Fullerenes: The attractive medium for harmonic generation

We review the results of systematic experimental studies of high-order harmonic generation (HHG) in C₆₀-rich laser-produced plasma under different plasma conditions and laser parameters. The morphology of fullerene clusters before and after ablation is analyzed to define the optimal conditions of excitation of C₆₀-containing targets. The enhancement of HHG efficiency in C₆₀-rich plasmas by using the two-color pump technique is discussed. The conversion efficiency for the odd and even harmonics in the vicinity of surface plasmon resonance of the C₆₀-containing plasma (40–70 nm) was estimated to be in the range of 10⁻⁴.     

Harmonic generation in the extended plasmas produced on the non-metal targets

The review of the high-order harmonic generation (HHG) studies in the extended plasma plumes produced on the surfaces of non-metal targets (elemental semiconductors, oxygen- and fluorine-contained crystals) is presented. The objective of those studies was to reveal the attractive properties of non-metal plasmas. We discuss the results of HHG optimization in the above plasma plumes using different methods. These studies demonstrate the usefulness of the plasma harmonic approach for the analysis of the nonlinear optical and spectroscopic properties of the extended laser-produced plasmas formed on the non-metal surfaces.     

Higher harmonic generation in laser plasma upon interaction of femtosecond laser pulses with doubly and singly charged ions under conditions of resonance frequency conversion of laser radiation

The higher harmonic generation (HHG) in plasmas formed on the surface of different solid targets (Pb, Ag, Ge, In, Au, Cr, Pt, V, Mn, Ga, Bi, Sb, Cu, Al, Ca, and Sn) by laser ablation is studied. The possibility of HHG upon interaction of femtosecond radiation with doubly charged ions is studied on the example of Mn plasma. This process allowed generation of higher harmonics of up to the 101st order. The results of investigation of individual enhanced harmonics in Sn, Sb, In, and Cr plasmas are presented. Comparison of the conditions of HHG in weakly and strongly excited plasmas showed that the latter is preferable for efficient frequency conversion. It is demonstrated that the use of laser plasma spectroscopy with high time resolution allows one to determine the optimal conditions for generation of harmonics with a plateaulike distribution in the far-UV spectral region.     

Generation of higher harmonics of laser radiation in plasma formed by pulses with a 1-kHz repetition rate

Studies of higher-order nonlinearities in plasma plumes by the method of higher-harmonic generation (HHG) upon laser ablation of different materials by pulses with a repetition rate of 1 kHz are reviewed. It is shown that an increase in the pulse repetition rate compared to the previous works on HHG in plasma using lasers with a pulse repetition rate of 10 KHz considerably increases the average power of converted radiation in the far-ultraviolet (FUV) region. The review considers the results of works on the interference of quantum trajectories of accelerated electrons, two-color pumping, HHG in graphite plasma, HHG in gases compared to HHG in plasma plumes, resonant enhancement of harmonics, and stabilization of the output parameters of radiation converted in plasma. It is shown that the new methods of optimization of the HHG process considerably increase the potential of the use of coherent FUV radiation owing to the improvement of some characteristics of harmonics in plasma generated by pulses with a high repetition rate.     

Use of carbon-containing materials for efficient high-order harmonic generation of laser radiation

A systematic study of the high-order harmonic generation (HHG) of laser radiation in various carbon-containing plasma plumes (CCPPs) is presented. The materials studied are: graphite, boron carbide, C₆₀, polytetrafluoroethylene, polyethylene, carbon nanotubes, and soot. These studies show that CCPPs present the best plasma media for efficient lower order (from 9th to 19th) harmonic generation, while the harmonic cutoff restricted to the 29th order. The advantages of CCPPs for the harmonic generation are confirmed by comparison of the HHG conversion efficiency with that in Ag and In plasma plumes, where the highest conversion efficiency was reported. Use of two-color pump scheme allows further enhancement of harmonic yield from the CCPPs.     

Interference and spectral broadening of higher harmonics of laser radiation in plasma torches containing ions,nanoparticles, and fullerenes

We analyze the interference between two processes of higher harmonic generation (HHG) in plasma containing mixtures of different materials (silver and gold nanoparticles, as well as graphite and boron). We find that, for mixtures and individual ingredients, the limiting orders of generated harmonics of laser radiation approximately coincide with one another. At the same time, for plasma torches formed by the ablation of mixtures of materials, the HHG efficiency is considerably reduced compared to the case of the frequency transformation of laser radiation in individual ingredients of these mixtures as a result of destructive interference in the former case. We demonstrate a considerable spectral broadening of harmonics generated in laser plasma with pulses passed through filaments formed in air. In this case, the HHG efficiency increases fourfold (from 3 × 10⁻⁶ to 1.2 × 10⁻⁵) compared to the case of radiation free of phase and frequency modulation. The generation of harmonics is also observed upon the passage of 120-fs laser pulses through plasma containing fullerenes. In this case, the limiting value of generated harmonics achieves the 33rd order. The efficiency of harmonics in fullerene plasma considerably exceeds a similar process in silver plasma.     

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.     

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.     

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.     

Laser radiation frequency conversion in carbon- and cluster-containing plasma plumes under conditions of single and two-color pumping by pulses with a 10-Hz repetition rate

This work reviews a series of investigations of different plasma plumes using single- and two-color laser systems that emit femtosecond pulses with a 10-Hz repetition rate. Results of investigation of the resonant enhancement of harmonics in tin plasma with the use of two types of pumps are analyzed, and it is shown that the tuning of the wavelengths of harmonics to ion-resonance levels plays an important role in increasing the conversion efficiency to high-order harmonics of the radiation to be converted. Investigations of different carbon-containing plasma media (carbon nanotubes, graphite, carbon aerogel, etc.) exhibit attractive properties of the nonlinear medium of this type for efficient generation of high-order harmonics. The results of the first experiments on the use of nanoparticles produced directly in the course of laser ablation of metals for increasing the efficiency of harmonics generated in this cluster-containing medium are analyzed. It is shown that new approaches realized in these investigations give hope that the nonlinear optical response of plasma media in the far-ultraviolet range can be further increased.     

Relativistic laser plasmas for novel radiation sources

Relativistic laser-plasma interaction results in new sources of short-pulsed x-ray radiation. Here we consider two options. The first one is betatron radiation of electrons accelerated in underdense plasmas and oscillating in transverse fields of the laser wake. This radiation is incoherent and broadband, the pulse duration is comparable with that of the driving laser. The second option is the high harmonic generation (HHG) from overdense plasma surfaces. This radiation is coherent. The relativistic high harmonics are phase locked and emerge in the form of (sub-)attosecond pulses. One- and three-dimensional regimes of relativistic HHG from overdense plasmas are considered.     

Enhanced harmonic generation in C60-containing plasma plumes

The results of enhanced harmonic generation in fullerene-containing plasma plumes using laser radiation of different wavelengths, pulse durations, and phase modulation are presented. Odd and even harmonics up to the 29^th order of 800 nm radiation have been extended in the case of two-color orthogonal polarization pump of C₆₀-containing plasma plumes. The conversion efficiency for the odd and even harmonics in the vicinity of SPR of the C₆₀-containing plasma (40–70 nm) was estimated to be in the range of 10⁻⁴.     

High-order harmonic enhancement using the quasi-phase-matching in a laser plasma

The quasi-phase-matching of the high-order harmonics generating in the multiple plasma jets produced on the surfaces of perforated Ag, V, and Mn targets is demonstrated. The 20× and 30× enhancement factors of quasi-phase-matched harmonics of 804 nm radiation in the range of the 35th harmonic in the cases of silver and vanadium plasmas were achieved.     

Low- and high-order nonlinear optical characterization of C60-containing media

Third- and higher-order nonlinear optical processes in fullerenes were studies to define the influence of low-order nonlinearities on the high-order harmonic generation in these media. We measured the nonlinear absorption coefficients of the C₆₀:toluene solution using the 532 and 1064 nm, 50 ps pulses. The high-order harmonic generation was studied during propagation of the 790 nm, 150 fs pulses through the plasmas produced on surfaces containing fullerene powder. These studies have shown that the low-order nonlinearities of fullerenes have no impact on the generation of harmonics in such mediums in the vacuum ultraviolet range at optimal intensity of laser radiation.     

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.     

Deposition of nanoparticles during laser ablation of nanoparticle-containing targets

We analyze the morphology of ablated nanoparticles after their laser-induced deposition on various substrates. We show that, at moderate laser intensity of the 210 ps pulses on the surface of nanoparticle-containing materials (<5×10⁹ W?cm^?2), the deposited material remains approximately the same as the initial nanoparticles. We compare these deposited nanoparticles with the debris obtained by the laser ablation of bulk material of the same origin as nanoparticles at different intensities of laser radiation. The presence of nanoparticles in laser plumes allowed for analyzing high-order nonlinear optical properties of nanoparticles. The efficient high-order harmonic generation was achieved during propagation of femtosecond pulses through such plasmas.     

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.     

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.     

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.     

Methods for Modifications of Harmonic Spectra from Laser-Produced Plasmas

We review the studies of the modifications of harmonic spectra from laser-produced plasmas. The substantial spectral broadening and blue shift of the harmonics generating in the laser plasma during transformation of the spectrum of the laser radiation formed the filaments upon passage of femtosecond pulses through the argon gas is analyzed. We also discuss the studies of harmonic spectra variations that occur as a result of the passage of the laser pulses through the carbon- and metal-containing plasmas at the variable density of ablated species and intensity of driving pulse. To show other type of modulation of harmonic emission spectra, the plasmas containing the small molecules of silver produced during ablation of the bulk silver and silver nanoparticles at the conditions suitable for efficient harmonic generation of the ultrashort pulses propagating through the laser-produced plasmas were analyzed. The time-of-flight mass-spectroscopy studies of plasmas confirmed the presence of these species in plasmas.