双原子分子排列及高次谐波辐射理论与实验研究
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摘要
在强飞秒脉冲激光场中,空间排列有序的分子辐射出的高次谐波(HHG)正在引起人们越来越广泛的兴趣。由于分子相对于原子来说具有非球对称结构及更多的空间自由度,导致分子辐射的高次谐波不但包含了更丰富的物理现象,而且可以在更大程度上被调节和控制,所以推动了当前排列有序分子辐射高次谐波研究的发展。本文首先研究了最高占据分子轨道(HOMOs)和转动温度对分子空间转动排列的影响。然后基于强场电离理论和含时薛定谔方程提出了两种全新的计算双原子分子高次谐波辐射的理论方法,一种是价键轨道方法,它不但能描述双原子分子高次谐波辐射随分子空间取向变化的性质,而且能详细分析不同价键轨道对高次谐波的贡献;另一种是比较精确的分子波函数方法,它能计算包含分子不同初始转动温度、空间取向、飞秒光强以及初始态是激发态等条件下的高次谐波辐射性质。此外,还进行了一系列高次谐波实验研究,理论计算结果与实验观测值进行了比较。
本文首先采用含时薛定谔方程数值计算和分析了分子在非共振激光场下的转动激发和空间无场排列性质。通过飞秒脉冲来激发一系列由共轭角空间定义的展宽分子波包,其展开系数通过求解一组耦合的线性方程来获得。通过分析HOMOs在CO和O2分子空间转动排列中的重要作用,得到了具有不同宇称分子角分布随温度变化的规律。
其次,通过引入空间转动算符推导出了采用价键轨道波函数来计算任意取向双原子分子高次谐波辐射的理论公式。详细计算了O2和N2分子每一个价键轨道对高次谐波辐射随分子取向变化的影响。指出N2分子轴平行于激光偏振方向时氮气的成键轨道决定了谐波辐射的最大值。对于O2分子两个反键轨道贡献了谐波辐射的最大值,而两个成键轨道则稍微影响最大谐波辐射的方向角使其并不精确等于分子轴与激光偏振夹角的450,这些性质与文献中相关实验观测结果相一致。
然后基于含时薛定谔方程我们又推导出了分子波函数法计算高次谐波的理论公式。其中分子波函数由一系列含时系数加权的包含不同分子轨道、转动和振动能级的电子谱项波函数的叠加而构成。数值计算了分子不同初始转动温度、不同空间取向排列以及初始电子态是不同的激发态或是混合态的条件下分子高次谐波强度的变化规律。并在此基础上根据大量的数值计算结果提出利用分子激发态操控高次谐波。
最后进行了N2和O2分子不同空间取向、不同转动温度、不同飞秒脉冲光强、不同椭圆偏振率以及双色场中不同气体压强等条件下的高次谐波实验研究工作,详细分析了不同实验条件下的高次谐波辐射性质。国外文献及我们的实验观测值与理论计算结果相吻合。
High-order harmonic generation (HHG) from aligned molecules in strong laser fields of femtosecond duration has attracted increasing interest due to the extra degrees of freedom and nonspherical symmetry of molecules as compared to atoms. Therefore current study of harmonic emission of aligned molecules is motivated by the properties of molecules which may lead to richer physics phenomena and a higher degree modulation of HHG. Firstly in this paper the influences of the highest occupied molecular orbitals (HOMOs) and rotational temperature on molecular spatial alignment are discussed. Secondly based on intense field ionization and time-dependent Schr?dinger equation we present two innovative methods of calculating the harmonic emission of diatomic molecule. One is the valence orbital method which not only can describe the properties of molecular alignment-dependent harmonic emission from diatomic molecule, but also can analyze the contributions to harmonic emission from different valence orbitals. The other is the molecular wave function method which can precisely calculate the harmonic emission with different initial condition including the rotational temperature, spatial alignment and the excited electronic states. The comparisons are carried out between theoretical calculations of molecular wave function method and a series of experimental results.
Firstly molecular rotational excitation and field-free spatial alignment in a nonresonant intense laser field are studied numerically and analytically by using time-dependent Schr?dinger equation. The broad rotational wave packets excited by the femtosecond pulse are defined in the conjugate angle space, and their coefficients are obtained by solving a set of coupled linear equations. The temperature-dependent properties of angular distributions of CO and O2 molecules are obtained through analyzing the influences of the HOMOs on molecular spacial alignment.
Secondly we present a valence orbital method for high-order harmonic generation from diatomic molecule with arbitrary orientation by using space rotation operator. We evaluated the effects of each valence orbital of N2 and O2 on harmonic emission with different molecular alignment in detail. The calculation results show that the bonding orbital of N2 decides the maximum of harmonic emission when the molecular axis of N2 is aligned parallel to laser vector. For O2 molecule the two antibonding orbitals contribute the maximum of harmonic yield and two bonding orbitals slightly influence the alignment angle of maximum of harmonic radiation not exactly at 450 which confirm the experimental results in references.
Furthermore we also present a method of molecular wave functions for calculating harmonic emission of diatomic molecules based on time-dependent Schr?dinger equation. The molecular wave functions are superposed by a series of wave functions of electron terms weighted by time-dependent coefficients for different molecular orbitals, rotational and vibrational levels. The molecular alignment and rotational temperature dependent properties of harmonic emissions are calculated in detail when the initial conditions are excited states or mixed states. We put forward the theory of manipulating the harmonic emission with excited states of molecule based on a lot of calculated results.
Finally we carry out a series of harmonic emission experiments of N2 and O2 under different molecular alignment, different rotational temperature, different intensity of femtosecond pulse, different ellipticity of fundamental pulse, and different gas pressure in two color field. The properties of harmonic emission under different conditions are analyzed in detail. We find a well agreement between theoretical calculations and experimental results including those in foreign references.
本文首先采用含时薛定谔方程数值计算和分析了分子在非共振激光场下的转动激发和空间无场排列性质。通过飞秒脉冲来激发一系列由共轭角空间定义的展宽分子波包,其展开系数通过求解一组耦合的线性方程来获得。通过分析HOMOs在CO和O2分子空间转动排列中的重要作用,得到了具有不同宇称分子角分布随温度变化的规律。
其次,通过引入空间转动算符推导出了采用价键轨道波函数来计算任意取向双原子分子高次谐波辐射的理论公式。详细计算了O2和N2分子每一个价键轨道对高次谐波辐射随分子取向变化的影响。指出N2分子轴平行于激光偏振方向时氮气的成键轨道决定了谐波辐射的最大值。对于O2分子两个反键轨道贡献了谐波辐射的最大值,而两个成键轨道则稍微影响最大谐波辐射的方向角使其并不精确等于分子轴与激光偏振夹角的450,这些性质与文献中相关实验观测结果相一致。
然后基于含时薛定谔方程我们又推导出了分子波函数法计算高次谐波的理论公式。其中分子波函数由一系列含时系数加权的包含不同分子轨道、转动和振动能级的电子谱项波函数的叠加而构成。数值计算了分子不同初始转动温度、不同空间取向排列以及初始电子态是不同的激发态或是混合态的条件下分子高次谐波强度的变化规律。并在此基础上根据大量的数值计算结果提出利用分子激发态操控高次谐波。
最后进行了N2和O2分子不同空间取向、不同转动温度、不同飞秒脉冲光强、不同椭圆偏振率以及双色场中不同气体压强等条件下的高次谐波实验研究工作,详细分析了不同实验条件下的高次谐波辐射性质。国外文献及我们的实验观测值与理论计算结果相吻合。
High-order harmonic generation (HHG) from aligned molecules in strong laser fields of femtosecond duration has attracted increasing interest due to the extra degrees of freedom and nonspherical symmetry of molecules as compared to atoms. Therefore current study of harmonic emission of aligned molecules is motivated by the properties of molecules which may lead to richer physics phenomena and a higher degree modulation of HHG. Firstly in this paper the influences of the highest occupied molecular orbitals (HOMOs) and rotational temperature on molecular spatial alignment are discussed. Secondly based on intense field ionization and time-dependent Schr?dinger equation we present two innovative methods of calculating the harmonic emission of diatomic molecule. One is the valence orbital method which not only can describe the properties of molecular alignment-dependent harmonic emission from diatomic molecule, but also can analyze the contributions to harmonic emission from different valence orbitals. The other is the molecular wave function method which can precisely calculate the harmonic emission with different initial condition including the rotational temperature, spatial alignment and the excited electronic states. The comparisons are carried out between theoretical calculations of molecular wave function method and a series of experimental results.
Firstly molecular rotational excitation and field-free spatial alignment in a nonresonant intense laser field are studied numerically and analytically by using time-dependent Schr?dinger equation. The broad rotational wave packets excited by the femtosecond pulse are defined in the conjugate angle space, and their coefficients are obtained by solving a set of coupled linear equations. The temperature-dependent properties of angular distributions of CO and O2 molecules are obtained through analyzing the influences of the HOMOs on molecular spacial alignment.
Secondly we present a valence orbital method for high-order harmonic generation from diatomic molecule with arbitrary orientation by using space rotation operator. We evaluated the effects of each valence orbital of N2 and O2 on harmonic emission with different molecular alignment in detail. The calculation results show that the bonding orbital of N2 decides the maximum of harmonic emission when the molecular axis of N2 is aligned parallel to laser vector. For O2 molecule the two antibonding orbitals contribute the maximum of harmonic yield and two bonding orbitals slightly influence the alignment angle of maximum of harmonic radiation not exactly at 450 which confirm the experimental results in references.
Furthermore we also present a method of molecular wave functions for calculating harmonic emission of diatomic molecules based on time-dependent Schr?dinger equation. The molecular wave functions are superposed by a series of wave functions of electron terms weighted by time-dependent coefficients for different molecular orbitals, rotational and vibrational levels. The molecular alignment and rotational temperature dependent properties of harmonic emissions are calculated in detail when the initial conditions are excited states or mixed states. We put forward the theory of manipulating the harmonic emission with excited states of molecule based on a lot of calculated results.
Finally we carry out a series of harmonic emission experiments of N2 and O2 under different molecular alignment, different rotational temperature, different intensity of femtosecond pulse, different ellipticity of fundamental pulse, and different gas pressure in two color field. The properties of harmonic emission under different conditions are analyzed in detail. We find a well agreement between theoretical calculations and experimental results including those in foreign references.
引文
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95夏元钦,陈建新等.飞秒激光在氦气中的高次谐波.光学学报.2002, 22(9): 1035~1038
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97杨增强,周效信.用双激光脉冲操纵N2分子取向.物理化学学报.2007, 23(5): 751~756
98杨增强,周效信.温度对激光场中N2、O2分子取向的影响.物理化学学报.2006, 22(8): 932~936
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101 Y. J. Chen and J. Liu. High-Order Harmonic Generation from Diatomic Molecules with Large Internuclear Distance: The Effect of Two-Center Interference. Phys. Rev. A. 2008, 77: 013410
102 C. M. Dion and A. Keller et al. Laser-Induced Alignment Dynamics of HCN: Roles of the Permanent Dipole Moment and the Polarizability. Phys. Rev. A. 1999, 59: 1382~1391
103 Tamar Seideman. Manipulating External Degrees of Freedom with Intense Light: Laser Focusing and Trapping of Molecules. J. Chem. Phys. 1997, 106: 2881~2992
104 B. Friedrich and D. Herschbach. Alignment and Trapping of Molecules in Intense Laser Field. Phys. Rev. Lett. 1995, 74: 4623~4626
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107 Tamar Seideman. Revival Structure of Aligned Rotational Wave Packets. Phys. Rev.Lett. 1999, 83: 4971~4974
108 V. Renard and M. Renard et al. Nonintrusive Monitoring and Quantitative Analysis of Strong Laser-Field-Induced Impulsive Alignment. Phys. Rev. A. 2004, 70: 033420
109 P. W. Dooley and I. V. Litvinyuk et al. Direct Imaging of Rotational Wave-Packet Dynamics of Diatomic Molecules. Phys. Rev. A. 2003, 68: 023406
110 Christer Z. Bisgaard, Simon S. Viftrup and Henrik Stapelfeldt. Alignment Enhancement of a Symmetric Top Molecule by Two Short Laser Pulses. Phys. Rev. A. 2006, 73: 053410
111 D. Pinkham and R. R. Jones. Interference Effects in Above-Threshold Ionization from Diatomic Molecules: Determining the Internuclear Separation. Phys. Rev. A. 2005, 72: 023418
112 C. B. Madsen and L. B. Madsen. High-Order Harmonic Generation from Arbitrarily Oriented Diatomic Molecules Including Nuclear Motion and Field-Free Alignment. Phys. Rev. A. 2006, 74: 023403
113 Erik W. Aslaksen. Dielectric Model of Diatomic Molecules. Phys. Rev. A. 1972, 6: 1367~1370
114 L. Veseth. Many-Body Calculation of Photoionization Cross Section in CO. Phys. Rev. A. 1994, 49: 939~949
115 Ashok Jain and K. L. Baluja. Total Cross Sections for Electron Scattering from Diatomic and Polyatomic Molecules at 10-5000 eV. Phys. Rev. A. 1992, 45: 202~218
116 M. Lewenstein, Ph. Balcou and M.Yu.Ivanov et al. Theory of High Harmonic Generation by Low Frequency Laser Fields. Phys. Rev. A. 1994, 49(3):2117~2132
117 G. F. Gribakin and M. Yu. Kuchiev. Multiphoton Detachment of Electrons from Negative Ions. Phys. Rev. A. 1997, 55: 3760~3771
118 Howard R. Reiss. Effect of an Intense Electromagnetic Field on a Weakly Bound System. Phys. Rev. A. 1980, 22: 1786~1813
119 M. Yu. Kuchiev and V. N. Ostrovsky. Quantum Theory of High Harmonic Generation as a Three-Step Process. Phys. Rev. A. 1999, 60: 3111~3124
120 Richard N. Zare. Angular Momentum: Understanding Spatial Aspects in Chemistry and Physics. John Wiley and Sons Press New York. 1988:89
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122 V. I. Usachenko and V. A. Pazdzersky. Reexamination of High-Energy Above- Threshold Ionization ATI: an Alternative Strong-Field ATI Model. Phys. Rev. A. 2004, 69: 013406
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