High-order harmonic generation in graphite plasma plumes using ultrashort laser pulses: a systematic analysis of harmonic radiation and plasma conditions

High-order harmonic generation in graphite plasma plumes using ultrashort laser pulses: a

systematic analysis of harmonic radiation and plasma conditions

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2012 J. Phys. B: At. Mol. Opt. Phys. 45 165402

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IOP PUBLISHING JOURNAL OF PHYSICS B: ATOMIC, MOLECULAR AND OPTICAL PHYSICS

J. Phys. B: At. Mol. Opt. Phys. 45 (2012) 165402 (13pp) doi:10.1088/0953-4075/45/16/165402

High-order harmonic generation ingraphite plasma plumes using ultrashortlaser pulses: a systematic analysis ofharmonic radiation and plasma conditionsR A Ganeev1,2,5, C Hutchison1, T Witting1, F Frank1, W A Okell1,A Zaır1, S Weber1, P V Redkin3, D Y Lei1, T Roschuk1, S A Maier1,I Lopez-Quintas4, M Martın4, M Castillejo4, J W G Tisch1

and J P Marangos1

1 Blackett Laboratory, Imperial College London, Prince Consort Road, London SW7 2AZ, UK2 Institute of Electronics, Academy of Sciences of Uzbekistan, Akademgorodok 33, Dormon Yoli Street,Tashkent 100125, Uzbekistan3 Samarkand State University, Samarkand 140104, Uzbekistan4 Instituto de Quımica Fısica Rocasolano, CSIC, Serrano 119, 28006 Madrid, Spain

E-mail: [email protected]

Received 19 April 2012, in final form 21 June 2012Published 16 July 2012Online at stacks.iop.org/JPhysB/45/165402

AbstractHigh-order harmonic generation in graphite-ablated plasmas was systematically studied usingultrashort (3.5 and 30 fs) laser pulses. We observed the efficient frequency conversion of 3.5 fsTi:sapphire laser pulses in the range of 15–26 eV. Stabilization of the harmonic yield at a 1 kHzpulse repetition rate was accomplished using a rotating graphite target. We also show theresults of harmonic generation in carbon plasma using 1300 nm, 40 ps pulses, which allowedthe extension of the harmonic cutoff while maintaining a comparable conversion efficiency tothe case of 780 nm driving radiation. The time-of-flight mass spectrometric analysis of theplasma components and the scanning electron microscopy of plasma debris under optimalconditions for harmonic generation suggest the presence of small carbon clusters (C10–C30) inthe plasma plume at the moment of femtosecond pulse propagation, which further aggregate onnearby substrates. We present the results of plasma spectroscopy obtained under unoptimizedplasma conditions that elucidate the reduction in harmonic signal. We also present calculationsof plasma concentration under different excitation conditions of the ablated graphite target.

(Some figures may appear in colour only in the online journal)

1. Introduction

Various recent proposals for the applications of short-wavelength femto- and attosecond radiation (medical/biological applications, ways of transporting energy intofusion targets, few-cycle-driven electron acceleration, intenseattosecond short-wavelength pulses from overdense relativisticplasmas, relativistic electron metrology and control, etc) [1–3]

5 Author to whom any correspondence should be addressed.

require the increase of conversion efficiency of these sourcesproduced using high-order harmonic generation (HHG) oflaser radiation by different means. Among them, the HHG inlaser-produced plasmas seems a promising method to producecoherent extreme ultraviolet (XUV) radiation. The quest forways of increasing the HHG efficiency in plasma plumes inthe XUV range remains a hot topic of strong-field laser–matter interaction studies. It has become obvious in recentyears that the important requirement for efficient HHG is aspecific composition of the laser plasma, which should contain

0953-4075/12/165402+13$33.00 1 © 2012 IOP Publishing Ltd Printed in the UK & the USA

J. Phys. B: At. Mol. Opt. Phys. 45 (2012) 165402 R A Ganeev et al

predominantly neutral atoms and singly charged ions. HHGstudies that use highly excited plasmas containing multiplecharged ions revealed several factors that limit the harmonicconversion efficiency and showed only a limited number ofharmonic orders [4–6].

Early studies show that several conditions have to befulfilled to optimize the conversion efficiency during theinteraction of the laser radiation with the plasmas [7–9].Since the temporal evolution of a laser ablation plasma spansfrom several tens to hundreds of nanoseconds, it is necessaryto synchronize the arrival of the laser pulse generating theharmonics (the ‘probe’ pulse) with the moment when theplasma is ‘optimal’. The term ‘optimal’ refers to the degree ofionization and excitation of atoms and ions, as well as theconcentration of the laser plasma, which ensure efficient high-order nonlinear frequency up-conversion of the probe pulsepropagating through the plasma. The position of the focusof the probe radiation with respect to different zones of theplasma is also of considerable importance. The optimizationof frequency up-conversion is accomplished by adjusting thedistance between the target surface and the propagating probebeam and by optimizing the delay between the ablating andthe probe pulses [9].

The characteristics of the laser plasma play a crucial role indetermining how efficiently high harmonics can be generatedin the plasma plumes. An increase in the free-electron densitywas likely to have been the limiting factor for the harmoniccutoff energy in early experiments with laser plasmas [4–6].A search for appropriate target materials, which can providefavourable ablation plasmas for efficient HHG, has motivatedthe analysis of plasma characteristics under the conditions ofhigh harmonic yield. Recent studies have shown that carbonablation plasmas are promising media to satisfy the aboverequirements [10–13].

The shot-to-shot stability of the harmonic signal is crucialfor any application of the generated radiation and also forthe measurement of the pulse duration of converted XUVradiation. Such temporal measurements were recently reportedin the case of HHG in a chromium plasma [14]. Using the‘reconstruction of attosecond beating by interference of two-photon transitions’ technique [15], the authors have shownthat the 11th–19th harmonics of a Ti:sapphire laser form,in the time domain, an attosecond pulse train. It was underlinedthat the instability of the harmonic signal in their experimentsusing a 10 Hz pulse repetition rate laser was the main obstaclefor an accurate measurement of the temporal structure ofplasma harmonics. Besides its fundamental interest, the HHGin plasma plumes could thus provide an intense source offemtosecond and attosecond pulses for various applications.

Optical parametric amplifiers (OPAs) operating in themid-infrared range are promising tools for harmonic cutoffextension and attoscience experiments. The spectral cutoff ofHHG obeys the scaling law Hc ∼ Iλ2 [16], where I is thepeak intensity of the probe field and λ its central wavelength,which allows one to extend the harmonic emission beyondthe 100 eV range by using longer wavelength laser sources.Another advantage of mid-infrared OPAs (MIR OPAs) is theirwavelength tunability, which allows one to tune the spectral

position of harmonics towards the ionic transitions with strongoscillator strengths. This feature allows the observation ofresonance-enhanced harmonics and broadens the range ofplasma samples where this phenomenon could be realizedcompared with the case of ∼800 nm lasers of essentiallyfixed wavelength [17]. Moreover, by using two-colour HHGtechniques, the application of MIR OPAs allows the studyof complex molecules during their ablation and HHG usingthe tuneable long-wavelength radiation. These features areinteresting for spectroscopic applications of HHG in the MIRrange [18, 19].

The use of MIR OPAs for HHG also leads to a reducedharmonic generation efficiency that scales as λ−5 [20, 21]. Itis of considerable interest to analyse the relative behaviourof plasma harmonics in the cases of ∼800 nm and MIRlasers and thereby to find the conditions when the reductionof harmonic yield becomes not so dramatic due to someenhancement mechanisms, such as the presence of in situproduced nanoparticles, which increase the HHG conversionefficiency. It is worth noting that previous studies of plasmaHHG in carbon plumes [10, 11] have inferred, throughthe analysis of plasma debris morphology, the formation ofnanoparticles during laser ablation of graphite targets.

Atomic carbon is a reactive species that stabilizesin various multi-atomic structures with different molecularconfigurations (allotropes). All the allotropic forms of carbon(graphite, diamond and amorphous carbon) are solids undernormal conditions, but graphite has the highest thermodynamicstability. Laser ablation of graphite have been intensivelyexamined during the last ten years to define plasma conditionsfor the synthesis of carbon structures with unique properties,in particular, fullerenes and carbon nanotubes [9, 17].The physical characteristics of the plasma plume, suchas concentration of atoms and clusters, directly affect theproperties of the material being formed in the dynamicexpansion of the ablated material. The successful synthesisof clusters is strongly dependent on the formation ofatomic and molecular species with the required chemistryand aggregation ability. Thus, to select the optimal plasmaconditions for HHG, a detailed understanding of the basicphysical processes governing the ablation plume compositionand reliable methods for controlling the plume species areneeded.

The reasons mentioned above and the consideration ofrecent studies of HHG in carbon plasmas [10, 11], as wellas recently reported comparisons of the HHG in graphite-ablated plasmas and argon gas [12, 13], have prompted usto systematically analyse the plasma conditions for optimalHHG conversion efficiency in graphite plasmas. Herein, wereport on the systematic analysis of HHG in graphite-ablatedplasmas using ultrashort (3.5 and 30 fs) driving laser pulses.We show efficient HHG frequency up-conversion of 3.5 fsTi:sapphire laser pulses in the range of 15–26 eV usingoptimally prepared plasma plumes and demonstrate the tuningof harmonic spectra under variable conditions of the secondstage of compression of the driving laser. We also presentresults on HHG in carbon plasmas using MIR driving pulses,which have allowed the extension of the harmonic cutoff while

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maintaining a comparable conversion efficiency with regardto the 780 nm driving radiation. Furthermore, we presentresults of an analysis of the composition of carbon plasmasoptimized for HHG using time-of-flight mass spectrometry(TOFMS) and scanning electron microscopy (SEM) of theplasma debris. These studies allow us to report on the presenceof small carbon clusters (C10–C30) in the plume, which furtheraggregate after deposition on the nearby substrates. We alsopresent an optical emission spectroscopic analysis of thegraphite ablation plasma under various excitation conditions(including unoptimized conditions) using ablating pulses ofdifferent duration (8 ps and 10 ns), as well as calculations ofthe corresponding plasma concentrations.

2. Experimental arrangements

The Ti:sapphire laser (Femtolasers Produktions GmbH)provided pulses of 25 fs and energies of up to 0.8 mJ at arepetition rate of 1 kHz. These pulses were focused into a1 m long differentially pumped hollow core fibre (250 μminner core diameter) filled with neon. The spectrally broadenedpulses at the output of the fibre system were compressed by tenbounces of double-angle technology chirped mirrors (UltrafastInnovations GmbH). A pair of fused silica wedges was usedto fine tune the pulse compression. High-intensity few-cyclepulses (760 nm central wavelength, 0.2 mJ, 3.5 fs, pulserepetition rate 1 kHz) were typically obtained in this system.The compressed pulses were characterized with a spatiallyencoded arrangement for direct electric field reconstructionby spectral shearing interferometry [22]. This radiation wasused as the probe pulses for frequency up-conversion in thespecially prepared carbon plasma.

A portion of the uncompressed radiation of this laser(central wavelength 780 nm, pulse energy 120 μJ, pulseduration 8 ps, pulse repetition rate 1 kHz) was split fromthe beam line, prior to the laser compressor stage and wasfocused into the vacuum chamber to heat the graphite targetand create a plasma on its surface (figure 1(a)). The picosecondheating pulses were focused by a 400 mm focal length lensand created a plasma plume with a diameter of ∼0.5 mm usingan intensity on the target surface of Ips = 2 × 1010 W cm−2.The delay between plasma initiation and femtosecond pulsepropagation was fixed at 33 ns. As an alternative ablation laser,we also used 10 ns, 1064 nm pulses from a 10 Hz repetitionrate Q-switched Nd:YAG, laser that provided an intensity onthe target surface of 1 × 109 W cm−2. In this case, the delaybetween the 10 ns heating and the 3.5 fs probe pulses wasvaried in the range of 10–60 ns to maximize the harmonicyield.

The 3.5 fs probe pulses, propagating in a directionorthogonal to that of the heating pulse, were focused intothe laser plasma using a 400 mm focal length reflectivemirror. The position of the focus with respect to the plasmaarea was chosen to maximize the harmonic signal, and theintensity at the plasma area under these conditions wasestimated to be Ifs = 6 × 1014 W cm−2. We also used 30 fs,780 nm, 2 mJ probe pulses from another Ti:sapphire laser(Red Dragon, KMLabs) operating at 1 kHz repetition rate

(a)

(b)

Figure 1. (a) Experimental setup for harmonic generation in plasmaplumes. FP: femtosecond probe pulse; HP: picosecond heatingpulse; A: aperture; HHGC: high-order harmonic generationchamber; FM: focussing mirror; L: focussing lens; T: target; P:plasma; XUVS: extreme ultraviolet spectrometer; FFG: flat-fieldgrating; MCP: microchannel plate and phosphor screen detector;and CCD: CCD camera. (b) Experimental scheme of thetime-of-flight mass spectroscopy system. 1: time of flight massspectrometer; 2: MCP detector; 3: sample holder; 4: Ng;YAGablation laser; 5: post-ionization F2 excimer laser; 6: high-voltageswitch; 7: oscilloscope; and 8: delay generator.

and producing approximately the same intensity inside thelaser plasma (4 × 1014 W cm−2). The details of this setup arepresented in [23]. The generated harmonics were analysedby an XUV spectrometer consisting of a flat-field grating(1200 lines/mm, Hitachi) and a microchannel plate (PhotonisUSA, Inc.) coupled to a phosphor screen. Images of harmonicswere recorded by a CCD camera [12].

In order to analyse the harmonic yield of the MIR sourcein the graphite-ablated plasma, we used an OPA pumped bythe 30 fs Ti:sapphire laser. A beam splitter inserted beforethe laser compressor of this Ti:sapphire laser allowed to pickoff 10% of the beam (780 nm, 1 mJ, 20 ps, 1 kHz pulses)to generate a plasma plume on the graphite targets, with theremaining 90% being compressed to 30 fs (7 mJ) to pumpa commercial computer-controlled OPA (HE-TOPAS, LightConversion). The OPA was optimized for high conversionefficiency and short duration of the converted pulses. Toachieve high reproducibility of the generated pulses, the lastamplification stage was driven to saturation. This devicegenerated signal pulses in the 1200–1550 nm range with amaximum power of 1.8 mJ at ∼1300 nm. The idler pulse

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covers the 1700–2200 nm range with a maximum power of1 mJ at ∼2000 nm. The pulse duration has been characterizedby a SPIDER-type setup with about 40 fs pulse duration in theoverall range. The delay between the heating ablation pulseand the MIR pulses from the OPA was set to 35 ns, as thisdelay was found to be optimal for the efficient generation ofextended harmonics.

Plasma characterization through optical spectroscopicmeasurements in the visible, ultraviolet (UV) and XUVranges under the conditions of different HHG efficiencieswere carried out using the above-described XUV-spectrometerand a fibre spectrometer (USB2000, Ocean Optics). Thefluences of heating pulses at which the spectra were recordedcorresponded both to optimal and to non-optimal conditions ofHHG. The acquisition times were set to 1 s, for measurementsof XUV spectra, and to 0.5 s, for measurements of visible andUV spectra.

Characterization of the plasma debris collected on siliconwafers placed 4 cm from the ablated target was carried bySEM (LEO 1540 XB, Carl Zeiss).

Cluster composition of the ablation plume producedby nanosecond laser pulses was investigated by TOFMS(figure 1(b)). A brief description of the experimental setup isgiven here; more details of the TOFMS can be found elsewhere[24]. The laser beam (1064 nm, 5 mJ, 10 ns pulse duration) wasfocused to a 0.2 mm spot on the surface of the graphite target,at normal incidence. The laser intensity was 1.5 × 109 W cm−2,which resulted in the creation of an optimal plasma for efficientHHG using the nanosecond ablation pulses. The target wasplaced in a vacuum chamber (pumped to ∼2 × 10−6 bar)between the extracting and accelerating plates of a linearTOFMS. The target surface was parallel to the flight axis ofthe spectrometer. The target could be rotated and displaced atvariable distances from the axis. Positive ions produced in theablation were deflected along the TOFMS axis by an electricfield typically in the range of 300–400 V cm−1 and acceleratedby a total voltage of ∼2500 V. A high-voltage switch was usedto apply the bias voltage at controlled delays with respect tothe laser ablation pulse. Ions entered the drift region (flightlength ∼1 m) and were detected by a set of microchannelplates. The analysis of neutral species produced in the ablationcould also be performed by the use of a second post-ionizationlaser (F2 excimer at 157 nm). The post-ionization laser pulseinteracted with the ablation plume perpendicularly to theplume propagation axis, at different distances from the targetsurface and at different delays with respect to the ablation laser.

3. Results

Since the goal of these studies was to analyse the graphiteablation plasma conditions under the conditions of efficientHHG of ultrashort laser pulses, we first optimized thisprocess by achieving the maximum conversion efficiency andhighest harmonic cutoff using the probe radiation from bothTi:sapphire lasers with fixed wavelengths and the tuneableOPA. Then, our effort was concentrated on the analysis ofthe ‘optimal’ plasma plume using three techniques: opticalemission spectroscopy of emitting plasma species in the

Figure 2. Carbon harmonic spectra as a function of neon pressure inthe hollow fibre. The corresponding probe pulse spectra measured infront of the vacuum chamber are presented on the left side. Theplasma was created using the 10 ns pulses. λ0 is the central weightedwavelength of the spectral distribution. The colour scale indicatesthe harmonic intensity.

visible, UV and XUV spectral ranges; SEM for inspectionof the deposited plasma debris; and finally, time-of-flightmass spectrometry for the analysis of the ionic componentsof the plasma. We also present a three-dimensional moleculardynamical simulation of carbon plasma concentration.

3.1. HHG in graphite plasma

3.1.1. HHG under the conditions of stabilized plasmaformation. In this subsection, we present our studies of HHGfrom graphite-ablated plasma by 10 ns pulses operating atthe 10 Hz repetition rate. The shortest available probe pulseswere used to analyse the various features of this processdepending on the spatio-temporal parameters of the convertingradiation. Harmonics from the carbon plasma were optimizedby choosing the delay between pulses, and the distancebetween the femtosecond beam and the target. The previousanalysis of low-order harmonic spectra using few-cycle pulsespropagating at different delays with respect to a 10 ns pulse-induced plasma [12] have shown that delays in the 30–40 nsrange yield the highest conversion efficiency and so we useddelays in this range as a basis for further improvement ofhigh harmonic yield. To analyse the influence of the spectro-temporal characteristics of the probe radiation on the harmonicyield, we changed the backing pressure of neon in the hollowfibre, which allowed the variation of pulse duration from 25to 3.5 fs [25]. The dependence of the spectral and intensitycharacteristics of the harmonic images recorded by the CCDcamera in the 15–25 eV range at different input pulse spectraand backing pressures of neon is shown in figure 2. One canclearly see that with the increase of backing pressure (from 1.2to 3 bar), the harmonic intensity increases, while the harmonicwavelength spectrally shifts towards the blue. During theseexperiments, the driving pulse energy was held constant.

We did not measure the pulse durations for each of theseconditions of driving radiation with different spectra; however,the measurements were carried out for extreme cases, i.e. inthe absence of neon gas in the fibre (0 bar, 25 fs) and in thefilled fibre (3 bar, 3.5 fs). One can note that the pulse duration

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and the corresponding spectra did not change significantlyat the lower pressures of Ne. The strong SPM and spectralbroadening appeared at pressures above 1.2 bar. Therefore, itis safe to expect some scaling of pulse duration for the spectrapresented on the left side of figure 2, which correspond to thescaling of spectral broadening.

An interesting feature of the carbon harmonic spectrumfrom the 10 ns induced plasma is that the spectral width is about2–3 times broader than that of harmonics generated in otheratom- and ion-rich plasmas at the same fluence and intensityof heating pulse, when using few-cycle pulses. For example,the full-width at half-maximum for medium-order harmonicswas 1.5 nm in the case of graphite plasma versus 0.4 nm fordifferent metal (Ag, Al and Cu) plasmas. The broader widthof the harmonics can be explained by self-phase modulationand chirping of the fundamental radiation propagating throughthe carbon plasma. The presence of nanoparticles in theplasma plume may also contribute to bandwidth broadeningof harmonics.

For practical applications of the coherent short-waveradiation generated in a graphite plasma using a 1 kHzdriving laser, it is necessary to analyse the stability of theplasma characteristics and of the generated harmonics. In theexperiments described below, we used the 8 ps heating pulsesoperating at 1 kHz in an attempt to improve the stabilityof plasma harmonics under these conditions, which havepreviously been unfavourable for stable plasma formation. Wehave recently introduced a new technique for maintaining astable ablation plasma for harmonic generation using highpulse repetition rate lasers (>1 kHz) based on ablation ofrotating metal targets [26]. Our present studies show that, inspite of the different properties of metal and graphite targets,the rotating target allowed stable HHG in both metal andgraphite plasmas. Figures 3(a) and (b) show the improvedstability over ∼106 laser shots of the 11th–25th harmonicswhen using a rotating graphite target and how the harmonicintensity rapidly decays after the target rotation is stopped.The rotating graphite rod allows maintaining a relatively stableharmonic yield well above 1 × 106 laser shots. Harmonics upto the 29th order were routinely observed in these studies usingthe 3.5 fs pulses.

It is worth noting that harmonic intensity is the samewhen returning to the same spot after one rotation of thegraphite rod. This reveals the unchanged morphological targetconditions. Indeed, the target analysis by optical inspection hasconfirmed that there is negligible surface modification due tolaser ablation provided that we continuously move the ablationspot along the target surface. This means that in graphite, underrepetitive ablation on the same target position at 1 kHz, theinstability of the plasma and generated harmonics is largelyrelated with the unstable conditions of the ablating spot. Aftermoving to a new spot, the previous irradiated target area coolsdown and becomes again available (one rotation later) forfurther ablation with the same harmonic output. Therefore,using a rotating graphite rod can significantly improve thestability of the harmonic signal.

The reason for the slow degradation of harmonic(figure 3(a)) is clearly due to effects on the surface of the target.

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Figure 3. Harmonic generation in graphite plasma using 3.5 fspulses. (a) Stability of harmonic intensity over 1 million shots on agraphite target integrated over the 11th to 25th harmonics. (b) Decayof harmonics after stopping the motor rotating the target.

Note that stable harmonics can be generated over a broad rangeof target rotation speeds. Given the target rotation speed aswell as the size of the ablation focus, the same target areawas repeatedly exposed to ablation for consecutive rotationsover the 20 min duration of our experiments. At the high pulserepetition rate, this could lead to thermal damage of the target.It is possible that once the solid surface is melted, the forcefrom a following laser shot and from the subsequently createdplasma causes the expulsion of part of the liquid target fromthe ablation area, creating a deeper hole out of the focus or withangled sides. These effects would result in plasma emissionin a range of directions around the normal to the surface andcan considerably diminished once the target starts to rotate.During rotation, the previously ablated area cools down suchthat, during the forthcoming ablation event of the same spot,the plasma formation occurs under approximately the sameconditions.

To prove that the ablated area cools down with rotation, werotated the target at different speeds (from 10 to 300 rpm) anddid not find a difference in the stability of the harmonic yield.These observations point to the importance of the periodic

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renewal of the ablation zone and confirm our suggestionthat the cooling of the ablation area leads to stable plasmageneration.

From the above consideration, one can conclude thatthe decay is mostly related with the creation of a micro-channel on the target surface. Our separate studies of thisphenomenon have shown that, in the case of metal targets,this decay becomes less pronounced compared with graphite.This difference is related to the thermodynamic propertiesof the latter material surface, which cannot withstand along series of ablation events without changing the surfaceproperties. The details of these studies are presented in [26].

Regarding the different error bars for similar timescalesand harmonic signals shown in figure 3(a), we note that ourregistration system allowed measuring the error bars for eachtimescale during measurements. The averaging of harmonicintensity was carried out during each 0.5 min (i.e. for 30 000laser shots). One should note that due to integration over the15–26 eV spectral range of the intensity of a few harmonics, thefluctuations of this parameter could be attributed to variationsof the free-electron density, which change the phase-matchingconditions for the harmonics. The error bars reflect thesevariations over each 30 s of the measurement.

3.1.2. Extension of harmonic cutoff using MIR laser pulses.Here, we present the results of HHG in carbon plasmas usingthe MIR OPA pulses (wavelength 1300 nm, pulse duration40 fs, 1 kHz pulse repetition rate) as probe radiation andcompare these results with those obtained with 780 nm, 30 fsdriving pulses operating at the same pulse repetition rate. Theupper panel in figure 4 shows the harmonic spectrum generatedin the case of 1300 nm probe pulses. Harmonics up to the 57thorder were observed under the conditions of carbon plasmaformation using the uncompressed 20 ps pulses from thislaser. It is worth noting that the application of less intense1400 nm pulses available by tuning the OPA, while generatingweaker harmonics, did not result in a higher harmonic cutoffthan in the case of 1300 nm. This observation suggests that theharmonic generation occurred under saturated conditions, withthe expectation of even stronger harmonics once the micro-and macro-processes governing the frequency conversion areoptimized.

Harmonic spectra up to the 29th order in the case of780 nm, 30 fs probe pulses, are presented in the bottom panelof figure 4. By comparing with the spectra collected with the1300 nm driving source (same figure, upper panel), one canclearly see the expected extension of harmonic cutoff in thecase of the longer wavelength driving source. The importantpeculiarities of these comparative studies are the broadbandharmonic spectra in the case of the 1300 nm laser and thesimilar yield of harmonics at the two driving wavelengths.Whilst the former feature depends on the bandwidth of the OPAoutput, the later observation requires additional consideration.We observed that the plasma harmonic yield from the MIRsource did not follow the expected Ih ∝ λ−5 rule. In fact,for the intensities of MIR and 780 nm pulses used (∼ (2–4) × 1014 W cm−2), the harmonic efficiency of the XUVradiation driven by MIR pulses was higher compared with the

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Figure 4. Plasma harmonic spectra using the 1300 nm (upper panel)and 780 nm (bottom panel) probe pulses. The energies of probepulses were 0.2 mJ (upper panel) and 0.54 mJ (bottom panel).Ablation was carried out using 20 ps, 780 nm, 1 kHz laser pulses.

case of 780 nm pulses, assuming lower energy of the formerpulses (0.2 and 0.54 mJ, respectively). We note that the Ih ∝λ−5 rule predicts a ∼13-fold decrease of conversion efficiencyfor the MIR (1300 nm) pulses compared with the 780 nmpulses at equal probe intensity.

3.2. Characterization of optimal plasma conditions

This section presents the characterization of the graphiteablation plasma plumes under the conditions of maximumHHG conversion efficiency. In graphite, the ablation plasmaplume may contain various species of carbon, i.e. neutralsand ions, small molecules, clusters, aggregates, etc, whichcan contribute to harmonic generation in various extents. Itis important to determine their presence in the region wherethe driving laser pulse interacts with the expanding plasma.In particular, the production of clusters in the laser plasmaduring laser ablation of various targets has a high probability,while their presence and concentration in the plasma areawhere the frequency conversion occurs is yet to be confirmeddirectly. Another issue is how we can define the density ofmonomers, dimers and clusters and their influence on theHHG yield. The analysis of post-ablation conditions of thedeposited debris can provide information on the nature ofthe nonlinear species, despite the differences between the

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composition of the plasma in its early stages and the depositedmaterial, due to the influence of conditions of aggregation inthe substrate [27]. Another issue of interest is whether thespectral characterization of the plasma emission in the visibleand UV ranges can provide some clues about the plasmaconditions, without the simultaneous analysis of the XUVemission. We attempt to address these issues below.

3.2.1. Plasma characterization by optical spectroscopicmeasurements in the visible, UV and XUV ranges at differentefficiencies of HHG. It has been shown previously thatefficient harmonic emission is observed only in the case whenthe visible and UV plasma emission is dominated by neutraland singly ionized carbon lines [9]. The present studies havealso confirmed this feature at the laser fluence used to heatthe target surface (figure 5(a)). The broad features near 470,515 and 555 nm could be assigned to the bands of excitedC2 molecules. These bands have been observed in the ablationof graphite at several wavelengths (see for instance [28–30]).Other lines in the spectra presented in figure 5(a) are attributedto the neutral and singly charged carbon.

The analysis of optical spectra in the visible and UVranges does not provide information about the presence ofhighly ionized species, which can be revealed by collectingthe plasma emission in the XUV range. The XUV spectrum ofcarbon plasmas (figure 5(b)) collected following excitationby a 8 ps heating pulse at high intensity, without furtherexcitation by the probe pulse, provides some insight intothe plasma components prior to interaction with the drivingradiation. This spectrum was collected under the conditionsof considerable decrease in the nonlinear optical response ofthe medium (i.e. plasma conditions unsuitable for HHG) andrevealed the appearance of many emission lines from C II andC III ions. Over-excitation of the target by 10 ns pulses alsoled to the appearance of emissions from high-charged (C III,C IV) ions (figure 5(c)).

It may be noted that these spectral measurements weretime integrated, so one could not say exactly which plasmacomponents existed at the moment of the propagation of thefemtosecond beam through the plume. However, the presenceof ionic lines from multi-charged species in the last twocases (figures 5(b) and (c)) gives a strong indication of over-excitation of the target and of its negative influence on HHGefficiency. We note that at this level of excitation of thegraphite plasma, harmonic generation was partially or entirelysuppressed. Specifically, a twofold increase in the intensityof 8 ps pulses (from 2 × 1010 to 4 × 1010 W cm−2) led to adecrease of harmonic intensity by a factor of 2.5. The samecan be said about the excitation using longer (10 ns) pulses,though the threshold, at which harmonics started to decay, wasconsiderably lower (2 × 109 W cm−2). Application of 10 nspulses with an intensity of 3 × 109 W cm−2 led to a substantialdecrease of harmonic efficiency and to the appearance ofemission lines from high-charged ionic species (figure 5(c)).Under the conditions of efficient HHG, no ion lines appearalongside the harmonic spectra.

The meaning of time-integrated spectral measurementsrefers to the collection of irradiation during the entire period

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C II

63.6

nm

C II

59.5

nm

C II

57.4

nm

C II

I

Wavelength (nm)

Plas

ma

emis

sion

inte

nsity

(arb

. uni

ts)

Photon energy (eV)

62.2482.99 23.5531.17 49.79

53.8

nm

C II

I

20 25 30 35 400

1000

2000

3000

28.9

nm

, C IV

31.2

nm

, C IV

37.2

nm

, C II

I

38.4

nm

, C IV

40.3

nm

, C V

43.6

nm

, C V

41.9

nm

, C IV

45.9

nm

, C II

I49

.3 n

m, C

III

51.1

nm

, C II

I53

.8 n

m, C

III

57.4

nm

, C II

I59

.5 n

m, C

II

63.6

nm

, C II

81.8

nm

, C II

I 68.7

nm

, C II

Wavelength (nm)

Plas

ma

emis

sion

inte

nsity

(arb

. uni

ts)

Photon energy (eV)

62.24 49.79 41.49 35.56 31.12

(a)

(b)

(c)

Figure 5. (a) Carbon plasma emission spectrum in the visible andUV ranges at optimal excitation of a graphite target by 8 ps heatingpulses (2 × 1010 W cm−2). (b) Spectrum of carbon plasma in theXUV range at over-excitation of the target by 8 ps pulses(5 × 1010 W cm−2). (c) Spectrum of carbon plasma in the XUV rangeat over-excitation of the target by 10 ns pulses (3 × 109 W cm−2).

of plasma formation, emission and decay after excitation bya single shot. One can assume that during the plasma lifetime(which is, under our conditions of excitation, of the order of

7

J. Phys. B: At. Mol. Opt. Phys. 45 (2012) 165402 R A Ganeev et al

100 ns and much less than the period between two pulsesat a repetition rate of 1 kHz), the emission spectra evolvefrom being relatively broad (at the initial stage of plasmaformation, ∼10–20 ns) to be composed of narrow lines atthe last moments of plasma expansion. This dynamics ofspectral lines bandwidth is caused by the collision betweenparticles during the initial stage of plasma formation and thedecrease of particle concentration at the cooling stage of plumeexpansion. This evolution of plasma spectral modification hasbeen considered in few previous works, where gated, time-resolved laser-induced spectroscopy was used to improvethe characteristics of emitting harmonics and to extend theharmonic cutoff from a few plasmas [31–33]. In our case,we did not gate the spectral registration. Correspondingly,we collected the integrated spectra in the 50–200 ns range(depending on the excitation conditions).

Regarding the comparison between the integrated spectrafrom carbon and metal plasmas, broadening of spectral lineswas observed in both cases (as was revealed in separatecomparative studies of these plasma plumes). It is not a surpriseto observe such a behaviour, since the dynamics of plasmaconcentration was similar during the ablation of both graphiteand various metal targets.

3.2.2. SEM of deposited graphite debris and time-of-flight mass spectroscopy of laser-produced plasma. Toprove the presence of clusters in carbon plasmas underoptimal conditions of harmonic generation, we analysed themorphology of deposited debris from the graphite-ablatedplasma during ablation using the picosecond and nanosecondpulses. It has already been mentioned that laser ablationof a solid material is a widely accepted technique forthe generation of nanoparticles. However, this process haspreviously been studied without taking into account the roleof free electrons and highly excited ions, which destroythe optimal conditions for phase-matched HHG. Our SEMmeasurements of the deposited debris were carried out atthe laser ablation conditions corresponding to optimal plasmaformation for efficient HHG. The substrates (glass plates andsilicon wafers) used to collect the deposited material wereplaced at a distance of 40 mm in front of the ablation area andthe debris was further analysed by SEM.

Under optimal plasma conditions, when the highestharmonic conversion efficiency from the carbon-containing8 ps pulses was measured, the SEM images did not revealthe presence of nanoparticles in the deposited debris withsizes above the limit of detection (10 nm) of the microscope(figure 6(a)). This was probably due to the small fluence (0.2J cm−2) of the heating radiation on the target surface (Ips =2.5 × 1010 W cm−2). It is possible that in the case of the carbonplasmas produced under these conditions, harmonics couldalso originate from nanoparticles with sizes below the limit ofdetection. A different pattern was observed upon ablation ofthe target with 10 ns pulses, where considerably higher heatingfluence (10 J cm−2) caused the appearance of nanoparticles ona nearby substrate. Under relatively moderate conditions ofablation using 10 ns pulses (Ins ≈ (1−2) × 109 W cm−2), ahigh density of nanoparticles appeared in the SEM images of

(a)

(b)

Figure 6. (a) SEM image of the deposited debris after ablation of agraphite target by 8 ps pulses under optimal conditions of HHG.(b) Histogram of size distribution of deposited nanoparticles andcorresponding SEM image of deposited debris in the cases ofablation of a graphite target using 10 ns pulses. The size bar on theSEM images is 2 μm.

the deposits, with sizes mostly distributed in the range between10 and 200 nm, with a mean size of 50 nm (figure 6(b)). Wereiterate that these debris characteristics were measured atthe maximum conversion efficiency of 15th–23rd harmonics.Thus, our morphological studies have confirmed the presenceof relatively large nanoparticles deposited on the substratesunder the conditions of ‘optimal’ ablation using 10 ns pulses.However, some uncertainty still remains about the correlationof these results with the presence of the same nanoparticlesin the carbon plasma during harmonic generation, due to thepossibility of aggregation of these clusters after deposition. Toaddress this issue, we carried out the TOFMS of nanosecondpulse-ablated graphite.

Figure 7 shows the mass-resolved spectrum of a carbonplasma after 60 shots of the 10 ns heating pulses. These studiesreveal that under plasma conditions close to optimal for HHG,the laser plume contains a group of small, singly ionized carbonclusters (C10–C30). Our attempts to find higher mass clustersfailed, though we searched for them over a longer range of

8

J. Phys. B: At. Mol. Opt. Phys. 45 (2012) 165402 R A Ganeev et al

0 100 200 300 400 500

0.002

0.004

0.006Number of particles in carbon cluster

R

elat

ive

inte

nsity

Mass (a. m. u.)

10 15 20 25 30

Figure 7. Mass spectrum (in atomic mass units) of carbon plasmaobtained during excitation of a graphite target using 10 ns pulsesunder the conditions close to optimal plasma formation for HHG.

delays (up to few μs) between the onset of laser ablation andthe switching on the triggering pulse in the TOFMS.

To ascertain the presence of neutral species in the ablatedplasma, an additional source of ionization can be used. Inthe present case, an F2 post-ionization excimer laser (λ =157 nm) served that purpose. Photons of this wavelength caninduce the ionization of neutral clusters through single-photonabsorption. However, once we focused the 157 nm pulse onthe plasma area (figure 1(b)), no evidence in the mass spectraof neutral clusters was found. This could be explained by thefact that the ionization potential of carbon (Ip = 11.2 eV)is higher than the photon energy of the ionizing laser (E =7.9 eV) and to the difficulty of ionizing the existing carbonclusters by two-photon absorption of 157 nm radiation, due tolow intensity of these pulses in the plasma area.

3.2.3. Calculations of plasma concentration. Here, wepresent a three-dimensional molecular dynamical simulationof laser ablation of graphite using the molecular dynamicscode ITAP IMD [34].

Although it is possible to predict material properties fromab initio simulations to high accuracy, the method has somedrawbacks. The long computational time required for thesecalculations makes them unpractical for typical treatmentsof laser ablation. The system sizes that can be simulated onmodern computers are still in the order of a few hundredsof atoms, which is far too small. In the case of moleculardynamics simulations, the system is simplified by not treatingthe ions and electrons separately. The modelled atoms areassumed not to have inner degrees of freedom, and they interactwith each other as classical particles. For the solution of themany-body problem, the classical Hamiltonian equations ofmotion are integrated. In general, for an N-particle system,this leads to 6N first-order differential equations. Let

H(p1, ..., pN, r1, ..., rN ) =N∑

i=1

p2i

2mi+ U (r1, ..., rN ) (1)

be the Hamiltonian of a configuration of N classical particles,with U ({ri}) being the potential. The equations of motion thenbecome

r j = p j

mj, p j = Fj = −∇r jU ({ri}) . (2)

The force Fj = p j, acting on atom j, is calculated bytaking the gradient of the potential U with respect to thecoordinate rj. These equations cannot be solved analyticallyfor large N. Instead, the equations are discretized in time. For agiven configuration (coordinates and momentum) at time t, theforces on all the atoms are calculated. After this, their positionsare adjusted accordingly for t + δt.

The time step δt is not arbitrary; in contrast, it has to besuitable for the underlying problem. Femtoseconds or evenless are necessary for atomistic simulations. The time step hasto be smaller than the timescales of characteristic motions to beresolved in the system. This dictates an upper bound for δt. Foratomistic simulations of solids, a time step between 0.1 and2 fs has been established. In the literature, there exist few well-known algorithms, like Gauss, Runge–Kutta or Verlet, whichare used to solve ordinary first-order differential equations.The latter method is applied in the IMD code [34, 35] and hasbeen used throughout this work.

By solving these standard Hamiltonian equations, it ispossible to characterize a system that does not exchangeparticles (N), volume (V) or energy (E) with its environment. Instatistical mechanics, such a system is called a microcanonicalensemble (NVE ensemble). It should be noted that during laserablation, the total energy of the system is changed, but duringone integration step of the equations of motion, the energy isunchanged; therefore, the NVE ensemble is quite sufficient fora simulation of laser ablation.

For the solution of equation (2), a potential has to bespecified. A general potential is obtained by taking multi-body contributions into account. The potential energy can beexpanded in a term related to an external potential, a pair term,a three-body term and so on. This leads to

U ({ri}) =∑

i

φ1(ri ) + 1

2

∑

i, ji�= j

φ2(ri, r j)

+ 1

6

∑

i, j,ki�= j �=kj �=k

φ3(ri, r j, rk) + · · · . (3)

For the simulation of carbon atoms in graphite crystals,only empirical interatomic potentials [35] were used.

If the physical mechanisms involved in the ablationprocess are not known, a modelling of the macroscopicbehaviour can be a workaround. For this approach, thetemperature near the surface has to be increased during thesimulation. The temperature of a system is related to theaverage kinetic energy of its atoms via

〈Ekin〉 = f

2kBT, (4)

where f is the number of degrees of freedom, and f = 3in the existing case. The basic idea of the direct approachis a rescaling of the kinetic energy of the atoms. After

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J. Phys. B: At. Mol. Opt. Phys. 45 (2012) 165402 R A Ganeev et al

each time step δt the momentum vector pi of the ith atomis rescaled accordingly, leading to an immediate rise intemperature model. A general form for the power densitycontains an amplitude factor S0, an absorption law d(x), anintensity distribution on the surface I(y, z), consideration ofthe reflectivity (1 – R) and the temporal beam shape f (t):

S(x, t) = (1 − R)S0d(x)I(y, z) f (t). (5)

For the absorption d(x), the Lambert–Beer law is used,where α is the inverse absorption length. The intensity I(y, z)can be adjusted according to the problem, while a Gaussianshape is assumed for the temporal distribution f (t):

S(x, t) = (1 − R)S0αe−αxI(y, z) e− (t−t0 )2

2σ2t . (6)

The power density S(x, t) is multiplied by the time stepδt and divided by the average atomic density ρn to achieve asmall energy difference. After each time step δt that amountof energy is added to the kinetic energy of the ith particle is

Eikin(t + δt) = Ei

kin(t) + δt

ρnS(xi, t). (7)

The atomic number density ρn can be calculated on-the-fly by averaging the atomic masses over the irradiatedvolume. This density is assumed as constant for pulses shorterthan 1000 fs. For significantly longer pulses, the materialmay change its phase, which results in a time-dependentdensity ρn(t). The huge advantage of this model clearlylies in its simplicity: no knowledge of material propertieslike the electron–phonon coupling or other processes duringablation are needed. Heat transfer, melting and vaporization aregoverned by the potentials used for the molecular dynamics.

Our simulations were performed for two ablation times(8 ps and 10 ns) with a time step of 1 fs. It should be notedthat, for graphite, the reflection coefficient is relatively smalland decreases with the increase of surface irregularity. So,it can safely be assumed to be 0. The Brown module wasconsidered as α = 0.01 ´A−1. The sample surface depth wasobtained from a one-dimensional density by estimating eachtime step. The positions and velocities of all carbon atoms werefixed every 50 fs. The velocity distribution was analysed bycounting the number of particles that have a sufficient velocityto be in a given region (200 μm above the ablated target)after 30 ns from the end of the pulse. Then, the number ofparticles was averaged for all measurements and divided by thevolume, which was the surface of the model sample multipliedby time and by the difference between the minimum and themaximum speeds allowed. For a simulation of ablation bynanosecond pulses, we had to use the following approximateassumption. First, the pulse intensity was considered constantand only the total energy is the same as in the experiments.Then, we directly simulated the ablation for approximately100 ps so that the velocity distribution of the ablated particlesbecomes almost constant. Finally, we extrapolated this velocitydistribution for the whole duration of the pulse and obtainedthe particle concentration. For a simulation of the nanosecondablation, we also used another approach, which suggests N =10 shorter simulations (5 ps) for the unmodified sample, butevery such simulation had a constant intensity correspondingto the intensity of the nanosecond pulse at N ns.

We calculated the concentrations of carbon plasmaunder the experimental conditions of target ablationallowing efficient harmonic generation. The correspondingconcentrations were found to be exceeding 1017 and1018 cm−3 in the cases of ablation by 8 ps and 10 nspulses, respectively. We also analysed the variations of theseparameters under different experimental conditions of graphitetarget excitation. The concentrations of carbon plasma onthe target surface at the intensities of the 10 ns pulses of0.33 × 109, 1 × 109, and 3 × 109 W cm−2 were calculated to be1 × 1018, 2.5 × 1018 and 3.7 × 1018 cm−3, respectively. Oncethe stronger intensities of shorter (8 ps) pulses (6.6 × 109,2 × 1010 and 6 × 1010 W cm−2) were used in calculations toform the plasma plume, the concentrations of plasma particlesabove the graphite target surface in the area of the femtosecondpulse propagation were calculated to be lower than in the caseof longer pulse-induced ablation (1.1 × 1017, 2.6 × 1017 and4 × 1017 cm−3, respectively). This highlights the important roleof the pulse energy, which is responsible for the difference inthe concentrations of plasma plumes in these two cases.

4. Discussion and conclusions

A few earlier studies have suggested that the presence ofnanoparticles in carbon laser ablation plasmas can explainthe observed strong harmonic yield from these media[10, 11]. It was reported that the debris from ablatedgraphite and carbon ‘lead’ targets contained nanoparticleswith sizes between 100 and 300 nm. The authors of thesestudies therefore suspected that nanoparticles formed in theplasma by ablation were the source of intense harmonics.Heterogeneous decomposition; liquid phase ejection andfragmentation; homogeneous nucleation and decomposition;and photomechanical ejection are among the processes thatcan lead to the production and disintegration of nanoparticles[36–39]. A number of different techniques were used in thesestudies to determine the aggregation state of the evaporatedmaterial, including time-resolved emission spectroscopy, CCDcamera imaging of the plasma plume, Rayleigh scattering andlaser-induced fluorescence.

In our studies, we used SEM for the debris analysis andTOFMS of plasma characterization. These two methods haveprovided useful clues about the conditions and dynamics ofplasma plume formed above the target surface. Whilst theformer method can provide information about the presence ofnanoparticles in the plasma, one has to cautiously considerthose results from the following point of view. The depositionprocess on the substrate happens much later than the timeof HHG emission, and the physical process of depositionmay lead to further aggregation. Since SEM is an ex situmethod, one cannot exclude the difference between the realcomposition of clusters in the plasma and the results of SEMmeasurements, although it clearly proves the presence ofclusters in the plasma. TOFMS yields information on the insitu presence of ionized clusters, although it requires ablationof the target under the same conditions as in the case of HHGexperiments and is not well suited for the detection of neutralnanoparticles in the ablated plasma.

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J. Phys. B: At. Mol. Opt. Phys. 45 (2012) 165402 R A Ganeev et al

Our TOFMS measurements did not reveal the presenceof neutral clusters in the 10 ns pulse produced plasma forthe reasons described in the previous section. However, otherstudies (see for example [30]) have indicated the presenceof neutral carbon clusters using two-photon ionization andprobably one-photon ionization with an ArF laser (photonenergy 6.4 eV). Early TOFMS studies of laser ablationof graphite have revealed the typical characteristics of theexpanding plasma species (average velocity 1.5 × 105 cm s−1)and their concentration (4 × 1018–6 × 1019 cm−3 [40]) forablation with 532 nm, 10 ns pulses at fluences of the orderof 3 J cm−2. These values are comparable to the results of thecalculation presented in section 3.2.3 of plasma concentrationusing picosecond and nanosecond heating pulses (2 × 1017–2 × 1018 cm−3), where the presence of clusters in the plasmaplume has been demonstrated.

The measured mass distribution shown in the spectrumof figure 7, revealing the presence of C10 to C30 species,is in good agreement with those observed in the previousstudies of graphite-ablated plasma under similar excitationconditions [40]. The restriction of cluster sizes to small-sized carbon nanoparticles has also been reported in [41],where it was argued that stronger excitation conditions arenecessary to observe clusters larger than C32. In that case,one should expect the appearance of closed cages made upof joined five and six member rings. It was confirmed thatC60 and C70 fullerenes are the most abundant species among thehigh-mass ions of the carbon plasma plumes at higher ablationfluences. It was also suggested [40] that it is very likely thatthe plasma is sufficiently dense for cluster growth to occurvia ion–molecule reactions. The kinetic mechanism can beresponsible for the formation of carbon cluster ions since thesupersonic entrainment method is expected to considerablycool down the cluster ions. The growth of clusters is basedon the addition of many small carbon neutral species to theions in a stepwise fashion. One must bear in mind that whilethese assumptions are correct for specific conditions of over-excited graphite targets, during our TOFMS measurements wemaintained conditions of ‘soft’ laser ablation to ensure efficientHHG.

An explanation for strong harmonic generation fromnanoparticles compared with single atoms or ions couldbe the higher concentration of neutral atoms inevitablyaccompanying the presence of nanoparticles. Unlike singleatoms and ions, whose density quickly decreases due to plasmaexpansion, nanoparticles retain local densities that are close tothe solid state. The increase of recombination cross-sectionfor clusters with respect to atoms can also potentially enhancethe HHG efficiency in nanoparticle-contained plasmas. Earlierstudies of HHG from gases [19, 42, 43], as well as fromplasmas containing various nanoparticles (Ag, Au, BaTiO3,etc) [9, 17], have proven these assumptions by demonstratingthe enhanced HHG from clusters as compared with singleatoms and ions. Further evidence of the cluster contributionto the enhancement of the harmonic generation process comesfrom investigations of very intense laser ablation of a silvertarget [44] that gave clues regarding the participation of in situgenerated nanoparticles.

The observation of a strong extended harmonic plateauin the case of the 1300 nm probe radiation also suggests theinvolvement of clusters in the HHG process with MIR pulses.Assuming the expected decrease of harmonic intensity fromsingle-particle emitters with the growth of driving radiationwavelength (Ih ∝ λ−5) [20, 21, 45, 46], one can anticipate atleast one order of magnitude decrease of harmonic yield fromMIR pulses as compared with the yield obtained with 780 nmradiation under other equal conditions, in particular, pulseenergy and duration. However, the experiment did not show aconsiderable difference between the intensities of harmonicsoriginated from these two driving sources (figure 4). Theenergy of the 1300 nm pulses in the plasma area (0.2 mJ) waslower than the Ti:sapphire pulse (0.54 mJ). This suggests theinvolvement of a mechanism that compensates for the expectedconsiderable decrease of harmonic efficiency for the longerwavelength laser. The involvement of a clustered componentof the laser plasma in the process of frequency up-conversioncould arguably explain the observed inconsistence with thetheoretical predictions of the Ih ∝ λ−5 rule.

In principle, the intensity enhancement of the harmonicspectrum from the carbon plume in the 15–26 eV rangeinvokes the involvement of surface plasmon resonances ofnanoparticles, analogously to the case of fullerenes [9, 17] inthe range of their giant resonance in the vicinity of 20 eV. Toprove this in the case of carbon plasma, one should provideevidence of giant absorption in the above range, but thishas not been reported yet in the literature. The plasmonicproperties of carbon nanoparticles can be responsible for theobserved enhancement of carbon harmonics; however, theirrole requires additional study. Another option for explainingthe high harmonic generation yield in the carbon plume is theindirect involvement of the clusters in HHG that, while notparticipating as harmonic emitters, could rather enhance thelocal field, analogously to recently reported studies using goldnanostructures enhancing gas HHG [47, 48].

Our experimental studies revealed the limitations of targetexcitation for these two regimes of plasma formation (8 ps and10 ns). However, it is possible to apply the advantages of theablation process by generating larger plasma plumes using acylindrical optics and maintaining the same optimal intensities(2 × 1010 and 1 × 109 W cm−2 for 8 ps and 20 ns pulses) alongthe whole extended area of ablation. In that case one can expectfurther enhancement of harmonic yield caused by the increaseof length of the nonlinear medium.

Recent comparative studies of lower order harmonicefficiency in argon gas and carbon plasmas have revealedstronger conversion efficiency in the carbon plasmas [12, 13].In this paper, we have presented evidence of the superiorproperties of graphite ablation for HHG. Some argumentswhich could explain the enhanced high harmonic yield fromthis medium are as follows: (a) the graphite target allowseasier generation of a relatively dense carbon plasma andthe production of adequate phase-matching conditions forlower order harmonic generation, (b) the first ionizationpotential of carbon is high enough to prevent the appearanceof high concentration of free electrons, a condition that is notnecessarily met in metal plasma plumes, (c) neutral carbon

11

J. Phys. B: At. Mol. Opt. Phys. 45 (2012) 165402 R A Ganeev et al

atoms dominate in the carbon plume under optimal conditionsof HHG before the interaction with the femtosecond laser pulseand (d) carbon species allow the formation of multi-particleclusters during laser ablation, which can enhance the HHGyield.

In conclusion, we reported on harmonic generation studiescarried out using ablation carbon plasma as a nonlinearmedium. We systematically analysed plasma HHG usingultrashort (3.5 and 40 fs) laser pulses. We showed the efficientfrequency conversion of 3.5 fs laser radiation in the rangeof 15–26 eV using optimally prepared plasma plumes anddemonstrated the tuning of harmonic spectra by changing thespectro-temporal characteristics of the probe pulse via pressuretuning of the hollow fibre pulse compression stage. We alsoshowed the results of harmonic generation in carbon plasmausing 1300 nm, 40 fs pulses, which allowed the extensionof the harmonic cutoff while maintaining a comparableconversion efficiency to 780 nm probe radiation, in surprisingdisagreement with the expected Ih ∝ λ−5 scaling. Strongharmonics from carbon plasma were attributed to the specificproperties of this medium, in particular, the presence of clustersin the plume and their involvement in the enhancement ofharmonic yield. We presented comparative studies of opticalemission spectroscopy of the graphite ablation plume inthe visible, UV and XUV ranges, of time-of-flight mass-spectroscopy of plasma components, and of SEM analysisof plasma debris under the optimal condition of harmonicgeneration, from which we concluded the presence of smallcarbon clusters (C10–C30) in the plume at the moment offemtosecond pulse propagation, which further aggregate afterdeposition on a nearby substrate. A carbon plasma massspectrum was discussed, which showed the value of thismethod for ascertaining the presence of carbon clusters inthe plasma during HHG. We presented results of calculationsof plasma concentration under different excitation conditionsof the ablating graphite target. Our studies revealed thecorrelation between the appearance of carbon clusters andthe strong harmonic yield from this medium and showed theadvanced properties of carbon plasma for efficient HHG.

Acknowledgments

These studies were supported by EPSRC programme (grantsnumbers EP/F034601/1, EP/E028063/1 and EP/I032517/1)and the European Marie Curie Initial Training Network (grantnumber CA-ITN-214962-FASTQUAST), and in part by theMinistry of Science and Innovation of Spain (MICINN) underProject CTQ2010-15680. RAG acknowledges support fromthe Marie Curie International Incoming Fellowship Grantwithin the 7th European Community Framework Programme(grant PIIF-GA-2009-253104) and ILQ from the FPI programof the MICINN.

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