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

ISSN 0030�400X, Optics and Spectroscopy, 2010, Vol. 108, No. 5, pp. 787–803. © Pleiades Publishing, Ltd., 2010.Original Russian Text © R.A. Ganeev, H. Singhal, P.A. Naik, J.A. Chakera, M. Tayyab, A.K. Srivastava, T.S. Dhami, M.P. Joshi, A. Singh, R. Chari, S.R. Kumbhare, R.P. Kushwaha,R.A. Khan, R.K. Bhat, P.D. Gupta, 2010, published in Optika i Spektroskopiya, 2010, Vol. 108, No. 5, pp. 831–848.

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INTRODUCTION

Higher harmonics generation (HHG) of laser radi�ation in gases and laser plasmas, as well as upon reflec�tion from surfaces of solids, is a well�developedmethod for creating coherent radiation sources in thefar (vacuum) ultraviolet (VUV) spectral range [1–3].There are a number of techniques that enable one toconsiderably modify the characteristics of this radia�tion for various applied problems. Among these tech�niques, changing the chirp of laser radiation plays asignificant role because it allows one to vary the spec�trum and intensities of generated harmonics and, cor�respondingly, to analyze high�energy ionic transitionsthat occur upon interaction of powerful laser pulseswith a material.

The radiation wavelength of a harmonic can betuned by tuning the wavelength of radiation to be con�verted [4, 5], by chirping laser radiation [6–8], by act�ing with powerful radiation on a nonlinear atomic orionic medium and controlling the degree of its ioniza�tion [9–12], as well as by applying adaptive controlwith specially formed laser pulses [13, 14]. It should benoted that the radiation wavelength of a harmonic canbe efficiently tuned in a range of several nanometersapplying the chirped laser radiation only if broadbandlaser radiation sources are used. In this case, only theleading edge of the pulse is involved in the HHG pro�cess. The leading edge of a positively chirped pulsepredominantly consists of long�wavelength compo�nents of the laser spectrum, and the spectrum of har�

monics is shifted toward the long�wavelength spectralrange. In contrast, the leading edge of a negativelychirped pulse predominantly consists of short�wave�length components of the laser spectrum, and thespectrum of harmonics is shifted toward the short�wavelength spectral range. Broadband laser sourcesmake it possible to obtain broadband radiation of har�monics and, correspondingly, lead to the generation ofattosecond pulses.

The phase self�modulation of laser pulses is widelyused to generate additional frequencies in the genera�tion spectrum of laser radiation. Optical media (suchas thick glass plates) placed in the path of powerfulfemtosecond pulses cause spectral broadening of laserpulses due to the phase self�modulation. In media withpositive (negative) nonlinear refractive indices, thesepulses are positively (negatively) chirped.

A relatively low HHG efficiency limits the applica�tion of higher laser harmonics. Various methods can beapplied to increase the HHG efficiency, such as phasematching, resonant amplification of single harmonics,and the use of nanostructured media [15, 16]. Thesearch for new approaches to increasing the conver�sion efficiency (η) into harmonics is an importantproblem of nonlinear optics. In the case of HHG ingases, the use of a so�called two�color pump is amethod for increasing the intensity and energetics ofharmonic pulses. The two�color pump is considered tomean the use of laser radiation and its second har�monic as the sources of the radiation to be converted.

NONLINEAR AND QUANTUM OPTICS

Particular Features of Higher Harmonics Generationin Nanocluster�Containing Plasmas Using Single�

and Two�Color PumpsR. A. Ganeeva, b, H. Singhala, P. A. Naika, J. A. Chakeraa, M. Tayyaba, A. K. Srivastavaa,

T. S. Dhamia, M. P. Joshia, A. Singha, R. Charia, S. R. Kumbharea, R. P. Kushwahaa, R. A. Khana, R. K. Bhata, and P. D. Guptaa

a Raja Ramanna Centre for Advanced Technology, 452013 Indore, Indiab Institute of Electronics, Uzbekistan Academy of Sciences, 100125 Tashkent, Uzbekistan

e�mail: [email protected] July 28, 2009

Abstract—The wavelength conversion of femtosecond laser pulses in laser plasmas containing clusters of dif�ferent nature and dimension (fullerenes, metal nanoparticles) is studied. Pulses of a titanium–sapphire laserare 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�modu�lated pulses. It is shown that the optimization of components of a nonlinear optical plasma medium, ofplasma excitation conditions by single� and two�color pumps, and of phase and spectral parameters of radi�ation to be converted leads to a considerable increase in the generation efficiency of higher harmonics.

DOI: 10.1134/S0030400X10050188

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Along with the generation of an additional group ofeven harmonics, the two�color pump is a practicalmethod of increasing the HHG efficiency [17–25].

This technique makes it possible to generate oddharmonics whose intensities exceed those of harmon�ics generated by a single�color pump, i.e., upon theconversion of laser radiation generated at a singlewavelength. The possibility of generation of even har�monics whose intensities are comparable with intensi�ties of odd harmonics, even in the case of relatively lowenergies of second�harmonic pulses, is a very attrac�tive property of this process. We note that, until now,this process was only observed in experiments onHHG in gases (gas harmonics). Controlling the phaserelations between the waves of the fundamental radia�tion and second harmonic made it possible to achievethe efficiency η = 5 × 10–5 for the 38th harmonic of atitanium–sapphire laser at a wavelength of 21.6 nm[24]. Another interesting property of this scheme is thepossibility of generation of attosecond pulses in thecase of orthogonally polarized pump radiations [17,18, 21, 22].

As was noted above, the use of nanoparticles as anonlinear medium also leads to a marked increase in η[26–32]. Various mechanisms were proposed toexplain this process, including the influence of therecombination cross section of an accelerated electronwith the particle from which it was extracted due totunnel ionization. This recombination cross section ishigher in the case of nanoparticles because their size islarge compared to the size of atomic particles. Anothermechanism is the influence of plasmon resonances ofclusters on the efficiency of nonlinear optical pro�cesses. An increase in the local field strength within ananoparticle increases its nonlinear optical response.In particular, efficient conversion into harmonics waspredicted for this case [33]. An increased probability ofintraatomic recombinations due to a high local densityof nanoparticles can be another factor that facilitatesan increase in the intensity of harmonics [34].

In this respect, fullerenes can be an interestingobject [35]. Their size (0.7 nm) and broad (10 eV)plasmon resonance near 20 eV (λ = 60 nm) made itpossible to demonstrate an efficient HHG near thisresonance [36]. Applying laser ablation to fullerenesensured the creation of relatively dense fullereneplasma (~5 × 1016 cm–3), which considerably exceededthe previously obtained densities of evaporated C60

molecules (~1014 cm–3).All of the aforementioned has made it possible to

formulate a number of problem that should be solvedto achieve a considerable increase in η of radiationharmonics of a titanium–sapphire laser in plasmamedia. This paper describes the results of complexinvestigations of this nonlinear optical process withthe aim of increasing both the intensity of generatedharmonics and the HHG efficiency. We present ourobservations of the enhanced HHG under conditions

of a two�color pump when the radiation intensity at400 nm was 50 times lower than that at 800 nm. In thiscase, we obtained highly efficient even and odd har�monics of up to the 38th and 45th orders, respectively.An analysis of a two�color pump with orthogonal andparallel polarizations of the radiations at λ = 800 and400 nm showed that orthogonally polarized pumpwaves are favorable for this HHG scheme. The inves�tigation results of spectral variations of harmonicsupon varying the chirp of radiation to be converted arepresented. The use of broadband converted radiationmade it possible to achieve a broader tuning range ofthe wavelength of harmonics. We analyze the HHG insilver nanoparticles that are contained in targets withimproved characteristics. In this case, a high efficiencyharmonics was obtained in the range of the 9th–19th orders. We present methods for creating targetsthat contain nanoparticles that demonstrate good sta�bility of generated harmonics. In this case, we alsoobserved a considerable broadening of the spectrum ofharmonics generated in plasma containing silvernanoparticles. The HHG in silver nanoparticles iscompared with the HHG in nanoparticles of othermaterials. We also present results of the use of fullereneplasma as a nonlinear medium for HHG. The genera�tion efficiency of harmonics in the range of the plas�mon resonance in С60 was close to 10–4.

EXPERIMENTAL

Generation of harmonics in laser plasma was stud�ied using a titanium–sapphire laser at the RajaRamanna Centre for Advanced Technology (Indore,India). Laser plasma on target surfaces was createdusing a part of chirped radiation, which was separatedfrom the total beam after its transmission throughamplifier stages. The chirped radiation was directed ata vacuum chamber that contained various targets (seeinset of Fig. 1). This prepulse radiation (the prepulseenergy was up to 30 mJ, the prepulse duration was210 ps, the wavelength was 800 nm, and the pulse rep�etition rate was 10 Hz) was focused by a spherical lenswith a focal length of 500 mm on the target such thatthe diameter of the focused beam was 0.6 mm. Theintensity of the picosecond prepulse (Ipp) was variedwith neutral filters from 2 × 109 to 5 × 1010 W cm–2.

Focused femtosecond radiation was transmittedthrough plasma formed on targets after a delay relativeto the beginning of laser ablation, which was variedwithin 6–60 ns. This radiation (the pulse energy wasup to 45 mJ, the pulse duration was 48 fs, the wave�length was 800 nm, the laser radiation spectral widthwas 19 nm, and the pulse repetition rate was 10 Hz)was focused by a spherical lens with a focal length of500 mm. The focusing was performed along a direc�tion that was perpendicular to the direction of theheating picosecond prepulse, not only into the plasmatorch region, but also in front of the plasma formation


PARTICULAR FEATURES OF HIGHER HARMONICS GENERATION 789

zone or behind it. The intensity of the femtosecondradiation in the plasma torch zone (Ifp) was varied inthe range 1014–1015 W cm–2. The laser made it possibleto ensure large intensities in the focal plane (the con�focal parameter of radiation was ~1 mm, and the max�imal possible intensity was ~2 × 1017 W cm–2). If theintensity of the used radiation exceeded this limit, anumber of negative factors manifested themselves(such as the appearance of excess amount of free elec�trons during tunnel ionization of neutrals and ions inplasma, phase self�modulation of radiation that prop�agates through plasma, and the corresponding elonga�tion of the laser pulse), which considerably limit theHHG efficiency. The same refers to the conditions ofcreation of the plasma torch, i.e., the action of pico�second radiation with an excessive intensity on the tar�get led to an excess of free electrons and, correspond�ingly, to the deterioration of optimal phase relationsbetween waves of the radiation to be converted andharmonics.

Therefore, the creation of optimal plasma (i.e., of aplasma torch with a maximal η) and the use of an opti�mal intensity of femtosecond radiation (i.e., such thatthe effect of different limiting processes is minimal)are the necessary conditions for the HHG in laserplasma to be efficient. These conditions were deter�mined empirically, and they proved to be different fordifferent targets. Selecting corresponding optimal tar�

gets (i.e., the ablation of which would make it possibleto create plasma that contains components maximallyfacilitating the achievement of high η) is another fac�tor that makes it possible to considerably vary both theefficiency of this process and the spectral characteris�tics of converted radiation. These problems weresolved in our investigations, and their solution will bedescribed in detail below. Here, we note that this com�plex optimization of HHG implemented in this cycleof investigations seems to be efficient in creating themost intense sources of short�wavelength radiationbased on the conversion of the radiation wavelength ofwell�developed laser systems that emit in the near�IRrange into the VUV range.

The radiation of higher harmonics was analyzed ona VUV spectrometer, which consisted of a grazing�incidence toroidal mirror with a gold coating (theangle of incidence was varied in the range ~3°–5°), agrazing�incidence diffraction grating with a variableruling spacing, which made it possible to obtain adeveloped spectrum of VUV harmonics in a plane per�pendicular to the plane of the grating (a flat�field grat�ing, Hitachi), and a microchannel plate. The spatialimage of the spectral distribution of harmonics, whichwas amplified by the microchannel plate and trans�ferred to a phosphorescent screen, was detected by aCCD device.

0.5

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910

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Inte

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its

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rel.

un

its

Fig. 1. Spectrum of harmonics obtained in chromium plasma: (1) 10th and (2) 16th harmonic. Scheme of experimental setup ispresented on top: (1, 2) focusing lenses, (3) crystal for generation of second harmonic, (4) wave plate, (5) filter, (6) target,(7) spectrometer slit, (8) cylindrical mirror, (9) diffraction grating, (10) screen for radiation reflected in the zeroth order,(11) microchannel plate, and (12) CCD detector. Inset: calculated time distributions of intensity of (solid curve) ordinary and(dotted curve) extraordinary waves of radiation with λ = 800 nm and (dashed curve) extraordinary wave of the second harmonicat the output of the crystal�converter.

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In these experiments, in addition to the single�color scheme, a two�color scheme of conversion of theradiation wavelength was also used that considerablydiffered from previously used schemes (in HHG in gasmedia). A particular feature of this scheme is that it isvery simple compared to previously used schemes(beam separation in the Michelson scheme into twocomponents, conversion into the second harmonic inone of the channels using very thin (a few hundredmicrometers) and, correspondingly, very expensiveBBO crystals (β�BaB2O4), polarization rotation of thesecond harmonic radiation by 90°, filtering from themain radiation, superposition of the two channels inone direction, and the high�precision superposition ofthe two beams in time and space after focusing theradiation in the nonlinear�medium zone). In our case,we simply placed a 1�mm�thick KDP crystal in thefocusing channel at approximately halfway betweenthe focusing lens and plasma torch. The laser radiationintensity inside the crystal was maintained at a level atwhich neither white light generation nor phase self�modulation (characterized by the broadening of thespectrum of the radiation and pulse elongation)occurs.

The application of this conversion scheme (in theconvergent beam) considerably reduced the second�harmonic generation efficiency. In our experiments, itwas 2%. However, as will be shown below, this effi�ciency level was quite sufficient to cardinally changethe generation conditions of harmonics and to achievea considerable transfer of the energy of the main radi�ation to both odd and even harmonics with compara�ble efficiencies. This scheme makes it possible to useorthogonally polarized pump components at thewavelengths of the main radiation (800 nm) and thesecond harmonic (400 nm) for efficient HHG. Thevelocity dispersion in the crystal did not lead to thetime separation of these two pulses. In the case of usingconvergent radiation, the absence of a noticeablewalk�off of the two beams (due to the angular disper�sion of o and e components of interacting waves) in thecrystal volume also led to an increase in the area ofspatial intersection of the two beams in the nonlinearmedium. Additionally, we performed HHG experi�ments using the radiation only of the second harmon�ics, for which purpose the main radiation was filtered�out by a BG39 filter.

The chirp of radiation to be converted was varied byvarying the distance between the gratings of the com�pressor. Decreasing the distance between the gratingsrelative to the position in which a maximal compres�sion of the pulse was achieved yielded a positive chirpat the compressor output and, conversely, increasingthe distance between the gratings gave rise to a nega�tive chirp of the laser radiation

In these experiments, we used targets with differentproperties from the viewpoint of the morphology oftheir surfaces and component compositions. We used

solid targets (silver, indium, chromium) that showedtheir positive properties in previous studies on creationof optimal plasma. These (and some other) targetswere used in our studies to mainly demonstrate spe�cific features of the spectra of harmonics obtained withthe two�color pump and in studies of HHG underconditions of phase�modulated converted pulses.

HHG in plasma that contained nanoparticles wasstudied mainly using as targets different matrices towhich silver nanoparticles were introduced. The aver�age size of silver nanoparticles as determined by anelectron microscope was 10 nm. We also studied HHGin plasmas that counted gold (14 nm) and strontiumtitanate (38 nm) nanoparticles. Colloidal solutions ofsilver nanoparticles were prepared according to themethod described in [37]. As a result, we obtainedsolutions with characteristic absorption ranges, whichare associated with surface plasmon resonances of sil�ver nanoparticles with triangular (638 nm) and spher�ical (420 nm) shapes. We studied different groups oftargets prepared by this method. In particular, we stud�ied two dried solutions of silver nanoparticles in poly�vinyl alcohol with different methods of drying (in thenatural way and in a furnace). We also studied solu�tions of spherical nanoparticles (Ag, Au) in water andethanol, which, after drying, were glued to glass sub�strates with rapidly drying glue. Strontium titanatenanoparticles were also glued to glass substrates.

A number of experiments were performed withfullerenes. Targets with these particles were preparedusing their mixtures with the glue and with polymeth�ylmethacrylate. To compare HHG in plasmas createdwith these targets, we used solid graphite targets, aswell as soot powders.

RESULTS AND DISCUSSION

A. Generation of Harmonics Using Two�Color Pump

Generation of higher harmonics in differentplasma torches using the 800�nm radiation was per�formed as the generation of odd harmonics, which wasaccompanied by a plateau�like intensity distributionof higher�order harmonics. In indium plasma, a con�siderable amplification of the 13th harmonic wasobserved, as was the case with previous HHG studiesin indium plasma [38]. Another characteristic resultwas a comparatively long plateau in silver plasma. Pre�viously, these two plasmas manifested themselves asthe most efficient nonlinear media in which the high�est η was achieved [39].

The main results of this series of experiments arepresented below. As is known, the single�color (i.e.,single�wavelength) pump can only cause the genera�tion of odd harmonics due to the symmetry inversionof the nonlinear medium. The use of the two�colorpump removes this inversion, which leads to theappearance of both odd and even harmonics in thespectrum [40]. In our experiments, the KDP crystal



placed in the path of the focused femtosecond radia�tion led to the generation of amplified odd harmonics(compared to the case without nonlinear crystal), aswell as even harmonics, the intensity of which in somecases was equal to or even higher than the intensity ofodd harmonics in the same spectral range, despite thefact that the conversion efficiency of the main radia�tion into the second harmonic was only 2%. Figure 1gives an example of such a spectrum for chromiumplasma. To generate harmonics only using the short�wavelength pump, we filtered the main radiation(800 nm) from the second�harmonic radiation(400 nm) using a thin UV filter. In this case, the gen�erated harmonics (5th, 7th, and, in some cases, 9th,which correspond to the 10th, 14th, and 18th harmon�ics radiation of a titanium–sapphire laser) wereweaker compared to the case of the two�color pump.

It should be noted that, under the conditions oftype�I phase matching in a KDP crystal, the interac�tion length of waves is defined by the expression

and is 0.3 mm for the pump at 800 nm. Here, t is thepulse duration and u2e and u1o are the group velocitiesof the ordinary wave of the main radiation and of theextraordinary wave of the second harmonic. As can beseen, this value does not exceed the thickness of thecrystal used in the experiment (1 mm). Under theseconditions, despite the mismatch between the groupvelocities of the interacting waves, the calculationsshow that the ordinary wave of the radiation 800 nmand the extraordinary wave of the radiation at 400 nmhave a fairly long time interval in which they overlapwith each other after emerging from the crystal (insetof Fig. 1). It follows from this figure that, at a conver�sion efficiency of 2%, the profiles of these pulses areoverlapped at the output of the crystal, which makes itpossible to expect a mutual influence on HHG inplasma. Therefore, the arrangement of the crystal inthe position in which neither the white light genera�tion nor the phase self�modulation was observed,made it possible to obtain an overlap between 800�nmand 400�nm radiation pulses in the laser plasma regionwith a linear size of about 0.8 mm. Under these condi�tions, the generation efficiency of odd harmonics wasconsiderably increased compared to the single�colorpump, and even harmonics of comparable intensitywere generated. Figure 2 presents images of spectraldistributions of harmonics (measured with a CCDdetector) in fullerene plasma under the single�colorpump at (a) 800 and (c) 400 nm and the two�colorpump at 800 nm + 400 nm (b). Thus, the intensities ofharmonics in the plateau range under the two�colorpump were three to eight times higher compared to thesingle�color pump. Note that, when 400�nm pulsesalone were used, only a few harmonics (fifth and sev�enth) were observed. In all these experiments, thecrystal was merely introduced in the scheme, and no

L t/ u2e1–

u1o1–

–( )=

additional optimization of experimental conditionswas performed.

Below, we will present results that were obtainedwith the two�color pump in various plasma media atdifferent parameters of radiation to be converted.Upon varying the chirp of the 800�nm pump, thespectral distributions of even and odd harmonics werechanged. The spectral characteristics of the convertedradiation were also changed by the phase modulationof the 800�nm radiation as a result of transmission ofintense pulses through the laser plasma. In this case,the width of the spectrum of the radiation at 800 nmwas increased from 19 to 30 nm, which also led to thebroadening of the spectra of even and odd harmonics.

Comparison of the distributions of harmonicsobtained with the single�color and two�color pumpsshowed that the optimization of HHG is achieved indifferent spectral ranges. Thus, in the silver plasma,the radiation at 800 nm is most efficiently convertedinto harmonics whose order exceeds 40 (with η beingmaximal between the 41th and 55th harmonics, i.e., inthe range 16–20 nm). This feature was recently ana�lyzed in [39] and was attributed to the effects of prop�agation through a nonlinear medium when macro�scopic processes (first of all, the phase matchingbetween pump and harmonic waves) begin to prevailover microscopic processes. Under these conditions,the use of a two�color pump led to a cardinal change inthe spectral distribution of harmonics along the pla�teau. The intensities of lower�orders harmonics con�siderably increased in the plateau range compared tothe single�color pump (Fig. 3). Now, the phase rela�tions were optimal for harmonics in the spectral range65–80 nm, with the intensities of these harmonicsbeing five to seven times higher than their intensitiesunder the single�color pump (at 800 nm). Figure 3 alsoshows the spectrum of harmonics obtained by a two�color pump with the parallel polarization. The parallelpolarization was obtained using a wave plate that wasplaced in the beam after the crystal converter and that

9 10 11 12 13 14 15 16 17(a)

(b)

(c)

Fig. 2. Images of spectral distributions of harmonics(orders of harmonics are shown on top) generated infullerene plasma and measured by CCD detector: (a) sin�gle�color pump by laser radiation at 800 nm, (b) two�colorpump at 800 nm + 400 nm, and single�color pump by sec�ond harmonic radiation at 400 nm.

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rotated the polarizations of the radiation at 800 and400 nm by 180° and 90°, respectively.

As was noted in the Introduction, the creation ofresonant conditions for increasing the nonlinear opti�cal response of the medium can be an alternative to thephase matching between the pump and harmonicwaves. The role played by atomic and ionic resonancesin increasing the harmonic generation efficiency wasactively discussed in terms of the perturbation theoryat early stages of studying the generation of low�orderharmonics [41]. In the case of HHG and descriptionof this process in terms of the three�stage model [42–44], theoretical estimates confirmed that it is possibleto efficiently amplify individual harmonics and groupsof harmonics, whereas no such peculiarities wereobserved in experimental studies on the generation ofharmonics in gas media. The latter circumstance canbe explained by the fact that the number of gases usedin HHG was limited, which considerably reduced theprobability of coincidence of frequencies of ionic tran�sitions in these media with frequencies of harmonics.In this respect, the use of laser plasma created on thesurface of numerous solid targets made it possible tosubstantially increase the probability of this process,

which was demonstrated in studies of recent yearsusing plasmas of indium, tin, chromium, and othermaterials [45]. Subsequent investigations showed thatthe use of radiation at wavelengths other than the radi�ation wavelength of the titanium–sapphire laser (e.g.,at the wavelength of the second harmonic of this laser)also makes it possible to create conditions of resonantamplification of an individual harmonic [9].

As was noted above, this amplification is character�istically exemplified by the very intense 13th harmonicgenerated in the indium plasma under the pump at800 nm. Studying the indium excitation and photo�ionization spectra showed that a considerable part ofthe plasma emission in the range 40–65 nm is causedby radiative transitions to the ground (4d105s2 1S0) andlow�lying excited (4d105s5p) states [46]. These studiesalso revealed a strong emission line at a wavelength of62.1 nm (19.92 eV), which corresponds to the transi�tion 4d105s2 1S0 4d95s25p(2D)1P1 with a large oscil�lator strength (gf = 1.11) and whose parameters are12 times higher than analogous parameters of adjacenttransitions. This transition can prove to be at reso�nance with the 13th harmonic of the titanium–sap�phire laser radiation (λ = 61.5 nm, Ef = 20.2 eV) dueto the Stark effect. The application of the two�colorpump in this scheme, along with the generation of theintense 13th harmonic, showed that the intensity ofthe adjacent even (12th) harmonic considerablyexceeds the intensities of all neighboring harmonicsand is comparable with the intensity of the 13th har�monic (Fig. 4a). It was reported previously that thegeneration efficiency of the latter harmonic is close to10–4 [38]. It is clear that the considerable generationefficiency of the 12th harmonic is also results from thefact that its wavelength is close to the wavelength of thetransition that caused amplification of the 13th har�monic. Therefore, the use of the two�color pumpmade it possible to demonstrate the resonantly ampli�fied even harmonic, whose intensity is three to fivetimes higher than the intensities of adjacent harmon�ics (except for the 13th). We note that, when the sin�gle�color pump at 400 nm was used, no such featurewas observed because it is impossible to generate the6th (even) harmonic of the radiation at 400 nm, whichcorresponds to the 12th harmonic of the radiation at800 nm (Fig. 4b).

The generation spectra obtained by different pumpmethods differ from each other not only by theappearance of even harmonics and higher intensitiesof converted radiation in the case of the two�colorpump. An important feature of the latter method ofconversion of the laser radiation wavelength into theVUV range is the smaller ultimate order of generatedharmonics compared to the single�color pump. Thus,when the 800�nm radiation alone was used, harmonicsof up to the 63th order were generated in the silverplasma, whereas, with all other conditions being thesame, the two�color pump make it possible to generate

40

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Fig. 3. Spectra of low�order harmonics generated in silverplasma: (a) single�color pump (800 nm), (b) two�colorpump (800 nm + 400 nm) with parallel polarizations, and(c) two�color pump (800 nm + 400 nm) with orthogonalpolarization.



only harmonics of no higher than the 43th order.Qualitatively, this peculiarity can be substantiated bythe following reasoning. The ultimately possible orderof generated harmonics is directly proportional to thefield intensity and square of the laser frequency [42,43]. Correspondingly, the influence of the second field(i.e., the radiation whose wavelength is two timessmaller than the wavelength of the laser radiation),which is obtained at the cost of a decrease in the inten�sity of the initial field, should reduce the ultimateorder of generated harmonics due to the two factorsindicated above. Another factor of a decrease in themaximal order of generated harmonics is the fact that,under the single�color pump, electrons to be acceler�ated move along both short and long trajectories.Under the two�color pump, harmonics are generateddue to electrons that only move along short trajecto�ries, and these electrons do not have time to acquirekinetic energy required for the generation of harmon�ics of higher orders.

According to the calculations of [24], the degree oftunnel ionization under the two�color pump deter�mined from the Amosov–Deloné–Kraіnov relations[47] considerably exceeds this parameter in the case ofthe single�color pump. Correspondingly, the orthogo�nally polarized two�color field is capable of generatingmore intense harmonics than the single�color field.This feature was previously described in experimentswith harmonics in gases. The results presented in thissection show that the orthogonal two�color pump oflaser plasmas is efficient and that it is possible toachieve large energies of laser pulses in the VUV range.The observation of the resonantly amplified harmonicin the indium plasma indicates that it is makes sense tosearch for media where the wavelengths of even har�monics either coincide or are close to the wavelengthsof atomic or ionic transitions in used materials, whichleads to the amplification of these harmonics similarlyto the amplification observed under the single�colorpump [48].

B. Generation of Harmonics in Plasmas under Frequency and Phase Modulation

of Radiation to Be Converted

Previous HHG studies in gases and plasmasshowed that laser sources with a large width of the gen�erated spectrum make it possible to obtain harmonicsthat can be tuned over large spectral range. The spec�trum itself of these harmonics is also broadened com�pared to harmonics obtained with narrowband laserradiation. We studied HHG in plasmas using broad�band pump radiation, which was varied with variousmethods. The objective of these studies was to demon�strate that the modulation of the spectrum of radiationto be converted leads to considerable changes in thecharacteristics of generated harmonics.

In the first series of these studies, the laser radiationspectrum was modulated upon propagation of a fem�

tosecond pulse through a glass plate 10 mm thick. Thespectrum of the radiation emerged from the plate wasbroadened due to additional frequencies as a result ofphase self�modulation. These frequencies appearupon the propagation of radiation through a mediumand are defined by the relation

where z is the coordinate along the z axis, n2 is the non�linear refractive index of the medium, k0 is the wave�number, ω0 and ω are the initial and resultant frequen�cies of the laser radiation, and dI/dt is the rate of vari�ation of the intensity of the laser field.

Figure 5 presents spectra of higher�order harmon�ics generated in the silver plasma using unmodulated(i.e., initial) and phase�modulated laser pulses. Har�monics generated by phase�modulated pulses wereshifted toward the long�wavelength range. The shiftswere 0.9 and 0.3 nm for the 17th and 37th harmonics,which corresponds to the shift of the central wave�length of the laser radiation by ~11 nm. The inset ofFig. 5 presents spectral distributions of the laser radia�tion that were measured before (thick line) and after(thin line) the propagation through the glass plate. Wenote that the phase modulation predominantly leadsto a short�wavelength shift of the central wavelength ofthe laser radiation. The phase�modulated pulse has

ω ω0 k0zn2dI/dt,–=

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22201816141210

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Order of harmonics

Fig. 4. Spectrum of harmonics generated in indiumplasma: (a) two�color pump (800 nm + 400 nm) and(b) single�color pump (400 nm).

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two peaks located near 804 and 779 nm. The totalspectral width of the pulse at half intensity increasedup to 32 nm. Opposite shifts in the radiation to be con�verted and harmonics are evidently caused by adecrease in the intensity of the phase�modulated laserpulse and by the elimination of the influence of theshort�wavelength shift in the plasma torch due to thephase self�modulation in the nonlinear medium. Thelatter factor leads to the generation of harmonics with�out any shifts in the spectrum.

Because the nonlinear refractive index of glass n2 > 0,the leading edge of the pulse (since dI/dt > 0) generatesharmonics that are mainly shifted toward the long�wavelength range, whereas the trailing edge (sincedI/dt < 0) is the source of harmonics shifted toward theshort�wavelength range. In this case, the laser pulse ispositively chirped as a whole. If a negative chirp isinduced on the pulse by varying the distance betweenthe compressor gratings, harmonics generated by thischirped pulse will be shifted toward the short�wave�length range. In addition, the spectrum of these har�monics will broaden.

The above results were obtained under conditionswhen the phase (and, correspondingly, the spectrum)was modulated upon propagation of focused radiationthrough a thick optical medium (in our case, the10�mm glass plate). However, as was already noted,the plasma torch in which harmonics are generated isitself a very efficient medium where a considerablephase modulation of the pulse is possible. This isdetermined, first of all, by the presence of ions and(mainly) free electrons in the medium, as well as byhigh intensities of the laser field in the region of thelaser torch. The phase self�modulation in plasma and

broadening of spectral lines of harmonics are mutuallyrelated parameters. This interrelation should espe�cially affect a plasma medium that consists of large�size particles, e.g., fullerenes. The particular featuresof HHG in fullerene plasmas will be discussed in thelast subsection. Here, we consider peculiarities ofspectral variations of fullerene harmonics because thissubject correlates to the general direction analyzed inthis section. A linear broadening of the spectrum ofharmonics with increasing intensity of the laser pulse,which was obvious for atomic (ionic) plasma torches,acquired an explosive behavior in fullerene plasmas.Thus, the width of the spectrum of the 11th harmonicgenerated in plasma that contained С60 increased from0.8 to 3.7 nm as the intensity of the laser pulse in theplasma torch increased from 1015 to 4 × 1015 W cm–2

(Fig. 6). This result shows that the fullerene plasmacan serve as a medium for generation of broadbandharmonics. We note that soot plasma with 2% offullerenes exhibited the same behavior.

An efficient broadening of the spectrum of har�monics can also be observed in plasmas that containnanoparticles. To this end, we studied HHG in plas�mas containing nanoparticles of different materials. Adetailed analysis of these experiments will be pre�sented below. Here, we will describe the part of theseinvestigations where the phase modulation of the con�verted wave is determined by the occurrence of nano�particles in the nonlinear medium because it corre�sponds to the subject we declared. Figure 7 showsHHG spectra in plasma formed on the surface of a tar�get that contained silver nanoparticles mixed with aliquid glue and dried in the form of a porous structure.This figure also shows spectra of harmonics generated

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Fig. 5. Spectra of harmonics (figures 45 and 19 indicate corresponding harmonics) generated in silver plasma using (thick curve)unmodulated and (thin curve) phase�modulated laser pulses. Inset shows spectra of (1) unmodulated and (2) phase�modulatedlaser pulses.



in plasmas from surfaces that contained silver nano�particles mixed either with a rapidly drying glue orpolyvinyl alcohol. Our search for optimal targets con�taining silver nanoparticles is related to attempts tofind structures that would be the most appropriate forobtaining stable harmonics during maximally possiblenumber of shots at the same place on the target sur�face. Previous studies of this process involving silvernanoparticles showed that these structures are promis�ing for increasing η provided that stable generationconditions of harmonics are found [49–52].

For all targets that contained silver nanoparticles,conversion efficiencies into harmonics lying in therange 40–100 nm were high. These efficiencies werecomparable with efficiencies in the case of fullerene�containing plasma torches (see below the last subsec�tion). Here, a characteristic feature was the generationof broadband harmonics. Thus, the spectral width ofthe 11th harmonic for the three above�listed plasma

torches that contained silver nanoparticles was 3.6,4.3, and 4.7 nm, respectively.

The results of this section can be interpreted basedon the following qualitative estimates. As intense radi�ation of short duration propagates through a thickmedium, the spectrum of the laser radiation exhibitsadditional frequencies, which are described by therelation presented above. This broadband radiationgenerates corresponding broadband harmonics. Notethat, in the presence of the phase self�modulation, theintensity of the laser radiation decreases due to thepulse elongation. Therefore, the influence of the phaseself�modulation should be less in the case of chirpedpulses, which was demonstrated in this work. More�over, the dispersion of group velocities in thick glassinduces a positive chirp on the laser radiation. If a neg�ative chirp is induced (due to the shift of the diffractiongratings in the compressor), the effects of the phaseself�modulation and dispersion of group velocitiescompensate each other. As a result, the characteristicsof the laser pulse become close to the characteristics ofthe initial pulse (i.e., free of the chirp, and phase andfrequency modulations). In this case, harmonics willalso have corresponding spectral characteristics.

C. Particular Features of HHG in Plasmas Containing Nanoparticles and Clusters

In this section, we consider some problems thatarise during HHG in plasma torches containing nano�particles. The majority of the results were obtainedhere with plasmas containing silver nanoparticles;though, for comparison, a number of investigationswere performed involving gold and strontium titanate

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Fig. 6. (a) Effect of phase self�modulation on HHG infullerene plasma: (top) phase�modulated femtosecondpulses and (bottom) unmodulated pulses; phase�modu�lated pump pulses shift wavelengths of harmonics towardthe long�wavelength range; the femtosecond pulse inten�sity in plasma region is Ifp = 1015 W cm–2. (b) Spectrallybroadened harmonics obtained upon ablation of (top) sootand (bottom) fullerenes; spectral broadening occurs due tophase self�modulation in laser plasma at the femtosecondpulse intensity in plasma region Ifp = 4 × 1015 W cm–2;with increasing laser pulse intensity, the halfwidth of the11th harmonic increased from ~0.8 to 3.7 nm. Figuresabove peaks indicate orders of harmonics.

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Fig. 7. Generation of higher harmonics in plasma uponlaser ablation of targets in the form of (1) porous spongecontaining silver nanoparticles mixed with liquid glue (1),mixture of silver nanoparticles with superglue, and (3)mixture of silver nanoparticles with polyvinyl alcohol. Fig�ures 17 and 9 indicate orders of corresponding harmonics.

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nanoparticles. These additional objects of study werechosen because of similarity between morphologicalcharacteristics and concentrations of silver and goldnanoparticles in targets and due to the differencebetween analogous parameters in the case of silver andstrontium titanate nanoparticles. Different nonlinearoptical responses in these two cases might determine anumber of quantitative and qualitative parameters thatfacilitate (or prevent) the achievement of high η in thecase of heterogeneous and homogeneous nonlinearmedia. We also present the results of investigation ofHHG in clusters of С60. This work continues the cycleof previous investigations [36] on harmonic genera�tion in fullerene plasmas. If the first investigations ofhigher�order nonlinearities in this interesting poly�atomic system demonstrated only capabilities forincreasing η, then we performed a cycle of systematicinvestigations involving various methods, radiationsources, and variable experimental conditions.

The definition of the notion of the cluster includesdimension characteristics of the polyatomic forma�tion. Conventionally, the cluster is defined as the sys�tem of particles whose size does not exceed 1 nm. Theclass of fullerenes can be referred to these formations.In particular, the diameter of fullerene С60 (which isalso referred to as polyatomic molecule) is 0.7 nm.Fullerenes can occur as solutions, gas phase, powder,etc. In the general case, fullerene powder can occur asan aggregated form that integrates a large number ofthese clusters. At the same time, dissolved fullerenesare likely to occur as single clusters. In our investiga�tions, we used two states of fullerenes subjected to laserablation, a dried solution of fullerenes and a mixture offullerene powder with a solidifier (in particular, glue).The notion of nanoparticles implies aggregated struc�tures with much larger sizes. Here, the generallyaccepted limits are the range 1–100 nm. Although thisdivision is quite arbitrary, we will follow this classifica�tion.

An important factor is the ability of these structures(clusters and nanoparticles) to survive under theaction of laser ablation. The latter process is the non�stationary heating of a small volume on the surface ofa target with a subsequent explosive propagation intovacuum. Here, common notions and processes of sta�tionary heating are inapplicable if for no other reasonthan the kinetic energy that particles acquire under theBoltzmann heating and evaporation enables atomsand ions to reach a velocity in the range 80–800 m s–1

(depending on the mass of particles). This velocity isdistinctly small for a large number of particles toappear in the zone of propagation of an ultrashort laserpulse (this is approximately 100–150 μm above thetarget surface) in the time interval equal to the delaybetween the heating prepulse and pulse to be con�verted (on the order of a few dozens of nanoseconds).Nevertheless, the experiment unambiguously showsthe occurrence of atoms and ions (at concentrations of

~1017 cm–3) in the zone of interaction with the laserpulse to be converted. This is evidenced by shadow�graphs of propagation of the plasma ablation front [53,54]. The velocities of propagation of the plasma torchfrom the target surface were measured to be 8 × 103–6 × 104 m s–1, which is in line with the possibility ofobserving harmonics generated in plasma. Numerousexperiments on the generation of harmonics in plasmatorch [39, 55, 56] are irrefutable proof of the rapidpropagation of the plasma torch.

The mechanism of the explosive propagation ofparticles has been studied in detail in a series of works,and we will not dwell on the peculiarities of this pro�cess; rather, we only note that a detailed analysis of thelaser ablation can be found in the monograph by Hora[57]. Here, we will pay attention to peculiarities andconditions of preservation of initial morphologicalcharacteristics of clusters and nanoparticles underlaser ablation up to the moment of interaction with anultrashort laser pulse. Clearly, to preserve the dimen�sion characteristics of studied formations, specialattention should be paid to conditions of the ablationitself. The action of a very intense light field of a rela�tively long heating pulse can cause considerablechanges in the structure of formed plasma compo�nents compared to the initial structure on the targetsurface. It is needless to say that the concentration offree electrons becomes excessive, which, as was notedabove, very negatively affects the HHG process. Theextreme excitation of the surface that contains thematerial under study can create a situation that aggre�gates of these particles and their fragments can occurin the interaction zone. This fully refers to fullerenemolecules, when large fragments consisting of a largenumber of carbon atoms (ions) can be formed in theplasma torch. In the case of nanoparticles (especially,metallic ones), the aggregation can prove to be a sig�nificant negative factor that reduces to zero advantagesof low�size nanoparticles compared to atomic (ionic)systems from the viewpoint of their use in HHG.

The formation of nanoparticles in plasma torchesdue to the laser ablation of solid targets (especially,with the use of ultrashort pulses) is a well�studied pro�cess, which was described in many publications. At thesame time, there are no reports in the literature onstudying morphological changes of nanoparticles thatwere initially on the surface upon laser ablation. Com�parison of sizes and structures of the initial materialand layers evaporated (due to the laser ablation nano�particles) on substrates adjacent to the target can pro�vide a rather valid analysis of the dynamics of struc�tural characteristics of evaporated media. It should benoted that this method makes it possible to find condi�tions of ablation of nanoparticles and clusters underwhich the highest η could be achieved. Below, we willpresent two examples of using this method for obtain�ing information on the state of evaporated polyatomicsystems in the course of their propagation through the



interaction zone with the ultrashort pulse. Note thatthe most complete information on this subject couldbe obtained using the method of time�of�flight spec�troscopy of spreading ablation objects. In this case,one could estimate both the weight characteristics ofparticles that arrive at a certain region of the plasmatorch in a certain time interval after the beginning ofablation and their charge composition. Taking intoaccount the high validity of this method compared tothe technique used in our experiments, we note thatthe use of time�of�flight spectroscopy under our con�ditions required cardinal modification of the experi�mental scheme.

For these comparative purposes, only the heatingprepulse was used, which was focused onto targetscontaining nanoparticles. The size of the laser beamon the target surface was 0.5–0.8 mm. The energydensity on the surface (Epp) was varied in the range0.5–3 J cm–2. Note that previous studies showed thatthis parameter plays a decisive role (compared to theintensity, i.e., the power density) in creation of optimallaser plasma [58]. A vacuum chamber was evacuated toa residual pressure of 8 × 10–6 mbar. Evaporated mate�rial was deposited on glass substrates and copper gridswith carbon films, which were arranged at a distance of30–50 mm from the surface subjected to laser abla�tion. Then, these deposited structures were analyzedwith an electron microscope.

The initial structure of nanoparticles was also stud�ied on the electron microscope. Figure 8 presents elec�tron�microscope images of silver, gold, and strontiumtitanate nanoparticles. As was noted in the Experimen�tal section, these nanoparticles had spherical and trian�gular shapes. Similar patterns were also obtained uponanalysis of materials deposited under conditions wherethe ablation was performed under the intensity ofthe heating prepulse of Ipp ≤ 7 × 109 W cm–2 (Epp ≤

1.4 J cm–2). The pattern was significantly changedwith increasing power density (and, correspondingly,energy density) on the target surface. At Ipp > 1.5 ×1010 W cm–2, disintegrated (and, in some cases, aggre�gated) nanoparticles (Fig. 8f) appeared on substratesurfaces. These investigations ultimately determinedthe high prepulse intensities on the surface of a mate�rial to be evaporated, at which morphological anddimensional characteristics of nanoparticles were pre�served.

The maintaining of initial spatial characteristics ofpolyatomic particles is especially important in the caseof fullerenes. Fullerenes are manifested as structurescapable of sustaining considerable light loads due tothe rapid dissipation of absorbed laser energy betweennumerous energy transitions in the С60 molecule [59,60]. Under these conditions, thorough analysis of thestructure of evaporated fullerenes made it possible todetermine (as in the preceding case) optimal excita�tion conditions of fullerene plasma. Here, the diffi�culty lies in the fact that these particles are very small

in size and that fullerenes (i.e., accumulations of car�bon atoms) interact poorly with the electron beam inthe electron microscope. Another problem is the largeaccumulation of fullerenes in powder. They occur asagglomerates of different sizes. For this reason, con�clusions on the static of evaporated material canmainly be derived from diffraction patterns (i.e., Fou�rier transforms) obtained using electron microscopy.

Figure 9a shows the electron�microscope photo�graph of the initial sample of fullerene powder. Thepattern of an extreme part of the aggregated formationis presented. It is seen that the used powders were inthe form of fullerene crystallites. The sizes of thesecrystallites were in the range 30–700 nm. This largespread in the size of particles was seemingly deter�mined by the preparation regime of these powders(which were purchased from Alfa Aesar). It is likelythat such aggregates of С60 clusters form structuresthat are similar to crystals or quasi�crystals. In Fig. 9a,interference fringes are seen in several areas, whichindicate that a regular crystallographic structure isformed. The characteristic spacings between fringes of0.6 and 0.8 nm approximately correspond to the dis�tance between lattice layers in a cubic structure [61].Crystal state of С60 aggregates was confirmed by meansof a Fourier transform (in other words, from the anal�ysis of the pattern of electron diffraction by aggregates;inset of Fig. 9a). Because various С60 aggregates werearranged randomly on the carbon grid, the electrondiffraction patterns observed in the electron micro�scope differ from each other. Similar patterns were alsoobserved upon the analysis of the deposited samples offullerenes at moderate prepulse intensities on the tar�get surface (Ipp ≤ 5 × 109 W cm–2).

As the intensity was increased to (1–2) ×1010 W cm–2, both interfringe spacings in the interfer�ence pattern, determined by the structure of the mate�rial under study, and the diffraction pattern werechanged (Fig. 9b). The interfringe spacing markedlydecreased (0.36 nm) and became close to the distancebetween planes in the graphite lattice (0.34 nm), char�acteristic of carbon (which forms С60 and which can bethe final product of dissociation of this molecule in astrong field). This pattern is characteristic of the so�called carbon black, which is an intermediate struc�ture between completely amorphous carbon andgraphite. The diffraction pattern shown in the insetalso qualitatively differs from the pattern presentedabove. This indicates the occurrence of an amorphousgraphite structure. These investigations agree satisfac�torily with the previous analysis of the morphology offullerenes and graphite aggregates [61]. These studiesalso determined the optimal prepulse intensities atwhich one can expect that С60 aggregates remainunchanged in laser plasma.

An important property of fullerenes is that they canwithstand the action of strong femtosecond lightfields. It was reported previously [62] that ionization

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(а) (b)

(c) (d)

(e) (f)

Fig. 8. Electron microscope photographs of nanoparticles: (a) dried solution of silver nanoparticles, (b) dried solution of goldnanoparticles, (c) strontium titanate nanoparticles, (d) chemically obtained triangular silver nanoparticles, (e) chemicallyobtained spherical silver nanoparticles, and (f) disintegrated silver nanoparticles obtained upon laser ablation at high prepulseenergy. Calibration lines on photographs correspond to 50 nm.

(а) (b)

Fig. 9. (a) Photograph of aggregate of fullerene powder prior to laser ablation; (b) photograph of deposited aggregate of fullerenepowder after laser ablation using a high�intensity prepulse (Ipp = 3 × 1010 W cm–2). White calibration lines on photographs cor�respond to 2 nm. Insets show corresponding diffraction patterns.



(and, partially, fragmentation) in moderate light fields(Ifp ~ 1014 W cm–2) predominantly occurs via a mul�tiphoton excitation of С60 surface plasmon resonances(20 eV). Experimentally observed survival of fullerenesin much stronger fields was attributed to the fact thatthe С60 molecule has a large number of internaldegrees of freedom, which leads to the dissipation oflight energy and inefficient ionization and fragmenta�tion [59, 60].

The spectrum of high�order harmonics generatedin plasma containing silver nanoparticles is shown inFig. 10. This figure also shows the spectrum of har�monics generated in plasma that was formed on thesurface of a solid silver target, which was measuredunder identical optimal experimental conditions, i.e.,conditions where η achieved a maximal value in thisspectral range. The intensity of harmonics in the lattercase was considerably lower compared to harmonicsgenerated by nanoparticles and, for the convenienceof comparison, this spectrum is shown with tenfoldmagnification. These results show that the intensity ofharmonics in the initial range of the plateau�like dis�tribution (from 9th to 17th) is very high, especiallycompared to the intensity of the harmonic generatedin the plasma of the solid target. Thus, intensities ofthe 9th harmonic in these two cases are related asapproximately 30 : 1. With increasing order of har�monics, this coefficient somewhat decreases. Anotherparticular feature of HHG with the use of nanoparti�cles is that the ultimate order of generated harmonicsis smaller compared to the solid target. The corre�sponding maximal orders of harmonics in these twocases were 69 and 29.

The HHG instability in plasmas of solid targets isabout 20%, and, in this case, the harmonic generationprocess can proceed arbitrarily long without shiftingthe target. A different situation is observed for targetsthat contain nanoparticles. Since the concentration ofnanoparticles is low (compared to the solid target) andbecause the morphological composition of the matrixthat contains them changes, the efficiency of theHHG process upon repeated action of the prepulse onone and the same spot decreases. Therefore, to retainthe stability of HHG, it is necessary to shift the targetafter several shots. As was noted above, the first obser�vations of this instability upon generation of harmon�ics in an analogous configuration gave impetus forsearching ways for improving this parameter. Methodsof preparation of targets with nanoparticles allowed usto considerably improve the stability of the HHG pro�cess. The use of the new procedure of target prepara�tion made it possible to generate intense harmonicswithout changing the target position during ~150 lasershots. Therefore, the stability of HHG using nanopar�ticles significantly increased compared to previouslyreported data [51].

The new procedure of target preparation made itpossible to homogeneously distribute nanoparticlesover a large depth of the matrix. This large thickness ofthe target layer with nanoparticles is a decisive factorfor increasing the stability of the harmonic generation.However, the intensity (more exactly, the energy den�sity) of the prepulse also play an important role in sta�bilization of the process. If this parameter is exces�sively increased, the intensity of harmonics initiallyincreases, but then the layer of nanoparticles is rapidlydepleted and, correspondingly, η sharply decreases.

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Fig. 10. Spectra of harmonics generated in plasma containing (solid curve) nanoparticles and (dotted curve) single atoms andions. Intensities of harmonics in plasma with single atoms and ions are magnified by a factor of ten for convenience of comparisonwith harmonics from nanoparticles. The intensity of the 9th harmonic from nanoparticles is ~30 times greater than the intensityof this harmonic generated in the plasma on the surface of solid silver target. Figures 17 and 9 indicate orders of correspondingharmonics.

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The same result was also obtained upon using of goldand strontium titanate nanoparticles.

A similar behavior was also observed for fullerenetargets. The methods of preparing thick fullerene�containing matrices that we developed allowed us togenerate stable harmonics during a much larger num�ber of pulses acting on the same target spot (Fig. 11).The main problems in studying HHG in fullereneplasmas were the search for ways for improving η andfor achieving higher orders of harmonics compared topreviously reported results (19th harmonic [36]). As inthe case of nanoparticles, experiments were performedin the predetermined limits of variations of the energydensity of the prepulse on the target surface, in whichthe morphology of evaporated particles in plasmaremained the same as that determined prior to laserablation.

In the previous work on HHG in fullerene plasma,the observed amplification of harmonics in the rangeof the С60 surface plasmon resonance (20 eV, λ =60 nm) was explained by the influence of the increasedlocal field and by the creation of more favorable con�ditions for generation and amplification for harmonicswithin the width of the plasmon resonance (10 eV).The amplification was observed for radiation harmon�ics of the titanium–sapphire laser whose orders werein the range 11–15. Another proposed explanation ofthe amplification, as in the case with nanoparticles, isbased on the fact that the electron recombination crosssection with a particle of a larger size is greater thanthat with an atomic ion. This can increase the proba�bility of radiation of harmonics in the case of poly�atomic particles.

The optimization of different experimental param�eters in our experiments with fullerene plasma allowedus to increase the ultimate harmonic order to 29 (λ =

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Fig. 11. Variations of the spectrum of harmonics generated in fullerene plasma after 1, 18, 26, 40, and 90 shots at one and the samespot on the surface containing С60. Orders of harmonics are shown on top.

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Fig. 12. Comparison of intensities of harmonics in(a) fullerene and (b) indium plasmas. It is seen that theintensity of the 13th harmonic in the indium plasma isapproximately equal to intensities of harmonics in thesame range that corresponds to the С60 surface plasmonresonance in the fullerene plasma. Figures above peaksindicate orders of harmonics.



27.6 nm). In this case, the intensity of harmonics con�siderably exceeded the analogous parameter for HHGin plasmas formed on solid targets. We compared theconversion efficiencies to harmonics of relatively loworders for indium and fullerene targets. It was reportedpreviously that η of the 13th harmonic in the indiumplasma (61.5 nm) is close to 10–4 [38]. This and otherharmonics generated in the indium plasma were com�pared to harmonics generated in the fullerene plasma(Fig. 12). It is worth noting that the efficiency of gen�erating the 13th harmonic in indium plasma is close tothe generation efficiencies of harmonics of closeorders in the fullerene plasma. The conversion effi�ciencies of harmonics generated in the carbon andsoot plasmas were also large, although smaller than inthe case of the fullerene plasma. In the latter case,maximal conversion efficiencies were observed in awide range of delays between pulses (20–60 ns).

A comparison of harmonics generated in the silverand fullerene plasmas showed the prevalence of theintensities of fullerene harmonics (approximately, by afactor of ten; Fig. 13a, 13c). We also depositedfullerenes (by laser ablation in the optimal regimewhen the deposited material retained its structure) onsilver substrates, then once again performed laser abla�tion of the deposited samples with subsequent genera�tion of harmonics (Fig. 13b). Naturally, the intensityof harmonics was lower in this case, as well as the sur�vival time of some areas of these targets (one to threeshots). These experiments indirectly confirmed thepresence of fullerenes on the deposited surface, sincethe spectral width of harmonics was similar to thewidth of harmonics generated from the initial targetcontaining a thick layer of fullerenes.

A number of other particular features of HHG inplasmas containing nanoparticles and clusters were

discussed above. The application of the two�colorpump and phase modulation considerably modifiedthe spectrum of harmonics, making it much richerfrom the viewpoint of both the occurrence of addi�tional even harmonics and increasing the width of thespectrum of generated harmonics. Proposed methodsof influence on the spectrum of harmonics generatedin plasmas make it possible to use them for solving var�ious basic and applied problems.

CONCLUSIONS

We presented different methods for improvingcharacteristics of higher harmonics generated in dif�ferent plasma torches. As a result of these investiga�tions, we obtained higher conversion efficiencies toharmonics in the initial part of the plateau�like distri�bution (to 10–4); increased ultimate orders of gener�ated harmonics in the case of fullerene plasma;increased frequency spectrum of harmonics due toboth phase self�modulation of the laser pulse and gen�eration of even harmonics upon addition of a weakwave at 400 nm to a strong pump wave at 800 nm; anda wider range of plasma formations with nanoparticleswhere HHG was highly efficient.

General conclusions following from our investiga�tions refer to the strategy of further improvement ofgeneration of higher�order harmonics in laser plas�mas. The application of torches that contain nanopar�ticles and clusters makes it possible to considerablychange the spectrum of harmonics. Plasmon reso�nance of these particles facilitates the increase in thehigher�order nonlinear response due to an increase inthe local field in the medium. Along with paying spe�cial attention to components of the plasma torch, it isnecessary to specially emphasize roles played by otherfactors (phase self�modulation, dispersion of groupvelocities, self�defocusing, etc.) that can affect theHHG process both positively and negatively. The two�color pump can also play a positive role. Combining allthese features can lead to the possibility of generatingattosecond pulses upon HHG in plasmas. Otherpromising directions can be the search for new mediawith resonant amplification of separate harmonics(taking into account the possibility of generating evenorders) and the further optimization of HHG inschemes with double excitation, extended plasma, andaction by a static electric field.

ACKNOWLEDGMENTS

R.A. Ganeev is grateful to the Raja Ramanna Cen�tre for Advanced Technology for the opportunity ofperforming these investigations.

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Fig. 13. Spectra of harmonics: (a) in silver plasma, (b) inplasma obtained on thin layer of fullerenes deposited onsilver substrate, and (c) plasma obtained on thick layer offullerenes mixed with polymethylmethacrylate. Figuresabove peaks indicate orders of harmonics.

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Translated by V. Rogovoi

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

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