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.     

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.     

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.     

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.     

Controlling the divergence of high harmonics from solid targets: a route toward coherent harmonic focusing

Harmonic generation from relativistically oscillating plasma surfaces formed during the interaction of high contrast lasers with solid-density targets has been shown to be an efficient source of extreme ultraviolet (XUV) and X-ray radiation. Recent work has demonstrated that the exceptional coherence properties of the driving laser can be mirrored in the emitted radiation, permitting diffraction limited performance and attosecond phase locking of the harmonic radiation. These unique properties may allow the coherent harmonic focusing (CHF) of high harmonics generated from solid density targets to intensities on the order of the Schwinger limit of 10²⁹ W cm^-2 with laser systems available in the near future [Phys. Rev. Lett. 93, 115002 (2004)] and thus pave the way for unique experiments exploring the nonlinear properties of vacuum on ultra-fast timescales. In this paper we investigate experimentally as well as numerically the prospect of focusing high harmonics under realistic experimental conditions and demonstrate, using particle in cell (PIC) simulations, that precise control of the wavefronts and thus the focusability of the generated harmonics is possible with pre-shaped targets.     

Phase characteristics of high-order harmonics in the cut-off region

The behavior of the phases of high-order harmonics generated upon interaction of intense laser radiation with matter is investigated. Some specific features typical of the harmonic phases in the high-frequency part of plateau (cut-off harmonic phases) are found. First, the phase difference between neighboring harmonics is a constant value. The width of the spectral range in which this regularity occurs determines the minimum duration of the attosecond pulse obtained from these harmonics by the so-called amplitude gating technique. Second, it is shown that the phase of each harmonic in the cut-off region depends linearly on the laser intensity. The proportionality coefficient is the same for all harmonics in this region and proportional to the cube of laser wavelength. Thus, this dependence is especially important for generating high-order harmonics by lasers with a wavelength of few micrometers.     

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.     

High-order nonlinear optical processes in ablated carbon-containing materials: Recent approaches in development of the nonlinear spectroscopy using harmonic generation in the extreme ultraviolet range

The nonlinear spectroscopy using harmonic generation in the extreme ultraviolet range became a versatile tool for the analysis of the optical, structural and morphological properties of matter. The carbon-contained materials have shown the advanced properties among other studied species, which allowed both the definition of the role of structural properties on the nonlinear optical response and the analysis of the fundamental features of carbon as the attractive material for generation of coherent short-wavelength radiation. We review the studies of the high-order harmonic generation by focusing ultrashort pulses into the plasmas produced during laser ablation of various organic compounds. We discuss the role of ionic transitions of ablated carbon-containing molecules on the harmonic yield. We also show the similarities and distinctions of the harmonic and plasma spectra of organic compounds and graphite. We discuss the studies of the generation of harmonics up to the 27th order (λ = 29.9 nm) of 806 nm radiation in the boron carbide plasma and analyze the advantages and disadvantages of this target compared with the ingredients comprising B₄C (solid boron and graphite) by comparing plasma emission and harmonic spectra from three species. We also show that the coincidence of harmonic and plasma emission wavelengths in most cases does not cause the enhancement or decrease of the conversion efficiency of this harmonic.     

Evidence of high harmonics from echo-enabled harmonic generation for seeding x-ray free electron lasers

Echo-enabled harmonic generation free electron lasers hold great promise for the generation of fully coherent radiation in x-ray wavelengths. Here we report the first evidence of high harmonics from the echo-enabled harmonic generation technique in the realistic scenario where the laser energy modulation is comparable to the beam slice energy spread. In this experiment, coherent radiation at the seventh harmonic of the second seed laser is generated when the energy modulation amplitude is about 2-3 times the slice energy spread. The experiment confirms the underlying physics of echo-enabled harmonic generation and may have a strong impact on emerging seeded x-ray free electron lasers that are capable of generating laserlike x rays which will advance many areas of science.     

Experimental characterization of nonlinear harmonic generation in planar and helical undulators

We present an experimental characterization of the process of coherent harmonic generation in single-pass free electron lasers. The harmonic radiation is obtained by seeding the electron beam stored in the Elettra storage ring with a Ti:sapphire laser. Different methods for generating harmonics are compared between them, and a detailed characterization of the emitted light is performed for different polarizations. Our results also contribute to the debate about the possible presence of a coherent on-axis signal in helical undulators. In this respect, we provide an experimental confirmation of recent theoretical studies that predict no coherent on-axis signal.     

Nonlinear analysis of relativistic harmonic generation by intenselasers in plasmas

A linearly polarized, ultraintense laser field induces transverse plasma currents which are highly relativistic and nonlinear, resulting in the generation of coherent harmonic radiation in the forward direction (i.e., copropagating with the incident laser field). A nonlinear cold fluid model, valid for ultrahigh intensities, is formulated and used to analyze relativistic harmonic generation. The plasma density response is included self-consistently and is shown to significantly reduce the current driving the harmonic radiation. Phase detuning severely limits the growth of the harmonic radiation. The effects of diffraction are considered in the mildly relativistic limit. No third-harmonic signal emerges from a uniform plasma of near-infinite extent. A finite third-harmonic signal requires the use of a semi-infinite or finite slab plasma. For an initially uniform plasma, no second-harmonic radiation is generated. Generation of even harmonics requires transverse gradients in the initial plasma density profile     

Spectral modulation of higher harmonic spontaneous emission from an optical klystron

Higher harmonics of spontaneous emission from an optical klystron have been observed. The modulation factor of the spontaneous emission spectrum for the higher harmonics can be described by considering the observation system. When the dispersive gap of the optical klystron was fixed, the microstructure interval of the spontaneous emission spectrum at a certain resonant wavelength became narrower as the order of the higher harmonic became larger. Some unique characteristics of the higher harmonics have been clarified, and these studies are likely to contribute to the development of free‐electron lasers using higher harmonics of an optical klystron in the shorter‐wavelengths region.     

Particular features of higher harmonics generation in nanocluster-containing plasmas using single- and two-color pumps

The wavelength conversion of femtosecond laser pulses in laser plasmas containing clusters of different nature and dimension (fullerenes, metal nanoparticles) is studied. Pulses of a titanium-sapphire laser are used in combination with orthogonally polarized second-harmonic pulses as radiation to be converted. Variations in the generation efficiency of higher harmonics are analyzed under conditions of phase-modulated pulses. It is shown that the optimization of components of a nonlinear optical plasma medium, of plasma excitation conditions by single- and two-color pumps, and of phase and spectral parameters of radiation to be converted leads to a considerable increase in the generation efficiency of higher harmonics.     

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.     

Influence of surface waves on plasma high-order harmonic generation

The influence of surface plasma waves on high-order harmonic generation from the interaction of intense lasers with overdense plasma is analyzed. It is shown that the surface waves lead to the emission of harmonics away from the optical axis, whereas the high-order on-axis harmonics are lowered in intensity. Our simulation results indicate that surface plasma wave generation plays a crucial role in surface high-order harmonic generation experiments. Furthermore, a novel surface plasma wave generation process different from the well-known two-surface wave decay is observed in the highly relativistic regime.     

相对论激光在Maxwell分布等离子体中产生的高次谐波

 研究了强激光与具有初始速度分布的等离子体作用产生的高次谐波。结果表明，对于Maxwell速度分布的等离子体，由于电子初始时刻的无规则热运动，在一定程度上抹平了辐射功率在谐波谱上的分布，使得高次谐波的辐射增强，低次谐波的辐射有所减弱，有利于高次谐波的产生。     

Frequency and intensity difference limens for harmonics within complex tones

A two-interval, two-alternative forced choice task was used to estimate frequency difference limens (DLs) for individual harmonics within complex tones, and DLs for the periodicity (i.e., number of periods per s) of the whole complexes. For complex tones with equal-amplitude harmonics, the DLs for the lowest harmonics were small (less than one percent). The DLs increased rather abruptly around the fifth to seventh harmonic. The highest harmonic in each complex was also well discriminated, and the discriminability of a single high harmonic was markedly improved by increasing its level relative to the other components. The DL for a complex tone was generally smaller than the frequency DL of its most discriminable component. The DL for a complex was found to be predictable from the DLs of the harmonics comprising the complex, using a formula derived by Goldstein [J. Acoust. Soc. Am. 54, 1496-1516 (1973)] from his optimum processor theory for the formation of the pitch of complex tones. The DL for a complex is sometimes primarily determined by high harmonics, such as the highest harmonic, or a harmonic whose level exceeds that of adjacent harmonics. We also measured intensity DLs for individual harmonics within complex tones. The intensity DLs were smallest for low harmonic numbers, and for the highest harmonic in a complex. An excitation-pattern model was used to determine whether the frequency DLs of harmonics within complex tones could be explained in terms of place mechanisms, i.e., in terms of changes in the amount of excitation at appropriate frequency places. We conclude that place mechanisms are not adequate, and that information about the frequencies of individual harmonics is probably carried in the time patterning of neural impulses.     

Generation of lower and higher harmonics in different plasma media with small <Emphasis Type="Italic">Z</Emphasis>

The generation of lower (third) and higher harmonics of femtosecond laser radiation in plasmas produced by laser ablation of different targets with a small atomic number Z (B, Be, Li) has been investigated. The high (10⁻³) efficiency of third-harmonic generation was observed in plasma produced on the boron surface. Efficient third-harmonic generation was also observed in beryllium plasma using femtosecond pulses of Ti:sapphire laser radiation (λ = 790 nm) and its second harmonic (395 nm). We could tune the higher harmonics generation spectrum by tuning the crystal converter when using 395-nm radiation to be converted. It is shown that, in plasmas formed on targets with small Z, the conversion efficiency and limiting generated harmonic order depend on the delay between the ablation pulse and the pulse to be converted.     

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。     

High-order harmonic generation in nanoparticle-containing laser-produced plasmas

Nanoparticle-containing media can be used for the efficient high-order harmonic generation (HHG) of laser radiation in the extreme ultraviolet range. We review the results of recent studies of the HHG in laser-produced plasmas containing Ag, Au, Pd, Pt, Ru, GaN, BaTiO₃, and SrTiO₃ nanoparticles. The harmonics of femtosecond radiation up to the 55th order were achieved using the nanoparticle-containing plumes, when the femtosecond radiation propagated through the preformed plasma. These results are compared with the high-order harmonics generated from the plasma produced on the surface of bulk targets at different delays between the subnanosecond heating prepulse and femtosecond pulse. We discuss a six-fold enhancement of the HHG yield, which was achieved in the case of nanoparticle-containing plumes with regard to the monoparticle-containing plasmas.