ISSN 00204412, Instruments and Experimental Techniques, 2010, Vol. 53, No. 4, pp. 596–600. © Pleiades Publishing, Ltd., 2010. Original Russian Text © E.Yu. Loktionov, A.V. Ovchinnikov, Yu.Yu. Protasov, D.S. Sitnikov, 2010, published in Pribory i Tekhnika Eksperimenta, 2010, No. 4, pp. 140–144.
LABORATORY TECHNIQUES
A Technique for Experimental Determination of the Condensed Media Laser Ablation Momentum Coupling Coefficient in Vacuum E. Yu. Loktionova, A. V. Ovchinnikovb, Yu. Yu. Protasova, and D. S. Sitnikovb a
Bauman Moscow State Technical University, Vtoraya Baumanskaya ul. 5, Moscow, 105005 Russia email:
[email protected] b Joint Institute of High Temperatures, Russian Academy of Sciences, ul. Izhorskaya 13, str. 2, Moscow 125412 Russia Received January 13, 2010
Abstract—An experimental technique for measuring the recoil momentum with an accuracy of ΔI < 10 ⎯11 N s during femtosecond laser ablation of condensed media has been developed. The technique is based on combined microinterferometry of the surface of an ablating target and nearsurface photoerosion gas plasma flows. The results of experimental determination of the momentum coupling coefficient and the effi ciency of the laserradiation energy conversion into the kinetic energy of a gasplasma flow under the action of short laser pulses on condensed media in atmospheric and vacuum conditions are presented. DOI: 10.1134/S0020441210040226
INTRODUCTION Under the action of femtosecond laser pulses on condensed media, the radiation absorption depth sub stantially decreases [1] (as compared to longer laser pulses), thus allowing an efficient action on con densed materials “transparent” at a given wavelength under ordinary conditions and removal of thinner lay ers of substances during laser ablation. Fine dosing of the mass flow down to Δm ~ 10–11–10–12 g under a femtosecond laser action makes it possible, at average expansion velocities of erosive vapors at a level of ve ~ 102–103 m/s, to impart a recoil momentum I ~ 10–11– 10–12 N s to the ablating target. Obtaining of such a small value of the minimum controlled momentum transferred as a result of a singleshot laser action is a necessary condition, which, unfortunately, cannot be achieved when using nanosecond or longer pulses of laser radiation [2]. The problem of increasing the sensitivity of meth ods for measuring the recoil momentum at the surface of a solid target resulting from a laser action is espe cially difficult to solve, when lowenergy radiation pulses are used. The sensitivity of ballistic pendulums and strain gauges for measuring the recoil momentum is approximately ΔI ~ 10–6–10–5 N s [3] (when inter ferometric methods are used to analyze oscillations of a ballistic pendulum, the resolution can be raised to ΔI ~ 3 × 10–9 N s [4]), and for torsion pendulums (tor sion balances), ~10–9–10–8 N s [5]. When a polymer condensed target is illuminated with femtosecond pulses of laser radiation with energies usually no higher than E ~ 10–4 J, the maximum value of the recoil momentum does not exceed I ~ 10–8 N s, and the resolution of the measurement technique thus must be no worse than ΔI ~ 10–9 N s.
To record the particle expansion velocity at a high accuracy (Δv ~ 10–102 m/s), there exist a number of widespread instrumental techniques (timeofflight probes [6], particle imaging velocimetry, etc. [7]). However, the methods used by the majority of researchers to determine the mass flow, such as pro filometry and scanning electron microscopy of sur faces, direct weighing of a target, or recording of the mass of a photoerosion vapor condensate [8], do not allow, except for the latter, in situ measurements, and their accuracy does not exceed Δm ~ 10–6 g [8]. A substantial feature of measuring the recoil momentum using ballistic and torsion pendulums or piezoelectric force sensors is, first, that they yield a spatially integral result and have a low time resolution Δτ > 10–5 s (8–9 and 3–5 orders of magnitude larger than the duration of ultrashort laser pulses and the characteristic times of gasdynamic processes, respec tively). Second, when recoil momenta I < 10–8 N s are measured, as a rule, a signal is recorded, which results from summing the results of several successive laser actions (n ~ 102–103 or higher [9]); i.e., the average value of the recoil momentum is measured, and the spread of values of single momenta remains indefinite. Third, the total momentum imparted to the target is determined by several processes—expansion of ion ized target vapors, formation and propagation of a shock wave in a buffer gas [6], slow expansion of prod ucts of a phase explosion in the volume of a solidstate target [7]—and, to analyze the optomechanical effi ciency of laser ablation, it is necessary to know the dynamics of the contribution of each of these compo nents to the total momentum. An important parameter characterizing the effi ciency of the laserradiation energy conversion into
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the kinetic energy of a photoerosion flow is the momentum coupling coefficient Cm, which is deter mined as the ratio of the total momentum of the gas plasma flow (time integral of the reactive force F, in the first approximation, a recoil momentum can be defined as the product of the mass flow Δm by the massaveraged particle velocity 〈v〉) to the laserpulse energy E or the pressure on the target surface to the laserradiation power density [10]: (1)
In essence, this criterion relates the efficiency of mass removal from the surface of an ablating target to the efficiency of utilizing the energy of laser radiation in generating a gasplasma flow. In contrast to the energy efficiency of laser ablation η = Δm〈v〉2/E and the specific momentum Isp = 〈v〉/g, which does not eventually depend on the mass flow rate, the processes on the target surface and in the nearsurface plasma plume equally contribute to the value of the parameter Сm. For most materials, the momentum coupling coef ficient at optimal parameters and regimes of laser action is no larger than Cm ~ 5 × 10–4 (N s)/J (for spe cial energetic (exothermal) polymer materials, this value can be higher by one order of magnitude [11]). The spectralenergy ablation threshold Wa and the efficient radiationabsorption coefficient αeff are also important parameters for characterizing and scaling the processes of laser ablation in condensed media. These parameters are determined in accordance with the Bouguer–Lambert–Beer law:
⎛ ⎞ (2) h = 1 ln ⎜ W ⎟, α eff ⎝Wa ⎠ where h is the maximum depth of an ablation crater resulting from a singleshot laser action and W is the energy density of the acting laser radiation. The objective of this study is to develop a technique for determining the momentum coupling coefficient during the formation of femtosecond laser ablation under both atmospheric and vacuum conditions. To implement it in an experimental diagnostic module based on a terawatt femtosecond laser system, we have used a technique of combined microinterferometry of the surface of an ablating target (Michelson scheme) and photoerosion gasplasma flows (Mach–Zehnder scheme). EXPERIMENTAL TECHNIQUE The experimental setup based on a Ti:Al2O3 tera watt femtosecond laser system (Coherent) makes it possible to produce power densities I0, 800 = 9.4 × 1014 W/cm2, I0, 400 = 2.5 × 1014 W/cm2, and I0, 266 = 2.1 × 1013 W/cm2 at wavelengths of ~800, ~400, and ~266 nm for laser radiation focused into a spot of radius r0 ~ 20 µm on the target surface at a pulse dura INSTRUMENTS AND EXPERIMENTAL TECHNIQUES
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Fig. 1. Interferogram of the surface of a (C2F4)n target (a) after laser irradiation (λ ~ 266 nm, W ~ 0.5 J/cm2) and (b) the crater shape reconstructed from it.
tion τ0.5 ~ 45–70 fs. Part of the radiation is diverted to diagnostic channels for microinterferometry of the surface of a target and photoerosion flows; the delays of the probing radiation relative to the heating radia tion are controlled in the range τ ~ 0–75 ns with a step Δτ ~ 100 fs. The optical systems of the interferometers are built inside a cylindrical vacuum chamber (400 mm in diameter and 300 mm in height) pumped down by an oilfree vacuum pump to a pressure p ~ 10 ⎯2 Pa (in experiments performed under atmospheric conditions, the chamber was filled with air). To implement interference microscopy, the surface of a solid target under study must be maximally smooth and have a high specular reflection coefficient at the probingradiation wavelength. The mass flow of the target substance was determined from the data of interference microscopy of the irradiated surface (Fig. 1), and the massaveraged particle velocities Vol. 53
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Fig. 2. Stages of processing the interferograms of a flow (a) initial flow interferogram, (b) distribution of the wavefront phase shift, (c) distribution of the refractive index, and (d) electronconcentration distribution.
were found from the data of microinterferometry of the gasplasma flow taking into account the electron concentration distribution in it. The experimental diagnostic module is described in more detail in [12]. Microinterferograms of gasplasma flows are pro cessed in several stages: (i) using the Phase Measurement program (VNIIOFI), quantitative data on the wavefront phase shift and the transmission coefficient of a near surface plasma plume are obtained; (ii) the refractiveindex distribution is calculated using the Abel equation from the phase shift within the approximation of ray optics under the condition of low refraction for axially symmetric inhomogeneities; (iii) the technique described in [13] and the data on the refractive index are used to calculate the spa tiotemporal distribution of the electron concentration (Fig. 2) on the basis of the Drude model: 15 8π2c 2ε0men0 (3) Δn ≈ 2.23 × 10 Δn2 , 2 2 λe λ where ne is the electron concentration, с is the velocity of light in vacuum, ε0 is the electric constant, me is the electron mass, n0 is the refractive index of the buffer gas, λ is the wavelength of probing radiation, е is the electron charge, and Δn is the change in the refractive index in the medium (all dimensions are in SI). To measure the recoil momentum, the mass and velocity distributions of particles must be known. In a
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certain approximation, it is acceptable to determine the total momentum of the gasplasma flow as the product of the summary mass of particles involved in the flow by their massaveraged velocity. The latter can be determined in a certain approximation from the data of interferometry as (4) v = ∑ nev /∑ ne, where ne is the electron concentration within an ele mentary volume (determined by the spatial resolution of the system for microinterferometry of gasplasma flows), and v is the axial velocity component defined as the ratio of the distance of the elementary volume considered from the target surface to the delay time of the probing pulse relative to the heating pulse (Fig. 3). The adopted assumption of the correspondence of the spatiotemporal distribution of the electron concentra tion to the distribution of ions and neutral particles in a gasplasma flow introduces an error into the deter mined value of the massaveraged velocity of the pho toerosion products, but, according to the femtosecond optical discharge spectroscopy with an ablating wall obtained in [14, 15], this error is within 5% of the recorded value. The accuracy of the interferometric method for recording the mass flow from the surface of an ablating target is limited from below by the interferogram pro cessing error, which is proportional to the probing radiation wavelength (the errors in determining the crater depth and radius are Δh ~ λ/200 and Δr ~ 2 µm,
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respectively; thus, Δm ~ 2 × 10–8πρλr, where ρ is the target material density and r is the crater radius). The accuracy is limited from above by an ambiguity in determining the phase shift in the case of deep craters with sharp edges, when an additional error in deter mining the crater depth Δh ~ nλ, where n is an integer, may appear. Thus, to reduce the error in determining the crater depth, it is necessary to reduce the probing radiation wavelength, and to extend the range of recorded values, the wavelength should be increased. The application of interference microscopy for deter mining the mass flow from the surface of an ablating target is substantially limited by the state of the target surface both before and after the laser action. The advantages of the interferometric scheme used to detect the recoil momentum at the surface of an ablating target over pendulum systems and force sen sors in experiments under vacuum conditions are as follows: the possibility of rapidly displacing the laser beam spot to a new area of a target without decapsulat ing the vacuum chamber; the possibility of performing measurements in a frequency mode (~10 Hz) without the necessity of waiting for damping of vibrations of the sensitive element; and the absence of problems associated with both the vibration insulation of sensi tive elements and taking into account of unavoidable vibrations from vacuumproducing pumps. EXPERIMENTAL RESULTS The values of the momentum coupling coefficient calculated from (1) on the basis of the data on the aver age particleexpansion velocity and the specific mass flow for condensed targets in vacuum are in good agreement with the data obtained both for other mate rials exposed to ultrashort laser pulses [6] and as a INSTRUMENTS AND EXPERIMENTAL TECHNIQUES
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Fig. 4. (a) Efficiency of the laserradiation energy conver sion into the gasplasma flow energy and (b) momentum coupling coefficient at the surface of a (C2F4)n target as functions of the spectral and energy parameters of laser action under atmospheric conditions.
result of extrapolating the data for analogous materials obtained under irradiation with longer laser pulses [3, 16]. The values of the parameter Cm are maximized at W/Wа (or I0/Iа) ~ e3/2 (this corresponds to the charac ter of the dependences m/E ∝ ln(W/Wа)/W according to (22), and v ∝ (ln(W/Wа))1/2). The results obtained indicate that the use of ultrashort pulses ensures more efficient conversion of the laserradiation energy into the total momentum of a gasplasma flow. Figure 4 shows the dependences of the momentum coupling coefficient and the laserablation efficiency for a (C2F4)n target. Analysis of these curves shows that the parameter Cm increases proportionally to the energy of a coherentradiation photon; an analogous trend is also observed for the efficiency reaching a maximum at W/Wа (I0/Iа) ~ e2. CONCLUSIONS The technique of combined pulsed laser microint erferometry developed makes it possible to record the mass flow of an ablating target with an accuracy of Δm < 10–11 g and the massaveraged particle velocity with an accuracy of Δ〈v〉 ~ 100 m/s. It offers new pos sibilities for measuring the recoil momentum with an accuracy (with allowance for instrumental and meth odological errors) no worse than ΔI ~ 10–11 N s. The high spatial and time resolutions, as well the possibility of evaluating the contributions of different optome chanical processes in the nearsurface zone of the irra diated target to the formation of the total recoil momentum, are substantial features of the laser inter ferometric method for measuring the optomechanical characteristics of ablation flows under irradiation with ultrashort laser pulses. Vol. 53
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