Experimental Investigation of the Dynamics of Laser Induced Gas–Plasma Flows under Femtosecond...

ISSN 0030�400X, Optics and Spectroscopy, 2013, Vol. 115, No. 5, pp. 764–773. © Pleiades Publishing, Ltd., 2013.Original Russian Text © E.Yu. Loktionov, Yu.S. Protasov, Yu.Yu. Protasov, 2013, published in Optika i Spektroskopiya, 2013, Vol. 115, No. 5, pp. 856–866.

764

INTRODUCTION

It is well known that interaction of ultrashort laserpulses with metals has a number of specific featuresrelated, in the first place, to the fact that the time ofoptical action is shorter than the electron–phononrelaxation time [1]. This leads to substantial reductionof heat dissipation and, consequently, to reduction ofthe heat�affected zone [2], i.e., to increase in energydensity deposited per unit volume of the target mate�rial, which is particularly important in the case ofhigh�melting�point metals and metals with high heatconductivity, because it considerably increases theefficiency of micro�scale processing [3], generation ofgas–plasma flows [4], resolution of analytical methods[5], etc. Hence, investigation of thermophysical andgas�dynamic processes of femtosecond laser ablationis topical both from the point of view of fundamentalphysics and from the point of view of applications.

Experimental study of gas–plasma flows inducedby ultrashort laser pulses interacting with condensedmatter has a number of specific features related, first ofall, to low laser pulse energy and, consequently, smalllinear dimensions of the gas–plasma flow and inten�sity of emitted by it radiation [6]. When using diagnos�tic equipment and methods that have insufficient sen�sitivity or spatiotemporal resolution, quantitative pro�cessing of the results of measurements is limited orimpossible [7]. Most frequently, only qualitative datacan be obtained by using methods of photo registration[8, 9], or 0� or 1�dimensional with respect to space(and frequently, in fact, time integrated, i.e., acquiredwith an exposure time much longer than the time scaleof characteristic processes) spectroscopic results [10].

Interferometric methods providing the required spa�tio�temporal resolution are seldom used due to theircomplexity. Processing of experimental resultsobtained by means of such methods turns out to be dif�ficult and, for this reason, frequently incomplete [8,11].

As a rule, correct comparison of 2D or 3D com�puter simulation results is possible only if correspond�ing experimental results are available. Using combinedpulsed�laser interferometry of the surface of an irradi�ated target and the near�surface zone [12] in combina�tion with a computerized complex of automatedexperimental data processing [13] allowed a wide vari�ety of parameters of gas–plasma flows generatedunder interaction of ultrashort laser pulses with differ�ent materials to be quantitatively established for thefirst time.

Copper is one of the most important technologicalmaterials. However, its laser�assisted processing iscomplicated by its high heat conductivity, whichrequires using not only more powerful laser systemsbut also reduces spatial resolution due to large heat�affected zone. Under femtosecond laser ablation inthe low�energy regime, the heat�affected zone is com�parable with the ablation�crater depth, while, in thehigh�energy regimes, it turns out to be smaller than theablation�crater depth [14]. For such regimes of laseraction on copper targets, research has been concen�trated on studying the efficiency of generation ofnanoparticles [15], thin�film deposition, micrometer�scale form shaping [16, 17], generation of reactiongas–plasma flows and short�wavelength radiation,etc., which makes experimental investigation of ther�

LASERS AND THEIR APPLICATIONS

Experimental Investigation of the Dynamicsof Laser�Induced Gas–Plasma Flows

under Femtosecond Laser Ablation of Copper in VacuumE. Yu. Loktionov, Yu. S. Protasov, and Yu. Yu. ProtasovBauman Moscow State Technical University, Moscow, 105005 Russia

e�mail: [email protected] November 7, 2012

Abstract—Thermophysical and gas�dynamic characteristics of gas–plasma flows induced by ultrashort laserpulses interacting with a thin�film copper target in vacuum were studied experimentally. Using combinedlaser interferometry and complex processing of experimental data, we estimated the momentum couplingcoefficient and the efficiency of laser�energy conversion to kinetic energy, spatiotemporal distributions of thenumber density and velocities of particles, pressure, and temperature in the gas–plasma flow. We providecomparative analysis of presented data with those found in the literature, which were obtained by other meth�ods.

DOI: 10.1134/S0030400X13110155

OPTICS AND SPECTROSCOPY Vol. 115 No. 5 2013

EXPERIMENTAL INVESTIGATION OF THE DYNAMICS 765

mophysical and gas�dynamic processes initiated byultrashort pulses of radiation topical both from thepoint of view of fundamental physics and from thepoint of view of practical applications.

This work aims at studying thermophysical andgas�dynamic properties of processes in gas–plasmaflows generated as a result of interaction of ultrashortlaser pulses with copper targets in vacuum.

EXPERIMENTAL SETUP AND METHOD

The experimental setup based on a terawatt femto�second laser complex (λ ~ 266, 400, 800 nm; τ0.5 ~ 70,60, 45 fs; I0 up to 2.1 × 1013, 2.5 × 1014, 9.4 ×1015 W/cm2, respectively) and the methods of investi�gation and experimental data processing weredescribed in details in [12, 13, 18]; similar resultsobtained in the case of laser action on polymer mate�rials were presented in [19, 20]. Using the method pro�posed in [13, 18] of complex processing of the resultsof surface interferometry (the Michelson scheme) andinterferometry of the near�surface zone of the target(the Mach–Zehnder scheme) allowed obtaining dataon spatiotemporal distribution of thermophysical andgas�dynamic parameters of the near�surface gas–plasma flow (number density of electrons, static andtotal pressure, temperature) along with a number ofintegral parameters that characterize the efficiency oflaser�energy conversion to kinetic energy andmechanical momentum and estimating the averagedegree of ionization. We used both thin films (δ ~200–400 nm) deposited by magnetron sputtering onglass substrates and bulk mechanically polished (Ra ~0.2) samples of technically clean copper as targets.

When processing the combined interferometryresults, we used the following basic equations. Thenumber density of electrons is given by [21] expression

where ne is the number density of electrons, с is thespeed of light in vacuum, ε0 is the electric constant, me

is the electron mass, n0 is the refractive index of thebuffer gas, λ is the wavelength of the probe radiation, еis the electron charge, and Δn is the variation of therefractive index in the medium (all values are in SIunits). It is known [22] that variation of the refractiveindex of the gas–plasma flow is determined by thenumber densities of positively and negatively charged,as well as neutral, particles. When one kind of particlesis substantially dominant, contributions of other parti�cles is neglected. In our estimates, we assumed that thecontribution of electrons is dominant; however, thedegree of ionization can substantially vary as a func�tion of distance from the target surface, which caninfluence the accuracy of the analysis.

One of the characteristic parameters of the pulsedprocesses of generation of gas–plasma flows is their

2 2150 0

2 2 2

82.23 10 ,e

ec m n nn n

e

π ε Δ≈ Δ ≈ ×

λ λ

lifetime. The axial dimension of the laser�inducedgas–plasma flow was larger than the spot size of thefocused laser radiation (d ~ 40 µm) at time delay Δt ~10–8 s after optical irradiation of the target. The life�time of the gas–plasma flow is determined based onspecific underlying processes or on threshold value ofone of its characteristics. In our case, the number den�sity of electrons (ne ~ 1017 cm–3) that ensures variationof the refractive index measurable by interferometricmethods was such a characteristic. Hence, the lifetimeof the gas–plasma flow analyzed by methods of inter�ferometry was Δt ~ 10–7 s.

Temperature was estimated using the integral for�mula for the linear coefficient of absorption k [23] (inCGS units),

(1)

where is the frequency of absorbed photon, zi is theion charge, and T is the electron temperature (assum�ing local thermodynamic equilibrium: T ~ Те ~ Тi).

The average longitudinal velocity of particles is

where is the average velocity of a particleover time t, L is the distance from the target to the par�

ticle at time t, and is the number density of elec�trons in unit volume. The similarity of velocity distri�butions of electrons and ions in the gas–plasma flowunder femtosecond laser irradiation was experimen�tally demonstrated in [24]. The static and total pres�sure are defined as Pe = nekTe and = Pe +

mene /2, respectively.

The unit mechanical recoil momentum is given by

where E is the laser�pulse energy and F is the reactionforce.

The efficiency of laser ablation can be calculatedtaking into account different forms of energy to whichlaser energy is converted and energy stored in the tar�get material. The most frequently used parameter isthe thrust efficiency of laser ablation, which is the ratioof kinetic energy of directed motion of particles in agas–plasma flow to the laser�pulse energy;

The efficiency of kinetic�energy conversion to use�ful work of recoil�momentum generation is character�ized by the degree of flow monochromaticity,

1/2 2 60

30

4 2 exp ,3 3

ii e

e B Be

z ek n n

m k T k Tcm

⎛ ⎞ ⎛ ⎞ωπ= ⎜ ⎟⎜ ⎟ω ⎝ ⎠⎝ ⎠

�

�

0ω

lon lon ,k k ke e

k k

V n V n=∑ ∑

lon /iV L t=

ken

*eP

Ve2

1 ( ) ,mm

C F t dtE E

Δ ⟨ ⟩= ≈∫

v

2 2

.2 2 2

m spm gC ImE E

Δ ⟨ ⟩η = ≈ ≈

∑ vv

2 2 2 2 ,zm mμ = ≈ ⟨ ⟩ ⟨ ⟩∑ ∑v v v v

766


LOKTIONOV et al.

where vz is the projection of particle velocity on thegas–plasma flow axis.

EXPERIMENTAL RESULTSAND DISCUSSION

As was shown in [25], the depth of crater in therange of laser pulse durations τ ~ 0.07–10 ps increaseswith decreasing pulse duration at fixed radiationpower density. The depth of the crater was measured in[10, 15, 26–31] from the results of multiple pulsed�periodic laser actions, which is known to reduce theresult relative to that produced by the first few shots.The results presented in [27, 31] show that the largerthe number of pulses in the pulse train, the more pro�nounced the reduction (Fig. 1). Theoretical estimatesof the specific mass removal under laser ablation in thecase of single�pulse irradiation made in [31] were afactor of two higher than the experimental resultsobtained in the same work for pulse trains consisting ofN ~ 200–1000 pulses, which is explained by very pro�nounced crystalline structure of the metal in the inter�action zone during the first few laser shots, despiteintegral coefficient of absorption of copper increasing

in direct proportion to the number of pulses and inten�sity of irradiation due to formation of nanoscale,microscale, and macroscopic structures on the irradi�ated surface [41].

As can be seen from the microphotographs of thetargets presented in [41, 42], the surface area exposedto laser radiation substantially increases, which leadsto lower local energy density, which is particularlyimportant under low�energy excitation and canexplain the fact that the scatter of experimental dataunder such regimes of irradiation is the largest (Fig. 1).It was shown in [43] that an increase in the number ofincident laser pulses from 1 to 103 causes the ablationthreshold to decrease by a factor of about 5. Takinginto consideration that the value of threshold wasdetermined from the visible diameter of the crater andthere was no indication of perforation of the 250�nm�thick copper film used in the experiment even after103 laser pulses with an energy density exceeding theidentified threshold value by ten times (i.e., the rate ofmaterial removal did not exceed 0.25 nm/pulse), it ismore appropriate to speak of desorption rather thanablation in this case [44]. For high�energy regimes oflaser irradiation, it was shown in [45] that the rate ofablation critically depends on focal distance of theused lenses.

The scatter of temperature and mass average parti�cle velocity data experimentally obtained for similarconditions is small [46], whereas scatter of mass�removal data for similar, at first sight, regimes of inter�action spans over several orders of magnitude (Fig. 1).In the case of irradiation of thin�film targets, the filmthickness is also important: as was shown in [47] forsteel, an increase in film thickness from 50 to 200 µmresults in an increase in the depth of the crater createdby a single�pulse laser action nearly by a factor of 20.In general, specific mass removal of metals underultrashort laser pulse irradiation is higher than underirradiation with longer pulses with the same energydensity [48, 49].

Velocity of the gas–plasma flow front v ~ 22–25 km/s is in agreement with the data obtained in [50]for a target located in the focal plane of the lens andthe data obtained in [15, 51] for Cu+. According to ourestimates, the mass average particle velocity is sub�stantially lower (Fig. 2a), in agreement with the dataobtained in [10, 15] for copper atoms (taking into con�sideration that the data in these works correspond tothe velocity of the atomic�cloud front). A similar rela�tion between mass average velocity of the ablation flow(⟨v⟩ ~ 3.9 km/s) and most probable velocity deter�mined by means of time�of�flight probe (v ~ 20–25 km/s) was obtained for UV nanosecond ablation ofcopper in [55]. Taking into consideration the charac�ter of formation of interference patterns obtained fordifferent delays relative to excitation pulse and energydensity of the laser radiation, we believe that the veloc�ity distribution of particles is characterized by a large

10−4

10310110−1

10−3

10−5

10−6

m/E, g/J

W, J/cm2

Fig. 1. Specific mass removal of copper as a function ofenergy density of femtosecond laser pulses at λ = 800 nm:(�) τ ~ 45 fs, N = 1; (�) τ ~ 100 fs, N ~ 20, [15]; (�) τ ~200 fs, N ~ 200, [26]; (�) τ ~ 70 fs, N ~ 104, [27]; (�) τ ~100 fs, [10]; (�) τ ~ 120 fs, N ~ 20, [28]; (�) τ ~ 100 fs, N ~100, [29]; ( ) τ ~ 200 fs, N ~ 100, [30]; ( ) τ ~ 120 fs, N ~200–1000, [31]; ( ) τ ~ 150 fs, N ~ 104, [32]; ( ) λ ~1053 nm, τ ~ 10 ps, N ~ 5, [33]; ( ) τ ~ 150 fs, N ~ 102–104, [17]; ( ) τ ~ 110 fs, [34]; (×) τ ~ 200 fs, N = 1, [35];(+) τ ~ 170 fs, [36]; () τ ~ 200 fs, N = 1, [37]; ( ) τ ~120 fs, ~ 103, [38]; ( ) τ ~ 100 fs, N ~ 20–1000, air, [39];() τ ~ 100 fs, N ~ 20 [40]; ( ) τ ~ 120 fs, N ~ 1–10 [30](for works in which mass removal or crater volume are notgiven explicitly, we assumed m/E = (0.5)ρh/W, where h isthe crater depth).

�

�

�×

�×



value of variance, which was experimentally observed(by means of a time�of�flight probe) for copper ions in[51]; taking into account the sensitivity of interferom�eter used in that work nе ~ 1017 cm–3, a large portion ofthe gas–plasma flow could be left unregistered (indi�rectly, this assumption is confirmed by low degree ofionization α ~ 0.4, compared, e.g., to ionizationdegree α ~ 1.5 of titanium measured under similarregimes of laser irradiation, the lines of Cu+ beingdominant in emission spectra that we registered also in[15]).

The velocity distribution of particles (Fig. 2a) hastwo distinct peaks corresponding to atoms and theirsingly charged ions [56] with Maxwell velocity distri�bution corresponding to temperatures in the ~1� to3�eV range. There are data in the literature on the fly�apart velocity of particles, which indicate that particlescan be separated into two large groups, high� and low�velocity ones. The data on velocities in the first groupwere obtained by means of time�of�flight probes [57]or photo registration [7] and correspond to ions.

According to the authors’ estimates, the latter com�prise between several percent to several fractions of 1%of the gas–plasma flow. Nevertheless, specific impulsehas been estimated from the velocity of these fast butsparse particles. In a number of works, the specificimpulse for copper was estimated to be larger than3000 s and was related to the fastest highly chargedions ejected along the surface normal. However, it isnot quite correct to extrapolate these data on entireflow, because initially Isp = Σmv/Σmg, i.e., contribu�tions of vapors and droplet phase must be taken intoaccount.

The data for the low�velocity group were obtainedeither by dividing the recoil momentum on massremoval from the target surface (Isp = P/Δmg, whererecoil momentum P is the closest to reality experi�mental estimate, provided the time integral of thelong�acting small forces determined by sensitivity ofthe method, can be neglected), or, as in our case, fromanalysis of interferograms of the gas–plasma flow witha degree of ionization close or exceeding unity.

1020

101 103 104

I0λτ0.5, W s1/2 cm–1

3

6

9

⟨v⟩,

km

/s;

(a)

800

400

0

I lo

n,

s

0.7410

0.78

0.82

μ

(b)

20 30 40W, J/cm2

Fig. 2. Mass average velocity of particles (a) ((�) 45 fs, 800 m, vacuum; ( ) 130 fs, 768 nm, vacuum [38]; (�) 7 ns, 532 nm, vac�uum [52]; (�) 10 ns, 1064 nm, air [53]; ( ) 23 ns, 366 nm, vacuum [54]; (�) 100 fs, 800 nm, vacuum [10]) and the degree of mono�chromaticity of the gas–plasma flow (b).

�+

768


LOKTIONOV et al.

For copper, the dependence of mass average veloc�ity on energy density of laser radiation is fuzzy. In thecase of nanosecond irradiation, it was shown in [58]that, even in the case of nominally clean material (alu�minum), the dependence of mass average velocity onlaser�pulse energy can either have a peak or be directlyor inversely proportional, depending on the conditionof the surface (anodized, cleaned with a metal brush,or mirrorlike). It was shown in [52] that, under nano�second laser irradiation, the mass average velocity of

particles in the case of residual air pressure of 5 Pa sub�stantially depends on the position of the target relativeto focus of the lens: translation of the target by 8 mmbehind the focal plane (f = 75 mm) increases the spe�cific impulse by a factor of 3.

Based on qualitative analysis of holographic inter�ferograms of gas–plasma flows, it has been suggested[9] that the gas–plasma flow contains particles with alarge momentum and direction of velocity close tonormal to the target surface (which corresponds to a

350

300

300

250

200350 400 450

1.0002.0404.1628.49017.3235.3372.08147.1300.0

ne × 10−17, сm−3(a)

350

300

300

250

200350 400 450

0.8621

Ts, eV(b)

1.0251.2191.4501.7242.0502.4382.9003.448

Fig. 3. Spatial distribution of (a) number density of electrons and (b) temperature of the gas–plasma flow 12 ns after laser irradi�ation (λ ~ 800 nm, W ~ 12.8 J/cm2). The scale is in μm.



high degree of flow monochromaticity µ). The resultspresented in Fig. 2b quantitatively support thisassumption. In so doing, for copper, µ is directly pro�portional to the energy density of the radiation in thestudied range. The degree of flow monochromaticity isusually not listed as an integral coefficient in publica�tions on studying the angular distribution of particleswith respect to velocity [38, 59–61]; instead, exponentn in the approximation v = v0cosnθ of this distributionis used for estimating this characteristic (although, in

fact, the dependence like v(θ) = a + bcosnθ [62] or aneven more complex form should be used). Seldom,another integral parameter is provided, namely, thesemi�opening angle of the gas–plasma flow ϕ [63].Assuming that μ ≈ cos2ϕ, the results for femtosecondIR and nanosecond UV irradiation of copper targetsbecome comparable. Qualitative analysis of the resultsof these works shows that the gas–plasma flow createdunder ultrashort pulse irradiation is better collimated

104

Ptot, Pa

6.396 × 104

4.091 × 105

2.606 × 106

1.673 × 107

1.070 × 108

6.845 × 108

4.378 × 109

2.800 × 1010

1.000

P × 10−4, Pa

2.6977.27419.6252.92142.7384.910382800

350

300

300

250

200350 400 450

(a)

350

300

300

250

200350 400 450

(b)

Fig. 4. Spatial distribution of (a) static and (b) total pressure 12 ns after laser irradiation (λ ~ 800 nm, W ~ 12.8 J/cm2). The scaleis in μm.

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LOKTIONOV et al.

(reveals higher degree of monochromaticity) relativeto the case of nanosecond laser irradiation.

The characteristic spatial distribution of electronnumber density (ne ~ 1019–1020 cm–3) is illustrated inFig. 3a. Close values were obtained by methods ofinterferometry for femtosecond [64] and picosecond[65, 66] laser ablation in air. Figure 3b shows a charac�teristic spatial distribution of temperature in the gas–plasma flow. Under above�threshold excitation, thetemperature on axis of the gas–plasma flow 27 ns afterirradiation and in its proximal part 42 ns after irradia�tion is nearly independent of the energy density oflaser pulses. Substantial differences in the numberdensity of electrons and temperature appearing in thedistal part of the flow 42 ns after irradiation with dif�ferent intensities can be explained by the difference ofthe fly�apart velocities of particles (this difference isless noticeable at shorter delays of exposure). Therange of temperatures agrees with data obtained undersimilar experimental conditions by means of emissionspectroscopy in [10, 67]. Temperatures measuredunder interaction in vacuum are substantially higherthan those measured in air [24]. The obtained values ofmaximum electron temperature (Te, max ~ 3.5 eV)agree with theoretical estimates of [31]. In contrast todata obtained under irradiation in air [68], the tem�peratures of gas–plasma flow in vacuum are higherunder femtosecond irradiation relative to nanosecondirradiation [69].

The measurement of spatiotemporal distributionsof static and total pressure in the gas–plasma flow is aunique result of experimental investigation of laser–matter interaction. As a rule, pressure induced in thebulk of the target (p ~ 1011–1012 Pa) is measured in thiskind of experiments. The data presented in Fig. 4 agreewith theoretical estimates for the case of femtosecondpulsed�laser irradiation [72]. The values of static pres�sure reach ~107 Pa, which is comparable to the pres�sure in the front of the shock wave under nanosecondirradiation under normal atmospheric conditions [73]and in water [74] and exceeds the value of this param�eter under femtosecond laser irradiation of polymers[19].

It is well known that the recoil momentum is deter�mined by the velocity of the reactive jet and the massof material it contains. The mean squared particlevelocity is determined by their temperature, while theaxial projection of velocity (the mass average velocity)is determined by the degree of flow monochromaticityµ. Data on specific mechanical recoil momentumgenerated under femtosecond laser irradiation of cop�per targets in vacuum are rare. As can be seen fromFig. 5, in the case of interaction in vacuum, the valuesof Сm for copper are an order of magnitude higher thanin the case of interaction in air [50], although an oppo�site dependence is known for the case of nanosecondlaser irradiation [52], probably due to losses caused byself�focusing and filamentation in the air in front ofthe target surface that occur under ultrashort�pulselaser irradiation (the specific mass removal in vacuumis also higher than in air [30]). It was shown in [50]that, for equal laser�energy densities (W ~ 600 J/cm2),the specific mechanical recoil momentum for copper,aluminum, iron, and carbon increases by a factor of2.5–3 with increasing pulse duration for τ ~ 0.05–12 ps and by a factor of about 2 with increasing laser�pulse duration τ in the interval from about 0.05 to 1 ps.This is because, under short�pulse excitation, due tooptical effects, radiation is absorbed predominantly ina thin surface layer, while the efficiency of thermalprocesses is so low that it can be neglected. However,the opposite tendency was observed for copper in [79],where thermal processes were dominant at largeenergy densities, which could be seen from an increasein the radiation�absorption depth compared to itsoptical value.

In general, under nanosecond laser irradiation, therecoil momentum as a function of the buffer�gas pres�sure and target position in the focal plane of the lens isproportional to ρ1/3 [52]. Generally speaking, com�parison of data on specific recoil momentum is com�plicated, because a wide variety of techniques is usedin experiments [80]. In addition, position of the targetrelative to the focal plane of the lens [52] (the value ofCm changes by up to a factor of 3 when the target ismoved 0.13f behind the focal plane) and absolutevalue of pulse energy E [50] (the value of Cm increases

10−4

102

10−3

10−5

10−6

Cm, N s/J

100 104

I0λτ0.5, W s1/2 cm–1

Fig. 5. Momentum coupling coefficient under femtosec�ond laser ablation of copper in vacuum ((�) 45 fs, 800 nm;(�) 130 fs, 768 nm [38]; (�) 4 ns, 532 nm [58]; (�) 6 ns,1064 nm [58]; (�) 7 ns, 532 nm [52]; ( ) 100 fs, 800 nm[10]; (�) 100 ps, 532 nm [75]) and in air ((�) 7 ns, 532 nm[52]; (�) 10 ns, 1064 nm [76]; (�) brass, 70 ns, 1064 nm[77]; () 10 ns, 1064 nm [53]; (�) 50 fs, 800 nm [50]; ()brass, 20 ns, 1064 nm [78]).



by a factor of 1.4 with threefold increase in E) can crit�ically influence the result.

It should be noted that the relative position of peakvalue of Cm for copper does not correspond to thatobtained for polymers (W/Wa ~ exp(3/2), where Wa isthe spectral energy threshold of laser ablation) [81–83], because the dependence of mass average particlevelocity on specific energy density does not follow thedependence ⟨v⟩ ∝ ln(W/Wa)1/2. In contrast to poly�mers [20] and aluminum alloys, the specific mechani�cal recoil momentum generated under microsecondand nanosecond pulsed�laser irradiation [84] isdirectly proportional to complex action parameterI0λτ

0.5 in a wide range of the laser pulse widths (Fig. 5).This kind of dependence can be explained by the factthat less heat is dissipated and more energy is trans�ferred to ablated particles under more intense excita�tion. In addition, spectral energy threshold of laserablation Wa decreases as τ–1/2 down to the laser pulseduration τ equal to electron–phonon relaxation time[85, 86], i.e., peak values of parameters proportionalto W/Wa shift toward lower�energy excitation.

There is almost no data in the literature on the effi�ciency of laser�energy conversion to kinetic energy ofthe gas–plasma flow generated under ultrashort�pulseirradiation of metallic targets. It was established onlyin [4] that η varies between about 7.5 × 10–3 and 1 forgold in vacuum, and in [87] it was established that ηvaries between about 0.055 and 0.15 for titanium in airfor nanosecond irradiation in the near�IR spectralrange. For comparison, we used estimates obtained bycombining experimental data (Fig. 6). As can be seenfrom the plot, energy�conversion efficiency η, whichis a combination of all considered parameters of the

recoil�momentum generation efficiency, is character�ized by a pronounced maximum and a relatively nar�row optimal regime. In contrast to polymers [81],positions of peaks of parameters η and Сm nearly coin�cide with each other, which greatly simplifies the taskof optimization of the excitation regimes.

CONCLUSIONS

As a result of experimental studies, we determineda number of thermophysical and gas�dynamic charac�teristics of the gas–plasma flows generated upon inter�action of ultrashort laser pulses with a flat copper tar�get in vacuum. In contrast to most similar works, weobtained spatiotemporal distributions of number den�sity of electrons (ne ~ 1017–1019 cm–3), temperature(T ~ 0.6–3.5 eV), static (p ~ 106–107 Pa) and total (p ~107–1010 Pa) pressure. For the first time, we deter�mined optomechanical characteristics for the case ofirradiation of titanium with ultrashort laser pulses:momentum coupling coefficient (Cm ~ 2 × 10⎯4 N/W)and efficiency of laser�energy conversion to kineticenergy of the gas–plasma flow (η ~ 0.1–0.5). Quanti�tative data on the degree of monochromaticity of thegas–plasma flow (µ ~ 0.75–0.83) indicate high con�version efficiency of radiation energy to energy ofdirectional motion of particles. Estimates of the spa�tiotemporal distribution of static and total pressure inthe laser�induced gas–plasma flow were experimen�tally obtained for the first time.

ACKNOWLEDGMENTS

This work was supported by the Ministry of Educa�tion and Science of the Russian Federation (state con�tracts nos. 14.518.11.7009 and 16.120.11.328�MK)and the Russian Foundation for Basic Research (grant11�08�00848). We are grateful to A.V. Ovchinnikovand D.S. Sitnikov for their help in conducting theexperiment on the femtosecond laser complex of theJoint Institute for High Temperatures of the RussianAcademy of Sciences and R.R. Khaziev for his help insetting up automated processing of experimental data.

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103

0.9

0.6

0.3

0

η

102 104

I0λτ0.5, W s1/2 cm–1

Fig. 6. Efficiency of laser�energy conversion to kineticenergy of the gas–plasma flow under laser ablation of cop�per in vacuum ((�) 45 fs, 800 nm; (�) 130 fs, 768 nm [38];(�) 7 ns, 532 nm [52]; ( ) 100 fs, 800 nm [10]; (�) 100 ps,532 nm [75]) and in air ((�) 10 ns, 1064 nm [53]).

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