High-order harmonic generation with a strong laser field and an attosecond-pulse train: The Dirac-Delta comb and monochromatic limits

In recent publications, it has been shown that high-order harmonic generation can be manipulated by employing a time delayed attosecond-pulse train superposed to a strong, near-infrared laser field. It is an open question, however, which is the most adequate way to approximate the attosecond-pulse train in a semianalytic framework. Employing the strong-field approximation and saddle-point methods, we make a detailed assessment of the spectra obtained by modeling the attosecond-pulse train by either a monochromatic wave or a Dirac-Delta comb. These are the two extreme limits of a real train, which is composed by a finite set of harmonics. Specifically, in the monochromatic limit, we find the downhill and uphill sets of orbits reported in the literature, and analyze their influence on the high-harmonic spectra. We show that, in principle, the downhill trajectories lead to stronger harmonics, and pronounced enhancements in the low plateau region. These features are analyzed in terms of quantum interference effects between pairs of quantum orbits, and compared to those obtained in the Dirac-Delta limit.     

Self-induced acoustic transparency of three-component longitudinal-transverse pulses

The features of the nonlinear dynamics of three-component elastic pulses in a low-temperature crystal containing paramagnetic impurities of electron and nuclear spins have been analyzed in the slowly varying envelope approximation. The presence of the electron spin subsystem makes it possible to equate the velocities of longitudinal sound and transverse acoustic waves; as a result, all components of the strain field efficiently interact with each other through the nuclear spin subsystem. The system of equations for envelopes of harmonics of the components of the strain field and the spin variables has been derived. The relations between the amplitudes and phases of the components have been obtained, the spectral composition has been analyzed, and the regimes of acoustic transparency of three-component longitudinal-transverse pulses have been discussed.     

Harmonics generation in ultra-thin nanofilms irradiated by intense nonrelativistic laser pulses

The problem of harmonics generation in nanotargets is considered at the range of parameters (a nanotarget diameter and a pump laser intensity) when the oscillation amplitude of an electron in a target is much larger than the target width. Electron motion in charged nanotargets in the presence of a laser field of different (non-relativistic) strength is considered. It is demonstarted that for lasers of infrared frequencies clusters do not possess strong enough potential to bound electrons with large oscillation amplitudes. Opposite to clusters, nanofilms were found to be very perspective targets in the problem considered. A simple analytic model and molecular dynamic simulations showed increased harmonics generation when the oscillation amplitude of electrons in a film becomes much larger, than the film width. Different regimes of generation are briefly discussed.     

Attosecond probing of vibrational dynamics with high-harmonic generation

The numerical solution of the time-dependent Schrodinger equation for vibrating hydrogen molecules in few-cycle laser pulses shows that high-harmonic generation is sensitive to the laser-induced vibrational motion. More intense harmonics are generated in heavier isotopes, the difference increasing with the harmonic frequency. Analytical theory reveals a dependence of the harmonics on the vibrational autocorrelation function. With the help of a genetic algorithm, the nuclear motion can be reconstructed from the harmonic spectra with sub-fs time resolution.     

Generation of harmonics during the interaction of ultrashort superstrong laser pulses with solid targets

Generation of even and odd harmonics in the skin layer formed during the interaction of a short relativistic laser pulse with solid targets is considered. The complex motion of free electrons in the skin layer along the electric field vector and along the direction of propagation of a laser wave is analyzed. The Fourier expansion of the trajectory of this motion is used to obtain the components of the conductivity tensor and of the amplitude of the transverse electromagnetic field of harmonics propagating along the electric field. Even harmonics appear due to relativistic effects. The efficiency of generation of even and odd harmonics at the leading front of a laser pulse is calculated.     

Theoretical Exploration of the Isotopic Effect on Molecular High-Order Harmonic Generation

The isotopic effect on the generation of the molecular high-order harmonics is studied by numerically solving the one-dimensional time-dependent Schrödinger equation when the model hydrogen molecule ions/hydrogen deuterium molecule ions are exposed to an intense laser pulse. To explain the effect more clearly, not only the ionization probabilities but also the electron–nuclear probability density distributions and time-frequency profiles are calculated. The results show that more intense harmonics are generated in the asymmetric diatomic molecule ions/hydrogen deuterium molecule ions than those of hydrogen molecule ions. Moreover, the interference minimum in the harmonic spectra is investigated by adjusting the laser intensity and the initial vibrational state. It is shown that the interference minimum is sensitive to the laser intensity and the initial vibrational level for hydrogen molecule ions; in contrast, it is only dependent on the initial vibrational level for hydrogen deuterium molecule ions.     

激光驻波中运动电子的谐波自发辐射

 采用单电子模型分析了电子在线极化激光驻波中的动力学及谐波自发辐射谱,数值计算了电子在驻波中的运动情况及辐射谱。结果表明:电子在波节和波腹处入射后,其辐射谱出现不同的特征;电子在波节处垂直磁场入射后,在洛伦兹力作用下快速振动并向前运动,其向后辐射的光谱发生红移,向前辐射的光谱发生蓝移,谱线出现展宽;当激光强度或者电子初始能量增大时,这些效应更加突出,以至于产生更高阶谐波,形成连续谱;而电子在波腹处以平行电场的方向入射后,仅在电场作用下作直线运动,其自发辐射谱线没有发生移动和展宽。     

Influence of constant electric field on generation of higher harmonics in semiconductor carbon nanotubes

The generation of higher harmonics by semiconductor carbon nanotubes in the presence of constant electric field polarized along the nanotube axis is considered. The analysis is performed in the semiclassical model of electron motion without taking into account interband transitions. The electron system of carbon nanotubes is described using the kinetic Boltzmann equation in the relaxation time approximation. The dependence of higher harmonic amplitude on the field characteristics is studied.     

Yield enhancement of elliptical high harmonics driven by bicircular laser pulses

We theoretically investigate the yield enhancement of elliptical high harmonics in the interaction of molecules with bicircular laser pulses by solving the time-dependent Schrödinger equation. It is shown that by adjusting the relative intensity ratio of the two bicircular field components in specific ranges the yield of the molecular high harmonics for the plateau and cutoff regions can be respectively enhanced. To analyze this enhancement phenomenon, we calculate the weights of the electron classical trajectories. Additionally, we also study the ellipticity distribution of harmonics for different intensity ratios. We find that these enhanced harmonics are elliptically polarized, which we mainly attribute to the recombination dipole moment of the major weighted trajectories. These enhanced elliptical extreme ultraviolet and soft x-ray radiations may serve as essential tools for exploring the ultrafast dynamics in magnetic materials and chiral media.     

Spectral densities of spherical harmonics for rotational Brownian motion

Spectral densities of spherical harmonics arising from the rotational Brownian motion of molecules are calculated. The molecules are supposed to be spherical or linear, and account is taken of the influence of their inertia. When the results for a spherical molecule are applied to nuclear magnetic resonance, an expression for spin-lattice relaxation time is deduced and this is shown to provide a small correction to one calculated by Bloembergen, Purcell and Pound⁸). It is pointed out that the theory may be extended to nuclear magnetic processes when the thermal molecular motion is anisotropic.     

Effects of electron relaxation on multiple harmonic generation from metal surfaces with femtosecond laser pulses

Calculations are presented for the first four (odd and even) harmonics of an 800 nm laser from a gold surface, with pulse widths ranging from 100 down to 14 fs. For peak laser intensities above 1 GW/cm² the harmonics are enhanced because of a partial depletion of the initial electron states. At 10¹¹ W/cm² of peak laser intensity the calculated conversion efficiency for 2nd-harmonic generation is 3 × 10⁻⁹, while for the 5th-harmonic it is 10⁻¹⁰. The generated harmonic pulses are broadened and delayed relative to the laser pulse because of the finite relaxation times of the excited electronic states. The finite electron relaxation times cause also the broadening of the autocorrelations of the laser pulses obtained from surface harmonic generation by two time-delayed identical pulses. Comparison with recent experimental results shows that the response time of an autocorrelator using nonlinear optical processes in a gold surface is shorter than the electron relaxation times. This seems to indicate that for laser pulses shorter than ∼30 fs, the fast nonresonant channel for multiphoton excitation via continuum-continuum transitions in metals becomes important as the resonant channel becomes slow (relative to the laser pulse) and less efficient.     

两束同色激光场和中红外场驱动氦原子在等离激元中产生的单个阿秒脉冲

通过数值求解一维氦原子由两束同色激光场和中红外形成组合场中的含时薛定谔方程,研究了氦原子在纳米等离激元中发射高次谐波的性质以及合成阿秒脉冲的特点.研究表明,在等离激元中氦原子在组合场驱动下发射的高次谐波相对于均匀场情况下截止位置会得到明显扩展,但等离激元对处在连续态电子的吸收效应会对高次谐波截止位置影响较大,通过改变激元的相对位置能明显提高其中一个轨道对谐波的贡献,抑制另一些电子轨道的贡献.经典分析表明,两个电子轨道发生并合,从而实现单个阿秒脉冲的输出.与原子在均匀场驱动的情况相比,阿秒脉冲的宽度明显缩短,最短可实现28 as的单个脉冲输出.     

相对传播的双脉冲激光与薄膜靶作用产生的强单色谐波

研究了相对传播的双脉冲激光与薄膜靶的作用,观察到很强的谐波产生.其物理图像是:圆偏振高对比度强激光脉冲作用于薄膜靶,由光压推动产生的高密度等离子体靶向前运动,同时由于电荷分离场的作用,使得离子束和电子束在纵向上都有好的聚束,从而产生以相对论速度向前运动的等离子体镜;反向入射一个探测光到已被加速的等离子体镜上,由多普勒频移产生强的单色N次谐波,探测光脉冲被"压缩"至原来的1/N.还讨论了激光和等离子体参数对等离子体镜的运动和谐波级次的影响,以及相对论运动等离子体镜的稳定性对谐波的影响.     

Spectroscopic characterization of vacuum ultraviolet free electron laser pulses

Because of the stochastic nature of self-amplified spontaneous emission (SASE), it is crucial to measure for single pulses the spectral characteristics of ultrashort pulses from the vacuum ultraviolet free electron laser (FLASH) at DESY, Germany. To meet this particular challenge, we have employed both photon and photoelectron spectroscopy. Each FEL pulse is composed of an intense and spectrally complex fundamental, centered at a photon energy of about 38.5 eV, with a bandwidth of 0.5% accompanied by higher harmonics, each carrying an intensity of typically 0.3 to 0.6% of that of the fundamental. The correlation between the harmonics and the fundamental is in remarkable agreement with a simple statistical model of SASE FEL radiation.     

Dynamic nature of the ion wake in dusty plasmas

The dynamic nature of the ion wake formed downstream a dust particle immersed in a plasma with flowing ions has been investigated via Particle-in-Cell simulation. It is found that the wake oscillates in time and the motion is characterized by some dominant frequencies. By means of signal processing analysis, three harmonics are detected (two at low frequencies and one at high frequencies) and compared to the characteristic plasma frequencies given by the dispersion relations for ions and electrons. Good matching is found between the high frequency harmonic and the electron plasma frequency, and between the low frequency harmonics and the ion acoustic and ion plasma frequencies.     

Dynamics of Na clusters in picosecond laser pulses

We investigate the electronic and ionic dynamics of Na clusters under the influence of a laser pulse in the range 100 femtoseconds to picoseconds. The dynamics is described by means of the time-dependent local-density approximation coupled to ionic molecular dynamics (TDLDA-MD). Variation of pulse length allows us to explore the time scales of ionic motion in a manner similar to pump and probe experiments. Resonant enhancement of electron emission serves as a measure for the time scale of Coulomb explosion. Received: 3 July 2001 / Published online: 10 October 2001     

Efficient generation of highly elliptically polarized attosecond pulses

We theoretically demonstrate a scheme to efficiently generate attosecond pulses with high ellipticity by a counter-rotating bicircular field with frequency ratio of 1 : 3 (800 + 267 nm) and 1 : 4 (1600 + 400 nm). It is shown that efficient attosecond pulses with high ellipticity of 0.54 (800 + 267 nm) and 0.79 (1600 + 400nm) can be generated. We also investigate the scaling law of high harmonic generation yield. It is shown that the intensity of the high harmonics can be increased by more than one order of magnitude in the bicircular fields with higher frequency ratios. The high ellipticity and high efficiency of high harmonics are explained by analyzing the symmetry of driving field and the classical electron trajectories.     

Odd harmonic generation of ultra-intense laser pulses reflectedfrom an overdense plasma

A method of generating odd harmonics from an intense laser incident upon a sharp vacuum-overdense plasma interface is presented. One- and two-dimensional simulations are used to investigate the interaction of ultra-intense laser pulses with a sharp vacuum-plasma interface. With an intensity greater than 10¹⁸ W/cm² , these pulses have a pressure greater than 10³ Mbar creating large density oscillations and relativistic electron velocities at the surface. This results in efficient odd harmonic generation. The author present is a physical model for this harmonic generation mechanism, along with some scaling of the power in the third harmonic. This is compared with relativistic particle-in-cell simulations that include mobile and immobile ions, as well as a variety of upper shelf densities. A discussion on how ion profile modifications influence the harmonics is also presented     

Optimization of attosecond pulse generation

The generation of attosecond pulses by superposition of high harmonics relies on their synchronization in the emission. Our experiments in the low-order, plateau, and cutoff regions of the spectrum reveal different regimes in the electron dynamics determining the synchronization quality. The shortest pulses are obtained by combining a spectral filtering of harmonics from the end of the plateau and the cutoff, and a far-field spatial filtering that selects a single electron quantum path contribution to the emission. This method applies to isolated pulses as well as pulse trains.     

Interaction of nuclear spins with a time-dependent electric field in ferroelectric KNbO3

The effect of transitions in the nuclear spin system on the motion of the electric polarization in ferroelectric potassium niobate is studied theoretically. The equations of motion of the polarization are derived with inclusion of the interaction of the polarization with the nuclear spins and employed to calculate the contribution from nuclear transitions to the dielectric susceptibility of the crystal. This contribution has resonance maxima at the frequencies of nuclear transitions and is proportional to the square of the background dielectric susceptibility of the crystal. For the ferroelectric, this contribution is far larger than for earlier studied nonferroelectric dielectrics. Numerical estimates show that, in potassium niobate, the contribution from the nuclei to the dielectric susceptibility is of the same order of magnitude as that to the magnetic susceptibility.