Controlling the macro- and micro-processes influenсing harmonic generation in laser-produced plasmas

We review the studies of the spatial conditions for the quasi-phase-matching in the multi-jet laserproduced silver plasma. These studies of the off-axis and on-axis spatial components of harmonics allowed the demonstration of significant enhancement of a group of harmonics in the latter case. We analyze the role of plasma emission, together with phase-mismatch, that deteriorate the conditions of high-order harmonic generation due to significant phase distortion between the interacting waves. We also discuss the resonanceinduced enhancement of single harmonic and the quasi-phase-matching-induced enhancement of the group of harmonics during propagation of the tunable mid-infrared femtosecond pulses through the perforated laser-produced indium plasma. Those studies have shown that the enhancement of harmonics using the macro-process of quasi-phase-matching is comparable with the one using micro-process of resonantly enhanced harmonic. We conclude that joint implementation of the two methods of the increase of harmonic yield could be a useful tool for generation of strong short-wavelength radiation in different spectral regions.     

Ultrahigh Harmonic Generation from an Atom with Superposition of Ground State and Highly Excited States

We investigate the high-order harmonic generation from an atom prepared in a superposition of ground state and highly excited state. When the atom is irradiated by an ultrashort pulse, the cutoff position of the plateau in the harmonic spectrum is largely extended compared with the case that the atom is initially in the ground state. The physics of the extension of the high-order harmonic plateau can be interpreted by the spatial structure of the atomic initial wave packet. We can optimize the generation of high-order harmonics by substituting the excited state for a particular coherent superposition of some highly excited states to form a spatially localized excited wave packet.     

High-order harmonic generation in laser plasma: Recent achievements

Recent studies of high-order harmonic generation of laser radiation in laser-produced plasma show new attractive developments in this field. Those include generation of extended harmonics in plasma plumes, new approaches in application of two-color pump, generation of extremely broadened harmonics, further developments in harmonic generation in clusters (fullerenes, carbon nanotubes, in-situ produced nanoparticles), destructive interference of harmonics from different emitters, resonance-induced enhancement of harmonics, applications of high pulse repetition rate lasers for the enhancement of average power of generating harmonics, observation of quantum path signatures, etc. We review some of these recent developments.     

Two Methods of Amplification of Coherent Extreme Ultraviolet Radiation During Harmonic Generation in Plasmas

Different recently revealed approaches of harmonic enhancement in plasmas are reviewed. The 4-step analytical model of resonant enhancement of high-order harmonic generation is extended to the systems possessing resonant transitions of inner-shell electrons. Role of inelastic scattering is discussed by simulation of excited state’s population dynamics. The enhancement of harmonics in the In plasma using different pumps is analyzed to prove the concept. We also discuss the plasma emission and harmonic generation spectra in the case of resonance enhancement of single harmonic using various laser-produced plasmas. The analysis of these spectra showed that the enhancement of harmonics depended on the oscillator strengths of the nearby ionic transitions rather than the plasma emission transitions. Finally, we review some recent experimental studies of the phase-matching of high-order harmonic generation in multi-jet plasmas.     

Higher-Order Bragg Resonance in Gravity Surface Waves over Periodic Bottoms

A calculation method based on the Bloch theorem is developed for the gravity surface waves over the periodic bottoms of large undulations. The study shows the existence of comparable high-order bandgaps, which are demonstrated to result from the higher-order Bragg resonances, i.e. the resonant interactions between surface waves and the harmonic components of the fluctuating bottom. It is also shown that the band widths of the high-order gaps are quite sensitive to the amplitudes of high-order harmonics of the bottom.     

Nonlinear second harmonic generation by light wave-plasma interaction in oscillating magnetic field

The nonlinear generation of second harmonic electromagnetic waves in a thin inhomogeneous (dense and rarefied) plasma layer (of lengthd) by obliquely and normally incident light waves is analyzed. We consider the effect of an external time-dependent magnetic field on the generation and amplification of waves. Two cases are considered, when the magnetic field oscillates at a frequency (i) equal to and (ii) double that of the incident wave. For normal incidence, waves are not radiated in case (i), while in case (ii) the second harmonics are radiated equally from the plasma boundaries atx=0 andx=d. For a rarefied plasma, the second harmonics are radiated with equal amplitudes in both cases.     

少周期激光脉冲附加太赫兹场对高次谐波发射的影响

本文通过数值求解非伯恩奥本海默近似下电子一维核一维的含时薛定谔方程,研究了少周期线偏振激光与氢分子离子相互作用下,太赫兹场的加入对高次谐波的发射影响.我们发现,在短周期线偏振激光脉冲的y方向上附加一个强度较弱的太赫兹场可以有效地扩展谐波的截止位置,并对量子轨道实现调控.通过时频分析、电子波包随时间变化以及半经典三步模型研究了高次谐波发射的物理机制,并对获得的物理现象给出合理的解释.     

Enhancement of high-order harmonics generated in laser-produced plasma using ionic resonances and nanoparticles

We review recently emerged methods of high-order harmonic enhancement in the extended laserproduced plasmas using ionic resonances and nanoparticles and show the difference of this approach with regard to previously used methods. Particularly, we analyze the harmonic generation in graphene and a few other clustered media using 800-nm-class lasers. We also discuss the application of parametric waves for frequency conversion towards the extreme ultraviolet range and show the resonance enhancement of harmonics in laser-produced zinc plasma using tunable mid-infrared pulses. The reviewed studies demonstrated the attractiveness of the joint application of the methods of harmonic enhancement using ionic resonances and nanoparticles.     

High-order harmonic generation from plasma mirrors

We discuss the two mechanisms involved in high-order harmonic generation from plasma mirrors, and show that they can be clearly identified experimentally. The very different phase properties of the corresponding harmonics lead to light beams with different divergences. This can be exploited to select a particular type of harmonic by spatial filtering in the far-field.     

高阶相对论谐波辐射的理论研究

对短脉冲强激光在非稠密均匀等离子体中传播时产生的相对论相干谐波辐射进行了一般性研究．在准稳态近似（ｑｕａｓｉｓｔａｔｉｃ ａｐｐｒｏｘｉｍａｔｉｏｎ）下得出ｎ阶谐波包络的演化方程，并用此方程研究了ｎ阶谐波的增长与饱和及转化效率等问题     

Frequency conversion in laser-produced boron plasma using longitudinal pump scheme

The high-order harmonic generation from boron plasma was studied using the longitudinal pump scheme. The harmonics up to the 57th order (λ=13.96 nm) were observed. The characteristics of plateau in the range of 15th to 57th harmonics were analyzed depending on fundamental radiation intensity and the saturation of harmonic cutoff was observed. The harmonic cutoff energy was restricted by the self-defocusing of femtosecond radiation. A comparison of longitudinal and orthogonal pump schemes of boron plasma excitation was presented.     

Phase properties of laser high-order harmonics generated on plasma mirrors

As a high-intensity laser-pulse reflects on a plasma mirror, high-order harmonics of the incident frequency can be generated in the reflected beam. We present a numerical study of the phase properties of these individual harmonics, and demonstrate experimentally that they can be coherently controlled through the phase of the driving laser field. The harmonic intrinsic phase, resulting from the generation process, is directly related to the coherent sub-laser-cycle dynamics of plasma electrons, and thus constitutes a new experimental probe of these dynamics.     

Cumulative solutions of nonlinear longitudinal vibration in isotropic solid bars

Based on the strain invariant relationship and taking the high-order elastic energy into account, a nonlinear wave equation is derived, in which the excitation, linear damping, and the other nonlinear terms are regarded as the first-order correction to the linear wave equation. To solve the equation, the biggest challenge is that the secular terms exist not only in the fundamental wave equation but also in the harmonic wave equation （unlike the Duffing oscillator, where they exist only in the fundamental wave equation）. In order to overcome this difficulty and to obtain a steady periodic solution by the perturbation technique, the following procedures are taken： （i） for the fundamental wave equation, the secular term is eliminated and therefore a frequency response equation is obtained; （ii） for the harmonics, the cumulative solutions are sought by the Lagrange variation parameter method. It is shown by the results obtained that the second- and higher-order harmonic waves exist in a vibrating bar, of which the amplitude increases linearly with the distance from the source when its length is much more than the wavelength; the shift of the resonant peak and the amplitudes of the harmonic waves depend closely on nonlinear coefficients; there are similarities to a certain extent among the amplitudes of the odd- （or even-） order harmonics, based on which the nonlinear coefficients can be determined by varying the strain and measuring the amplitudes of the harmonic waves in different locations.     

Stable generation of high-order harmonics of femtosecond laser radiation from laser produced plasma plumes at 1 kHz pulse repetition rate

We present a method for the creation of stable weakly ionized plasmas from laser ablation of solid targets using a 1 kHz pulse repetition rate laser, which can be used for stable high-order harmonic generation from plasma plumes. The plasma plumes were generated from cylindrical rotating targets. Without target rotation the intensity of harmonics in the 40-80 nm range drops by more than one order of magnitude during less than 10(3) shots, while, with rotation of the target at typically 30 revolutions per minute, stable emission of high-order harmonics from aluminum plasma plumes with variation of less than 10% was maintained for >10(6) laser shots.     

Phase-matched high-order harmonics by interaction of Ar atoms with high-repetition-rate low-energy femtosecond laser pulses

High-order harmonics are generated by coherent interaction of an intense laser and atoms or molecules[1]. With the development of the intense ultrashort pulse laser, the research of high-order harmonic generation has reached the water-window in spectral region[2] and subfemtosecond in time domain[3]. Especially, the generation and application of subfemtosecond pulse led the study of high-order harmonic generation into a completely new world[4, 5]. It has made the study of ultrafast science fro…     

High-order harmonic generation with a two-color laser pulse

We theoretically investigate the electron dynamics of the high-order harmonics generation process by combining a near-infrared 800 nm driving pulse with a mid-infrared 2000 nm control field.We also investigate the emission time of harmonics using time-frequency analysis to illustrate the physical mechanisms of high-order harmonic generation.We calculate the ionization rate using the Ammosov-Delone-Krainov model and interpret the variations in harmonic intensity for different control field strengths and delays.We find that the width of the harmonic plateau can be extended when the control electric field is added,and a supercontinuum from 198 to 435 eV is generated,from which an isolated 61-as pulse can be directly obtained.     

High-order harmonic generation with a two-color laser pulse

We theoretically investigate the electron dynamics of the high-order harmonics generation process by combining a near-infrared 800 nm driving pulse with a mid-infrared 2000 nm control field. We also investigate the emission time of harmonics using time-frequency analysis to illustrate the physical mechanisms of high-order harmonic generation. We calculate the ionization rate using the Ammosov-Delone-Krainov model and interpret the variations in harmonic intensity for different control field strengths and delays. We find that the width of the harmonic plateau can be extended when the control electric field is added, and a supercontinuum from 198 to 435 eV is generated, from which an isolated 61-as pulse can be directly obtained.     

Resonance processes during harmonic generation in plasmas using mid-infrared radiation

A few recently introduced approaches of the high-order harmonic generation in laser-produced plasmas are reviewed. We show how the tuning of odd and even high-order harmonics of ultrashort pulses along the strong resonance of laser-produced indium plasma using optical parametric amplifier of white-light continuum radiation (1250?1400 nm) allows observation of different harmonics enhanced in the vicinity of the transition of In II ions possessing high oscillator strength. We discuss various peculiarities and discuss the theoretical model of the phenomenon of tunable harmonics enhancement in the region of 62 nm using indium plasma. With the theoretical analysis, we present the approach allowing reproduce the experimental observations and characterize the dynamics of the resonant harmonic emissions. We also discuss the resonance enhancement of harmonics using mid-infrared radiation in the tin, chromium, and antimony plasmas and show the calculations of this process.     

Characteristics of high-order harmonic spectrum by using laser-ablated two targets combination

We demonstrated a high-order harmonic generation from lowly charged ions in laser-ablation two-compound plumes (Ag-In, Ag-Mn, and Cr-Te). The high-order harmonic spectra from two-compound plumes were composed of those obtained from each target. Our results show that the control of cutoff energy and intensity of single high-order harmonics can be achieved by using the appropriate target combination.     

Entanglement generation between two colliding particles

Harmonics with the photon energy of up to ~150 eV were studied using extended ablation plumes as the nonlinear media. The application of the ablation pulses of different duration covering the range between a few tens of femtoseconds and a few tens of nanoseconds revealed the advanced features of the extended plasmas produced by the subnanosecond pulses for efficient harmonic generation. The examples of the quasi-phase-matching of a group of harmonics in the plateau range and the advantages of using the two-color pump and cluster-containing plasmas are presented. We analyze the spatial and coherence characteristics of the high-order harmonics produced during propagation of the 64 fs pulse through the extended plasma plume produced by 370 ps pulses. It is shown that the divergence of plasma harmonics in the plateau range is 7 times smaller than the divergence of the driving radiation used for high-order harmonic generation. The measurements of the coherence properties of the lower-order harmonics showed that the visibility of interference fringes in the far field was in the range of 0.54–0.73.