Controlling high harmonic generation with molecular wave packets

We show that, by controlling the alignment of molecules, we can influence the high harmonic generation process. We observed strong intensity modulation and spectral shaping of high harmonics produced with a rotational wave packet in a low-density gas of N2 or O2. In N2, where the highest occupied molecular orbital (HOMO) has sigma(g) symmetry, the maximum signal occurs when the molecules are aligned along the laser polarization while the minimum occurs when it is perpendicular. In O2, where the HOMO has pi(g) symmetry, the harmonics are enhanced when the molecules are aligned around 45 degrees to the laser polarization. The symmetry of the molecular orbital can be read by harmonics. Molecular wave packets offer a means of shaping attosecond pulses.     

不同核轴取向的O2的高次谐波

分子的高次谐波是强场超快物理的重要研究课题. 采用建立在形式散射理论基础上的频域方法计算了O₂在线偏振激光场下的高次谐波, 探讨了核轴被准直在与激光传输方向垂直的平面内时, 高次谐波随核轴与光电场偏振方向所成夹角θ₀的依赖关系. 结果表明: 各次谐波都是在θ₀约为45°时强度最大, 并有较宽的峰值宽度; 当偏离此角度, 高次谐波的强度变小; 到达平行或垂直取向时, 降到最低. 分析表明, 这是由于高次谐波的强度取决于分子基态的电子在动量空间中的电场方向的布居. 针对核轴被准直在激光传输方向与电场偏振方向所确定的平面内的情况, 计算了高次谐波随θ₀的依赖关系, 结果与前一种情况基本相同. 分析发现, 当核轴被准直固定后, 分子绕核轴旋转的角度ψ没有固定, 所以最后的高次谐波强度需要对不同的ψ 时的高次谐波的贡献求和平均. 平均后相当于波函数相对于核轴旋转对称, 从而导致O₂的高次谐波仅与θ₀有关, 而与核轴被准直在哪个面上无关.     

Interferences from fast electron emission in molecular photoionization

We present a theoretical study of fast-electron emission produced in H2 and H2+ photoionization. We show that, when the electron wave length is comparable to the molecular size, the electron angular distributions arising from fixed-in-space molecules exhibit pronounced interference effects that critically depend on orientation and energy sharing between electrons and nuclei. In particular, for molecules oriented parallel to the polarization direction, the angular patterns reveal a complex nodal structure, while for molecules oriented perpendicularly, typical Young's double-slit interferences are observed. These patterns change dramatically as the molecule vibrates.     

A link between the second-order Jahn-Teller effect and the highest occupied molecular orbital postulate for molecular shapes

For a closed-shell molecule, a connection is drawn between two recent models for molecular shapes, namely, those based on the second-order Jahn-Teller (SOJT) effect and the highest occupied molecular orbital (HOMO) postulate respectively. Two necessary and sufficient conditions are derived within the molecular orbital framework for the approximation inherent in the SOJT model to be valid. One of these conditions is akin to the HOMO postulate.     

Numerical Simulations of femtosecond-laser-induced dynamic alignment of molecules in the high-frequency off-resonance regime

The motion equation for ? between the molecular axis and laser polarization direction in a high-frequency off-resonance femtosecond laser field is deduced while simultaneously examining the effects of a permanent dipole moment and field-induced polarizability and hyperpolarizability to molecular rotation. Femtosecond-laser-induced dynamic alignment of CO, N₂, and Br₂ molecules are investigated by numerically solving the obtained rotation equation for the angle ?. The effects of the molecular permanent dipole moment and the field-induced polarizability and hyperpolarizability on the degree of alignment are presented at different intensities. Our computational results show that the dynamic alignment of molecules is primarily determined by field-induced polarizability and the second hyperpolarizability for the laser intensity range from 5 × 10¹⁴ to 5 × 10¹⁶ W/cm². The contributions of higher order correction terms to molecular alignment can usually be neglected. The polarizability-field interaction makes the angular distributions of a molecule have a maximum along the polarization axis and a minimum perpendicular to it. The role of the second hyperpolarizability keeps the molecular counts maximum along the laser polarization direction but minimum at an angle of 45° between the molecular axis and the polarization direction. There is also a second maximum of molecular counts perpendicular to the polarization axis. For CO, N₂, and Br₂ molecules, the dependences of laser-induced dynamic alignment on laser intensity exhibit completely different characteristics.     

Forced molecular rotation in an optical centrifuge

Intense linearly polarized light induces a dipole force that aligns an anisotropic molecule to the direction of the field polarization. Rotating the polarization causes the molecule to rotate. Using femtosecond laser technology, we accelerate the rate of rotation from 0 to 6 THz in 50 ps, spinning chlorine molecules from near rest up to angular momentum states J approximately 420. At the highest spinning rate, the molecular bond is broken and the molecule dissociates.     

How to measure the internuclear vector from photoelectron angular distributions

This paper uses a nonperturbative scattering theory to study photoelectron angular distributions of homonuclear diatomic molecules irradiated by circularly polarized laser fields. This study shows that the nonisotropic feature of photoelectron angular distributions is not due to the polarization of the laser field but the internuclear vector of the molecules. It suggests a method to measure the molecular orientation and the internuclear distance of molecules through the measurement of photoelectron angular distributions.     

Selective excitation of the molecular rotational wave packet by two time-delayed laser pulses

In this paper, we investigate the control of the molecular wave packet of a linear molecule by two femtosecond laser pulses. It is shown that the odd and the even rotational wave packets created by a single laser pulse can be selectively excited by accurately controlling the time delay of another laser pulse. By inserting the peak of the second laser pulse at the position of maximum or minimum value around quarter or three quarter rotational period of the slope curve with odd (or even) rotational wave packet contribution that is created by the first laser pulse, the odd rotational wave packet can be enhanced (or suppressed) while the even rotational wave packet is suppressed (or enhanced). As a result, the molecular alignments around quarter and three quarter rotational periods can be obtained. Moreover, it is also shown that by inserting the second laser pulse around the quarter or three quarter rotational periods, the changes in the maximum degree of the molecular alignment for the odd and the even rotational wave packet contributions are consistent with their corresponding slope curves at these positions.     

Amplitude and rotation of the ellipticity of harmonicsfrom a linearly polarized laser field

We simulate the dynamic response of H₂⁺ in a linearly polarized laser field by numerically solving the time-dependent Schrödinger equation. The elliptically polarized high-order harmonics generated by H₂⁺ irradiated by the linearly polarized laser field are systematically investigated. The result shows that the amplitude and rotation of the ellipticity of harmonics are affected by the alignment angle and internuclear distance of the molecule. Analyzing the change in forces acted on the ionized electrons and the trajectories of the electrons, the phenomena are found to be due to the change in the direction of the total Coulomb forces from the two nuclei felt by the recollided ionized electrons in the direction perpendicular to the laser polarization direction. Based on the influence law, we can select the harmonics with a specific frequency band under different alignment angles and then synthesize the isolated attosecond pulses with different rotations, which can be continuously converted from right-handed circular polarization, linear polarization, and left-handed circular polarization by changing the alignment angle. This study provides a new possible approach to the real-time detection of molecular states by using attosecond pulses and obtaining more optimized harmonics with molecular properties.     

Field-free molecular orientation enhanced by tuning the intensity ratio of a three-color laser field

We theoretically study the field-free molecular orientation induced by a three-color laser field. The three-color laser field with a large asymmetric degree can effectively enhance the molecular orientation. In particular, when the intensity ratio of the three-color laser field is tuned to a proper value of I_3: I_2: I_1= 0.09 : 0.5 : 1, the molecular orientation can be improved by ～ 20% compared with that of the two-color laser field at intensity ratio I_2: I_1= 1 : 1 for the same total laser intensity of 2×10~(13)W/cm~2. Moreover, we investigate the effect of the carrier-envelope phase(CEP) on the molecular orientation and use the asymmetric degree of the laser field to explain the result. We also show the influences of the laser intensity, rotational temperature, and pulse duration on the molecular orientation. These results are meaningful for the theoretical and experimental studies on the molecular orientation.     

Scattering of N2 from Ni(111)

A cold (T_rot<10 K) beam of N₂ with an initial translational energy of 0.40 eV strikes an Ni(111) surface at surface temperatures from 300 to 873 K at several incident angles from 15 to 60°. The rotational energy and angular distributions of the scattered molecules are probed using (2+1) resonance-enhanced multiphoton ionization. Molecules scattered in the specular direction have mean rotational energies that are independent of surface temperature, whereas those scattered at angles far from the specular show a dependence on surface temperature, caused likely by multiple collisions with the surface before escape. A rotational rainbow, seen in systems such as CO–Ni(111) and N₂–Ag(111), is not seen in this system. For molecules that scatter close to the specular direction, approximately 10% of the initial translational energy is converted into rotational energy of the scattered N₂. For surface temperatures above room temperature, the angular distributions indicate that molecules that scatter into low-J states also tend to exit in a broad peak (10–20° FWHM) near the specular, and this peak is broadened with increasing incident angle. The molecules that scatter into high-J states have a much broader distribution, indicating that they are trapped rotationally during the initial collision and suffer multiple collisions before leaving the surface.     

Field-free molecular orientation induced by combined femtosecond single- and dual-color laser pulses：The role of delay time and quantum interference

The coherent control of field-free molecular orientation of CO with combined femtosecond single- and dual-color laser pulses has been theoretically studied. The effect of the delay time between the femtosecond single- and dual-color laser pulses is discussed, and the physical mechanism of the enhancement of molecular orientation with pre-alignment of the molecule is investigated. It is found that the basic mechanism is based on the creation of a rotational wave packet by the femtosecond single-color laser pulse. Furthermore, we investigate the interference between multiple rotational excitation pathways following pre-alignment with femtosecond single-color laser pulse. It is shown that such interference can lead to an enhancement of the orientation of CO molecule by a factor of 1.6.     

Laser-induced Alignment and Coulomb Explosion of CO2

实验研究了CO₂分子在飞秒强激光脉冲作用下的动力学过程,包括分子取向,隧穿电离和库仑爆炸,激光强度从1×10¹³W/cm²变化到6×10¹⁴W/cm². 当激光强度小于分子的电离阈值时,CO₂分子的非绝热转动激发形成一个相干转动波包,波包演化导致分子沿激光电场方向取向. 激光脉冲结束后,分子取向可以周期性地再现,利用另一束激光可以对取向结构进一步进行修饰. 当激光强度大于分子     

Effects of the internuclear vector on the photoelectron angular distributions of H<Subscript>2</Subscript><Superscript>+</Superscript>

We study the photoelectron angular distributions (PADs) of diatomic molecule H₂ ⁺ irradiated by intense laser fields using a nonperturbative scattering theory. We find that the internuclear vector may change the PADs. The PADs have qualitative changes with the increasing of the internuclear distance. The molecular orientation affect the symmetry of the PADs. When the internuclear vector is vertical or parallel to the laser polarization vector, the PADs are four-fold symmetric; for other case the PADs are two-fold symmetric. Due to the modulation effect resulting from the molecular multi-core nature, the size of the jet and the main lobe can be enlarged or reduced. The molecular modulation effect become obvious for large internuclear distance.     

Direct measurement of the angular dependence of ionization for N2, O2, and CO2 in intense laser fields

We experimentally measure the ionization probability as a function of alignment angle of three molecules in intense laser fields: nitrogen, oxygen, and carbon dioxide. Unlike atoms, molecules have a rotational degree of freedom. By controlling the alignment of the molecule relative to the laser field, molecules offer additional ways to understand strong-field ionization. The angular dependence of ionization directly maps to the orbital symmetry of each molecule. Carbon dioxide is seen to have a very sharp preference for ionization when aligned at 45 degrees to the laser field, in significant disagreement with current theories.     

The multielectron dissociative ionization dynamics of N2 molecule in intense femtosecond laser fields with arbitrary polarization

The field-ionization Coulomb explosion model is extended to investigate the multielectron dissociative ionization process of N₂ molecule irradiated by an intense femtosecond laser field with an arbitrary polarization. The ionization process of N₂ molecule is found to be optimal at the critical internuclear distance R_c=7a.u., which is independent of the laser polarization state, the molecular explosion channel and the angle between the molecular axis and the direction of laser electric field. The kinetic energies of the ion fragments are identical in the cases of linear and circular polarizations at the same incident laser intensity. However,the probability of electron ionization is very sensitive to the above three parameters. At the critical distance R_c=7a.u. the angular dependence of the threshold intensity for the over-the-barrier ionization leads to the geometric alignment of molecules in the case of linear polarization. The threshold intensity in the case of circular polarization is apparently higher than that in the case of linear polarization, which can well explain the significant decrease of ionization in the case of circular polarization. The numerical calculations are compared with the experimental measurements.     

Orientational selection of molecules in combined laser and electrostatic fields

It is shown that the combined effects of electrostatic and resonant laser fields on a molecular ensemble can be used to control the orientation of molecules by changing their internal state. In contrast to most other schemes for controlling molecular orientation, the proposed method does not require rotational cooling and can be highly efficient at room temperature.     

Laser-field-free molecular orientation

We demonstrate laser-field-free molecular orientation with the combination of a moderate electrostatic field and an intense nonresonant rapidly turned-off laser field, which can be shaped with the plasma shutter technique. We use OCS (carbonyl sulfide) molecules as a sample. Molecular orientation is adiabatically created in the rising part of the laser pulse, and it is found to revive at around the rotational period of an OCS molecule with the same degree of orientation as that at the peak of the laser pulse in the virtually laser-field-free condition. This accomplishment means that a new class of molecular sample has become available for various applications.     

Controlling attosecond double ionization dynamics via molecular alignment

We investigate the dynamics of double ionization in aligned nitrogen molecules. An ultrashort, weak laser pulse creates an aligned ensemble of molecules that is ionized with a subsequent, strong probe pulse. We find that the two electrons involved in nonsequential double ionization more likely exit the molecule in the same direction if it is parallel to the probe laser polarization, indicating that they are ejected within a few hundred attoseconds of each other. Double ionization is less probable and takes longer for perpendicular molecules.     

Valence orbital method of calculating harmonic emission from diatomic molecule

We present a valence orbital method of calculating high-order harmonic generation from a diatomic molecule with arbitrary orientation by using a space rotation operator. We evaluate the effects of each valence orbital on harmonic emissions from N₂ and O₂ molecules in detail separately. The calculation results confirm the different properties of harmonic yields from N₂ and O₂ molecules which are well consistent with available experimental data. We observe that due to the orientation dependence of \sigma and \pi orbitals, the bonding orbital (\sigma _{2pz} )^2 of N₂ determines the maximum of harmonic emission when the molecular axis of N₂ is aligned parallel to the laser vector, and the magnitude of the high harmonic signal gradually weakens with the orientation angle of molecular axis increasing. But for O₂ molecule the antibonding orbitals (\pi _{2py}^\ast )^1 and (\pi _{2pz}^\ast )^1 contribute to the maximum of harmonic yield when O₂ is aligned at 45^{\circ} and bonding orbitals (\pi _{2py} )^2 and (\pi _{2pz} )^2 slightly influence the orientation angle of maximum of harmonic radiation not exactly at 45^{\circ}.