M.Lewenstein,Ph.Balcou,M.Yu.Ivanov,Anne L'Huillier and P.B.Corkum,Phys.Rev.A 49,2117(1994).
[31]P.B.Corkum,Phys.Rev.Lett.71,1994(1993).
[32]Ying Wu and Xiaoxue Yang,Phys.Key.Lett.98,013601(2007).
[33]H.R.Reiss,Phys.Rev.A 22,1786(1980).
[34]R.Bavli,and H.Metiu,Phys.Rev.A 47,3299(1993).
[35]B.R.Mollow,Phys.Rev.188,1969(1969).
[36]Bambi Hu,Baowen Li,Jie Liu,and Yan Gu,Phys.Rev.Lett.82,4224(1999);Phys.Rev.E 58,1743(1998).
[37]E.E.Aubanel,J.M.Gauthier,and A.D.Bandrauk,Phys.Rev.A 48,2145(1993).
[38]V.I.Usachenko,V.A.Pazdzersky,and J.K.Mciver Phys.Rev.A 69,013406(2004)
[39]J.Qhen,Shih-I Chu,and J.Liu,Time-Frequency Analysis of Molecular High-Harmonic Generation Spectrum by Means of Wavelet Transform and Wiagner Distribution Techniques,to appear in J.Phys.B.(2006).
[40]Marian O.Scully,and M.Suhail Zubairy,quantum optics,(University,Cambridge 1997).
[41]M.Lein,N.Hay,R.Velotta,J.P.Marangos,and P.L.Knight,Phys.Rev.A.66,023805(2002).
[42]M.Lein,P.P.Corso,J.P.Marangos,and P.L.Knight,Phys.Rev.A.67,023819(2003).
[43]G.Lagmago Kamta and A.D.Bandrauk,Phys.Rev.A 71,053407(2005).
[44]Anh-Thu Le et al,Phys.Rev.h 73,041402(R)(2006).
[45]R.de Nalda,E.Heesel,M.Lein,N.Hay,1 R.Velotta,E.Springate,M.Castillejo,and J.P.Marangos,Phys.Rev.A 69,031804(R)(2O04).
[46]J.Itatani et al.,Phys.Rev.Lett 94,123902(2005).
[47]Yanjun Chen,Jing Chen,and Jie Liu,Phys.Rev.A.74,063405(2006).
[48]M.F.Ciappina,C.C.Chirila.and M.Lein,Phys.Rev.A 75,043405(2007)
[49]J.Chen and S.G.Chen,Phys.Rev.A.75,041402(R)(2007).
[50]J.Itatani,J.Levesque,D.Zeidler,Hiromichi Niikura,J.C.Kieffer,P.B.Corkum,and D.M.Villeneuve,Nature 432,867(2004).
[51]M.Hentschel et al.,Nature(London) 414,509(2001);M.Drescher et al.,ibid.419,803(2002);Z.Chang et al.,Phys.Rev.Lett.79,2967(1997).
[52]J.Levesque,D.Zeidler,J.P.Marangos,P.B.Corkum,and D.M.Villeneuve,Phys.Rev.Lett.98,183903(2007).
[53]J.Muth-Bohm,A.Becker,and F.H.M.Faisal,Phys.Rev.Lett.85,2280(4)(2000)
[54]R.Velotta et al.,Phys.Rev.Lett.87,183901(2001).
[55]C.B.Madsen and L.B.Madsen,Phys.Rev.A 74,023403(2006).
[56]J.Itatani et al.,Nature 432,867(2004).
[57]S.Patchkovskii et al.,Phys.Rev.Lett.97,123003,(2006).
[58]R.Torres et al.,Phys.Rev.Lett.98,203007(2007).
[59]Van-Hoang Le et al.,Phys.Rev.A 76,013414(2007).
[60]S.Patchkovskii et al.,J.Chem.Phys.126,114306(2007).
[61]D.B.Milosevic,Phys.Rev.A 74,063404(2006).
[62]W.Becker et al.,Phys.Rev.A 76,033403(2007).
[63]M.V.Ammosov,N.B.Delone and V.P.Krainov,Sov.Phys.JETP 64,1191(1986).
[64]Gennady L.Yudin and Misha Yu.Ivanov,Phys.Rev.A 64,013409(2001).
[65]X.M.Tong,Z.X.Zhao,and C.D.Lin,Phys.Rev.A 66,033402(2002).
[66]D.Pavicic et al.,Phys.Rev.Lett.98,243001(2007).
[67]Anh-Thu Le,X.M.Tong,and C.D.Lin,Phys.Rev.A.73 041402(2006).
[68]C.Figueira de Morisson Faria,Phys.Rev.A.76,043407(2007).
[69]T.Kanai,S.Minemoto,and H.Sakai,Phys.Rev.Lett.98,053002(2007).
[70]N.Wagner et al.,Phys.Rev.A.76,061403(2007).
[71]M.F.Ciappina,A.Becket and A.Jaron-Becker,Phys.Rev.A.76,063406(2007).
[72]Y.J.Chen,et al,High-Order Harmonic Generation and Molecular Orbital Tomography:Characteristics of Molecular Recollision Electronic Wave Packets,unpublished.
[73]Y.J.Chen and J.Liu,Phys.Rev.A.77,013410(2008).
[74]A.Jaron-Becker,A.Becker,and F.H.M.Faisal,Phys.Rev.A.69,023410(2004)
[75]T.K.Kjeldsen and L.B.Madsen,J.Phys.B.37,2033-2044(2004).
[76]I.V.Litvinyuk,Kevin F.Lee,P.W.Dooley,D.M.Rayner,D.M.Villeneuve,and P.B.Corkum,Phys.Rev.Lett.90,233003(2003).
[77]A.S.Alnaser,S.Voss,X.M.Tong,C.M.Maharjan,P.Ranitovic,B.Ulrich,T.Osipov,B.Shan,Z.Chang,and C.L.Cocke,Phys.Rev.Lett.93,113003(2004).
[78]A.S.Alnaser,C.M.Maharjan,X.M.Tong,B.Ulrich,P.Ranitovic,B.Shan,Z.Chang,and C.D.Lin,C.L.Cocke,and I.V.Litvinyuk,Phys.Rev.A.71,031403(2005).
[79]C.Guo,M.Li,J.P.Nibarger,and G.N.Gibson,Phys.Rev.A.58,R4271(1998).
[80]F.Grasbon,G.G.Paulus,S.L.Chin,H.Walther,J.Muth-B(o|¨)hm,A.Becker,and F.H.M.Faisal,Phys.Rev.A.63,041402(2001).
[81]Merrick J.DeWitt,E.Wells,and R.R.Jones,Phys.Rev.Lett.87,153001(2001).
[82]J.Itatani,D.Zeidler,J.Levesque,Michael Spanner,D.M.ViUeneuve,and P.B.Corkum,Phys.Rev.Lett 94,123902(2005).
[83]D.Pavicic,K.F.Lee,D.M.Rayner,P.B.Corkum,and D.M.Villeneuve,Phys.Rev.Lett 98,243001(2007).
[84]G.F.Gribakin and M.Yu.Kuchiev,Phys.Rev.A.55,3760(1997).
[85]Y.J.Chen,et al Phys.Eev.A.74,063405(2006).
[86]C.B.Madsen and L.B.Madsen,Phys.Rev.A 74,023403(2006).
1871 T.K.Kjeldsen,C.Z.Bisgaard,and L.B.Madsen,Phys.Rev.A 71,013418(2005);T.K.Kjeldsen and L.B.Madsen,ibid.71,023411(2005);J.Phys.B.37,2033-2044(2004).
[88]T.Seideman,J.Chem.Phys.103,7887(1995).
[89]J.Ortigoso et al.,J.Chem.Phys.110,3870(1999).
[90]G.Lagmago Kamta and A.D.Bandrauk,Phys.Rev.A 74,033415(2006).
[91]Y.J.Chen and J.Liu,Phys.Rev.A.77,013410(2008).
[92]Y.J.Chen,et al,Reading molecular messages from the intersections of high-order harmonic spectra at different orientations,unpublished.
[93]M.Hentschel et al.,Nature(London) 414,509(2001);M.Drescher et al.,ibid.419,803(2002);Z.Chang et al.,Phys.Rev.Lett.79,2967(1997).
[94]Xibin Zhouet al.,Phys.Rev.Lett.100,073902(2008)
[2]T.Kreibich,M.Lein,V.Engel,and E.K.U.Gross,Phys.Rev.Lett.87,103901(2001).
[3]R.Kopold,W.Becker,and M.Kleber,Phys.Rev.A 58,4022(1998).
[4]M.E.Sukharev,and V.P.Krainov,Phys.Rev.A 62,033404(2000).
[5]P.Dietrich,M.Yu.Ivanov,F.A.Ilkov,and P.B.Corkum,Phys.Rev.Lett.77,4150(1996)
[6]S.Chelkowski,A.Conjustean,T.Zuo,and A.D.Bandrauk,Phys.Rev.A 54,3235(1996).
[7]Taiwang Cheng,Jie Liu,and Shigang Chen,Phys.Rev.A 62,033402(2000).
[8]A.D.Bandrank,S.Chelkowski,H.Yu,and E.Constant,Phys.Rev.A 56,R2537(1997).
[9]H.Nikura et al.,Nature(London) 417,917(2002).
[10]A.D.Bandrauk,S.Chelkowski,and I.Kawata,Phys.Rev.A 67,013407(2003).
[11]M.Lein et al.,Phys.Rev.Lett 88,183903,(2002).
[12]G.Lagmago Kamta,and A.D.Bandrauk,Phys.Rev.A 70,011404(R)(2004);ibid 71,053407(2005).
[13]X.X.Zhou et al.,Phys.Rev.A 72,033412(2005).
[14]C.C.Chirila,and M.Lein,Phys.Rev.A 73,023410(2006).
[15]Xi Chu,and Shih-I Chu,Phys.Rev.A 63 023411(2001).
[16]X.M.Tong,and Shih-I Chu,Phys.Rev.A 61 021802(2000).
[17]K.Miyazaki,M.Kaku,G.Miyaji,A.Abdurrouf,and F.H.M.Faisal,Phys.Rev.Lett.95,243903(2005).
[18]A.D.Bandrauk,and Huizhong.Lu,Phys.Rev.A 68,043408(2003).
[19]Bingbing Wang,Taiwang Cheng,Xiaofeng Li,Panming Fu,Shigang Chen,and Jie Liu Phys.Rev.A 72,063412(2005)
[20]The spectrum due to CR states exhibits a shorter but higher plateau,termed as the molecular plateau;The second plateau corresponding to higher photon energy extends to 3.17U_p is named as the atomic-like plateau.Details refers to following cititaion[24]and our following discussions.
[21]C.Vozzi et al.,Phys.Rev.Lett.95,153902(2005),and references therein.
[22]G.Castiglia,P.P.Corso,R.Daniele,E.Fiordilino,F.Morales,and F.Persico,J.Mod.Opt.51(8)1163(2004)
[23]D.Zeidler,A.Staudte,A.B.Bardon,D.M.Villeneuve,R.D(o|¨)rner,and P.B.Corkum,Phys.Rev.Lett.95,203003(2005).
[24]Kanai.Tsuneto,Minemoto.Shinichirou,and Sakai.Hirofumi,Nature 435,470-473(2005).
[25]M.Yu.Ivanov,and P.B.Corkum,Phys.Rev.A 48,580(1993).
[26]R.S.Mulliken,J.Chem.Phys.7,20(1939).
[27]A.D.Bandrauk,and M.L.Sink,Chem.Phys.Lett.57,569(1978);J.Chem.Phys.74,1110(1981).
[28]T.Zuo,S.Chelkowski,and A.D.Bandrauk,Phys.Rev.A 48,3837(1993).
[29]T.Zuo,S.Chelkowski,and A.D.Bandrauk,Phys.Rev.A 49,3943(1994).
[30]M.Lewenstein,Ph.Balcou,M.Yu.Ivanov,Anne L'Huillier and P.B.Corkum,Phys.Rev.A 49,2117(1994).
[31]P.B.Corkum,Phys.Rev.Lett.71,1994(1993).
[32]Ying Wu and Xiaoxue Yang,Phys.Key.Lett.98,013601(2007).
[33]H.R.Reiss,Phys.Rev.A 22,1786(1980).
[34]R.Bavli,and H.Metiu,Phys.Rev.A 47,3299(1993).
[35]B.R.Mollow,Phys.Rev.188,1969(1969).
[36]Bambi Hu,Baowen Li,Jie Liu,and Yan Gu,Phys.Rev.Lett.82,4224(1999);Phys.Rev.E 58,1743(1998).
[37]E.E.Aubanel,J.M.Gauthier,and A.D.Bandrauk,Phys.Rev.A 48,2145(1993).
[38]V.I.Usachenko,V.A.Pazdzersky,and J.K.Mciver Phys.Rev.A 69,013406(2004)
[39]J.Qhen,Shih-I Chu,and J.Liu,Time-Frequency Analysis of Molecular High-Harmonic Generation Spectrum by Means of Wavelet Transform and Wiagner Distribution Techniques,to appear in J.Phys.B.(2006).
[40]Marian O.Scully,and M.Suhail Zubairy,quantum optics,(University,Cambridge 1997).
[41]M.Lein,N.Hay,R.Velotta,J.P.Marangos,and P.L.Knight,Phys.Rev.A.66,023805(2002).
[42]M.Lein,P.P.Corso,J.P.Marangos,and P.L.Knight,Phys.Rev.A.67,023819(2003).
[43]G.Lagmago Kamta and A.D.Bandrauk,Phys.Rev.A 71,053407(2005).
[44]Anh-Thu Le et al,Phys.Rev.h 73,041402(R)(2006).
[45]R.de Nalda,E.Heesel,M.Lein,N.Hay,1 R.Velotta,E.Springate,M.Castillejo,and J.P.Marangos,Phys.Rev.A 69,031804(R)(2O04).
[46]J.Itatani et al.,Phys.Rev.Lett 94,123902(2005).
[47]Yanjun Chen,Jing Chen,and Jie Liu,Phys.Rev.A.74,063405(2006).
[48]M.F.Ciappina,C.C.Chirila.and M.Lein,Phys.Rev.A 75,043405(2007)
[49]J.Chen and S.G.Chen,Phys.Rev.A.75,041402(R)(2007).
[50]J.Itatani,J.Levesque,D.Zeidler,Hiromichi Niikura,J.C.Kieffer,P.B.Corkum,and D.M.Villeneuve,Nature 432,867(2004).
[51]M.Hentschel et al.,Nature(London) 414,509(2001);M.Drescher et al.,ibid.419,803(2002);Z.Chang et al.,Phys.Rev.Lett.79,2967(1997).
[52]J.Levesque,D.Zeidler,J.P.Marangos,P.B.Corkum,and D.M.Villeneuve,Phys.Rev.Lett.98,183903(2007).
[53]J.Muth-Bohm,A.Becker,and F.H.M.Faisal,Phys.Rev.Lett.85,2280(4)(2000)
[54]R.Velotta et al.,Phys.Rev.Lett.87,183901(2001).
[55]C.B.Madsen and L.B.Madsen,Phys.Rev.A 74,023403(2006).
[56]J.Itatani et al.,Nature 432,867(2004).
[57]S.Patchkovskii et al.,Phys.Rev.Lett.97,123003,(2006).
[58]R.Torres et al.,Phys.Rev.Lett.98,203007(2007).
[59]Van-Hoang Le et al.,Phys.Rev.A 76,013414(2007).
[60]S.Patchkovskii et al.,J.Chem.Phys.126,114306(2007).
[61]D.B.Milosevic,Phys.Rev.A 74,063404(2006).
[62]W.Becker et al.,Phys.Rev.A 76,033403(2007).
[63]M.V.Ammosov,N.B.Delone and V.P.Krainov,Sov.Phys.JETP 64,1191(1986).
[64]Gennady L.Yudin and Misha Yu.Ivanov,Phys.Rev.A 64,013409(2001).
[65]X.M.Tong,Z.X.Zhao,and C.D.Lin,Phys.Rev.A 66,033402(2002).
[66]D.Pavicic et al.,Phys.Rev.Lett.98,243001(2007).
[67]Anh-Thu Le,X.M.Tong,and C.D.Lin,Phys.Rev.A.73 041402(2006).
[68]C.Figueira de Morisson Faria,Phys.Rev.A.76,043407(2007).
[69]T.Kanai,S.Minemoto,and H.Sakai,Phys.Rev.Lett.98,053002(2007).
[70]N.Wagner et al.,Phys.Rev.A.76,061403(2007).
[71]M.F.Ciappina,A.Becket and A.Jaron-Becker,Phys.Rev.A.76,063406(2007).
[72]Y.J.Chen,et al,High-Order Harmonic Generation and Molecular Orbital Tomography:Characteristics of Molecular Recollision Electronic Wave Packets,unpublished.
[73]Y.J.Chen and J.Liu,Phys.Rev.A.77,013410(2008).
[74]A.Jaron-Becker,A.Becker,and F.H.M.Faisal,Phys.Rev.A.69,023410(2004)
[75]T.K.Kjeldsen and L.B.Madsen,J.Phys.B.37,2033-2044(2004).
[76]I.V.Litvinyuk,Kevin F.Lee,P.W.Dooley,D.M.Rayner,D.M.Villeneuve,and P.B.Corkum,Phys.Rev.Lett.90,233003(2003).
[77]A.S.Alnaser,S.Voss,X.M.Tong,C.M.Maharjan,P.Ranitovic,B.Ulrich,T.Osipov,B.Shan,Z.Chang,and C.L.Cocke,Phys.Rev.Lett.93,113003(2004).
[78]A.S.Alnaser,C.M.Maharjan,X.M.Tong,B.Ulrich,P.Ranitovic,B.Shan,Z.Chang,and C.D.Lin,C.L.Cocke,and I.V.Litvinyuk,Phys.Rev.A.71,031403(2005).
[79]C.Guo,M.Li,J.P.Nibarger,and G.N.Gibson,Phys.Rev.A.58,R4271(1998).
[80]F.Grasbon,G.G.Paulus,S.L.Chin,H.Walther,J.Muth-B(o|¨)hm,A.Becker,and F.H.M.Faisal,Phys.Rev.A.63,041402(2001).
[81]Merrick J.DeWitt,E.Wells,and R.R.Jones,Phys.Rev.Lett.87,153001(2001).
[82]J.Itatani,D.Zeidler,J.Levesque,Michael Spanner,D.M.ViUeneuve,and P.B.Corkum,Phys.Rev.Lett 94,123902(2005).
[83]D.Pavicic,K.F.Lee,D.M.Rayner,P.B.Corkum,and D.M.Villeneuve,Phys.Rev.Lett 98,243001(2007).
[84]G.F.Gribakin and M.Yu.Kuchiev,Phys.Rev.A.55,3760(1997).
[85]Y.J.Chen,et al Phys.Eev.A.74,063405(2006).
[86]C.B.Madsen and L.B.Madsen,Phys.Rev.A 74,023403(2006).
1871 T.K.Kjeldsen,C.Z.Bisgaard,and L.B.Madsen,Phys.Rev.A 71,013418(2005);T.K.Kjeldsen and L.B.Madsen,ibid.71,023411(2005);J.Phys.B.37,2033-2044(2004).
[88]T.Seideman,J.Chem.Phys.103,7887(1995).
[89]J.Ortigoso et al.,J.Chem.Phys.110,3870(1999).
[90]G.Lagmago Kamta and A.D.Bandrauk,Phys.Rev.A 74,033415(2006).
[91]Y.J.Chen and J.Liu,Phys.Rev.A.77,013410(2008).
[92]Y.J.Chen,et al,Reading molecular messages from the intersections of high-order harmonic spectra at different orientations,unpublished.
[93]M.Hentschel et al.,Nature(London) 414,509(2001);M.Drescher et al.,ibid.419,803(2002);Z.Chang et al.,Phys.Rev.Lett.79,2967(1997).
[94]Xibin Zhouet al.,Phys.Rev.Lett.100,073902(2008)
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