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.     

Interplay of polarization geometry and rotational dynamics in high-order harmonic generation from coherently rotating linear molecules

Recent reports on intense-field pump-probe experiments for high-order harmonic generation (HHG) from coherently rotating linear molecules have revealed remarkable characteristic effects of the simultaneous variation of the polarization geometry and the time delay on the high-order harmonic signals. We analyze the effects and give a unified theoretical account of the experimental observations. Furthermore, characteristic behavior at critical polarization angles are found that can help to identify the molecular orbital symmetry in connection with the problem of molecular imaging from the HHG data.     

Probing orbital structure of polyatomic molecules by high-order harmonic generation

The effects of electronic structure and symmetry are observed in laser driven high-order harmonic generation for laser aligned conjugated polyatomic molecular systems. The dependence of the harmonic yield on the angle between the molecular axis and the polarization of the driving laser field is seen to contain the fingerprint of the highest occupied molecular orbitals in acetylene and allene, a good quantitative agreement with calculations employing the strong field approximation was found. These measurements support the extension of the recently proposed molecular orbital imaging techniques beyond simple diatomic molecules to larger molecular systems.     

Elliptic dichroism, ellipticity and the offset angle of high harmonics generated by arbitrary homonuclear diatomic molecules

The nth harmonic emission rate has contributions of the components of the T-matrix element in the direction of the laser-field polarization and in the direction perpendicular to it. Using both components of the T-matrix element we present a theoretical approach for calculation of the ellipticity and the offset angle of high harmonics. The molecular bound state is represented by HOMO or by HOMO-1. We show that high harmonics, generated by molecules oriented by an angle ??_L with respect to the major semiaxis of the laserfield polarization ellipse, are elliptically polarized even if the applied field is linearly polarized. Using examples of N₂ and O₂ molecules we show the existence of extrema and sudden changes of the harmonic ellipticity and the offset angle for particular molecular alignment. The interference between different contributions to the T-matrix element depends on the molecular symmetry. Presenting partial or total parameters of elliptic dichroism in the (??_L, n) plane clear interference minima are observed. Therefore, the measurement of the elliptic dichroism may reveal information about the molecular structure and symmetry.     

High-order harmonic generation in laser-irradiated homonuclear diatomics: The velocity gauge version of the molecular strong-field approximation

The strong-field process of high-order harmonic generation in laser-irradiated light homonuclear diatomics (H ₂ ⁺ , N₂, and O₂) is studied compared to atomic counterparts (of nearly identical ionization potential) within the velocity gauge version of conventional strong-field approximation. The applied strong-field approach (we alternatively developed earlier to incorporate rescattering effects beyond the quasiclassical saddle-point approximation) is currently extended to molecular case by means of supplementing the standard linear combination of atomic orbitals and molecular orbitals method. The associated model proved to adequately reproduce a general shape and detailed structure of molecular harmonic spectra, which demonstrate a number of remarkable distinctive differences from respective atomic spectra calculated under the same laser pulses. These revealed differences as well as other generic features (such as the extent of the high-frequency plateau and harmonic emission rates) are found to be strongly dependent on internuclear separation and also very sensitive to the orbital and bonding symmetry of the contributing molecular valence shell. In particular, for some group of harmonics, the emission rates were ascertained to dominate by contribution from inner molecular shells of higher binding energy and different orbital symmetry compared to the outermost molecular orbital normally predominantly contributing. Finally, due to a high suppression in ionization of O₂ relative to counterpart atomic Xe, the harmonic spectrum calculated for O₂ proved to demonstrate a noticeably longer plateau extending far beyond the harmonic cutoff in the Xe spectrum, in a fairly good accordance with relevant experiments.     

Ellipticity dependence of high-order harmonic generation from aligned molecules

We report ellipticity dependence of high-order harmonic generation (HHG) from aligned N2, O2, and CO2 molecules. Experimentally, we find that the ellipticity dependence is sensitive to molecular alignment and to the shape and symmetry of the valence orbitals. It is also found that the destructive interference in the recombination process affects the ellipticity dependence. Theoretically, we extend the original Lewenstein model to a more generalized model, which can be applicable to HHG from molecules, by introducing an electron acceleration parameter xi(theta) and by combining the molecular orbital method. The present observations are successfully explained by our model.     

Molecular recollision interferometry in high harmonic generation

We use extreme-ultraviolet interferometry to measure the phase of high-order harmonic generation from transiently aligned CO(2) molecules. We unambiguously observe a reversal in phase of the high-order harmonic emission for higher harmonic orders with a sufficient degree of alignment. This results from molecular-scale quantum interferences between the molecular electronic wave function and the recolliding electron as it recombines with the molecule, and is consistent with a two-center model. Furthermore, using the combined harmonic intensity and phase information, we extract accurate information on the dispersion relation of the returning electron wave packet as a function of harmonic order. This analysis shows evidence of the effect of the molecular potential on the recolliding electron wave.     

Role of highest occupied molecular orbitals in molecular field-free alignment by a femtosecond pulse

This paper studies the molecular rotational excitation and field-free spatial alignment in a nonresonant intense laser field numerically and analytically by using the time-dependent Schr?dinger equation. The broad rotational wave packets excited by the femtosecond pulse are defined in conjugate angle space, and their coefficients are obtained by solving a set of coupled linear equations. Both single molecule orientation angles and an ensemble of O₂ and CO molecule angular distributions are calculated in detail. The numerical results show that, for single molecule highest occupied molecular orbital (HOMO) symmetry σ tends to have a molecular orientation along the laser polarization direction and the permanent dipole moment diminishes the mean of the orientation angles; for an ensemble of molecules, angular distributions provide more complex and additional information at times where there are no revivals in the single molecule plot. In particular, at the revival peak instant, with the increase of temperature of the molecular ensemble, the anisotropic angular distributions with respect to the laser polarization direction of the π _g orbital gradually transform to the symmetrical distributions regarding the laser polarization vector and for two HOMO configurations angular distributions of all directions are confined within a smaller angle when the temperature of the molecular ensemble is higher.     

Angle-resolved high-order above-threshold ionization of a molecule: sensitive tool for molecular characterization

The strong-field approximation for ionization of diatomic molecules by an intense laser field is generalized to include rescattering of the ionized electron off the various centers of its molecular parent ion. The resulting spectrum and its interference structure strongly depend on the symmetry of the ground state molecular orbital. For N2, if the laser polarization is perpendicular to the molecular axis, we observe a distinct minimum in the emission spectrum, which survives focal averaging and allows determination of, e.g., the internuclear separation. In contrast, for O2, rescattering is absent in the same situation.     

Retrieving angular distributions of high-order harmonic generation from a single molecule

We present a novel method to retrieve angular distributions of high-order harmonic generation from a single molecule. This technique uses an iterative procedure based only on experimental results of time and angle-dependent harmonic signals, and no actual shape of molecular orbital is assumed. The molecular axis distribution in a target gas can simultaneously be deduced in this procedure. The angle-dependent signal retrieved for a single N2 and O2 molecule is demonstrated to reflect the highest occupied molecular orbital, excluding the ambiguity due to the imperfect alignment.     

High harmonic generation and molecular orbital tomography in multielectron systems: beyond the single active electron approximation

It was recently shown that the highest molecular orbital of N2 could be reconstructed from a series of high harmonic measurements. Existing theories of high harmonic generation and orbital tomographic imaging are based on the single active electron approximation that ignores essential quantum mechanical properties such as the indistinguishability of identical particles and the Pauli exclusion principle. We show that, when fully antisymmetrized multielectron wave functions and electronic relaxation in the cation are considered, molecular orbital tomography records the image of the Dyson orbital plus exchange contributions from inner shells. The mixing of contributions from more than one molecular orbital gives access to additional wave function information. By utilizing the exchange term, harmonic emission from a closed-shell 4-electron system can be interpreted as a complete Hartree-Fock wave function.     

Manifestation of anisotropic collisional generation of higher polarization moments in polarization of quadrupole emission

Direct observability of polarization moments of a higher order—octupole orientation of atomic angular momenta (κ=3) and their hexadecapole alignment (κ=4)—from polarization of quadrupole radiation is discussed. The case when atoms are excited through dipole absorption of light producing orientation or alignment of angular momenta with κ=1 or 2 and higher polarization moments are induced by collisions with a beam of particles is considered. It is shown that differences in the laws of transformation of polarization moments of various ranks κ in rotations of coordinate axes allow us to select the pure contribution of the higher polarization moment under study from the signal of polarization of quadrupole emission by excluding the contribution of orientation or alignment with κ=1 or 2. Optimum systems of coordinate axes for the observation of octupole orientation from circular polarization of light and for the observation of hexadecapole alignment from linear polarization of light, in which the pure contribution of the higher polarization moment under study to polarization of quadrupole emission reaches its maximum, are calculated.     

Accurate prediction of interference minima in linear molecular harmonic spectra by a modified two-center model

We demonstrate that the interference minima in the linear molecular harmonic spectra can be accurately predicted by a modified two-center model. Based on systematically investigating the interference minima in the linear molecular harmonic spectra by the strong-field approximation(SFA), it is found that the locations of the harmonic minima are related not only to the nuclear distance between the two main atoms contributing to the harmonic generation, but also to the symmetry of the molecular orbital. Therefore, we modify the initial phase difference between the double wave sources in the two-center model, and predict the harmonic minimum positions consistent with those simulated by SFA.     

Dynamic properties of angle-dependent high-order harmonic generation from coherently rotating molecules

High-order harmonic generation from coherently rotating N2 and O2 molecules has been observed for different alignment angles in a pump and probe experiment using femtosecond laser pulses. The results obtained are in excellent agreement with those calculated using a recently developed theory, which represent the characteristic properties predicted for angle-dependent harmonic generation. It is shown that polarization geometry and alignment distribution play essential roles in potential applications to probe electronic structure and dynamics of molecular systems.     

LB膜的各向异性与二次谐波超平方增长

用偏振紫外－可见吸收及旋转样品二次谐波方法研究了半花菁／花生酸Ｙ型交替ＬＢ多层膜中由垂直浸渍过程诱导和层间相互作用增强的分子在基板平面内的定向排列，提出并证实了随层数增长的平面内附加偶极矩导致光学二次谐波强度随ＬＢ膜厚度的超平方增长关系。     

飞秒激光脉冲在氮气中产生高次谐波的实验研究

报道了以氮气为介质产生高次谐波的实验结果。实验中主要研究了不同的气体密度、不同入射激光能量和不同偏振对高次谐波辐射强度及谐波级次的影响。并从理论上进行了定性分析。分析结果表明：要想得到较高次、较强的谐波辐射，必须反复进行实验，确定最佳的激光能量和气体密度，以减少由于自由电子密度的提高而导致的相位失配的影响。     

极化条件对偶氮化合物薄膜中分子取向的影响

 为探索不同的极化条件对分子取向的影响,用旋涂法制备了偶氮主客体掺杂薄膜,并用电晕极化的方法分别在不同温度和厚度条件下使分子取向,通过测量极化前后紫外-可见吸收谱,研究了平均取向因子的变化,并和二次谐波产生结果进行了比较。实验结果表明：对于厚度相同的偶氮薄膜,随着温度的升高,平均取向因子增大,但二次谐波信号强度先增大后减小;温度越接近聚合物玻璃转变温度,分子越容易取向,但温度过高,聚甲基丙烯酸甲酯变为粘滞态,部分偶氮分子容易在高温下蒸发掉,导致二次谐波信号强度降低,而平均取向因子增大;随着薄膜厚度的增大,针-板电极电场造成薄膜内部电场分布的不均匀性增加,极化效率降低,平均取向因子不断减小,二次谐波信号强度先增大后减小。     

相对论涡旋高次谐波的产生与调控理论研究

目前,具有螺旋相位波前和环状光强分布的涡旋光束已在光学领域获得了广泛应用,其产生与调控自然成了研究的热点。利用三维粒子模拟程序对双色拉盖尔高斯激光驱动固体等离子激发同时携带自旋角动量与轨道角动量的高次谐波的物理过程进行了研究,根据高次谐波产生过程中的光子能量与角动量守恒定律对其内在物理机制进行了理论分析,并讨论了对谐波阶次、偏振态（自旋角动量）以及拓扑荷数（轨道角动量）进行调控的方法。研究结果为开发高亮度、超短超快、短波长、自旋与轨道角动量可调控的涡旋光束辐射源提供了理论依据,在光学微操控、超分辨成像、光通信以及离子加速等领域具有较大的实际应用前景。     

超强激光作用下相对论电子振荡所导致的谐波辐射

研究发现，在超强激光作用下电子运动的相对论效应可导致高次谐波辐射，采用单电子模型计算分析了不同偏振微光作用下的高次谐波发射，表明圆偏振激光较线偏振激光更有利于高次谐波产生。     

Perfect valley polarization in MoS<Subscript>2</Subscript>

We study perfect valley polarization in a molybdenum disulfide (MoS₂) nanoribbon monolayer using two bands Hamiltonian model and non-equilibrium Green’s function method. The device consists of a one-dimensional quantum wire of MoS₂ monolayer sandwiched between two zigzag MoS₂ nanoribbons such that the sites A and B of the honeycomb lattice are constructed by the molecular orbital of Mo atoms, only. Spin-valley coupling is seen in energy dispersion curve due to the inversion asymmetry and time-reversal symmetry. Although, the time reversal symmetry is broken by applying an external magnetic field, the valley polarization is very small. A valley polarization equal to 46% can be achieved using an exchange field of 0.13 eV. It is shown that a particular spin-valley combination with perfect valley polarization can be selected based on a given set of exchange field and gate voltage as input parameters. Therefore, the valley polarization can be detected by detecting the spin degree of freedom.