radiative models of laser-induced plasma and pump-probe diagnostics relevant to laser-induced...

Spectrochimica Acta Part B 65 (2010) 345–359

Contents lists available at ScienceDirect

Spectrochimica Acta Part B

j ourna l homepage: www.e lsev ie r.com/ locate /sab

Review

Radiative models of laser-induced plasma and pump-probe diagnostics relevant tolaser-induced breakdown spectroscopy

Igor B. Gornushkin a,⁎, Ulrich Panne a,b

a BAM Federal Institute for Materials Research and Testing, Richard-Willstaetter Str. 11, D-12489 Berlin, Germanyb Humboldt Universitaet zu Berlin, Chemistry Department, Brook-Taylor-Strasse 2, D-12489 Berlin, Germany

⁎ Corresponding author.E-mail address: [email protected] (I.B. Gornu

0584-8547/$ – see front matter © 2010 Elsevier B.V. Aldoi:10.1016/j.sab.2010.03.021

a b s t r a c t
a r t i c l e i n f o
Article history:Received 3 December 2009Accepted 25 March 2010Available online 9 April 2010

Keywords:Laser ablationModelingPlasma diagnosticsLaser-induced breakdown spectroscopy

The paper describes past and present efforts in modeling of laser-induced plasma and overviews plasmadiagnostics carried out by pump-probe techniques. Besides general information on existing plasma models,the emphasis is given to models relevant to spectrochemical analysis, i.e. models of radiating plasma. Specialattention is paid to collisional-radiative (CR) and collisional-dominated (CD) plasma models where radiativeprocesses play an important role. Also, calibration-free (CF) models are considered which may endow withthe possibility for standardless spectroscopic analysis. In the diagnostic part, only methods based on the useof additional diagnostic tools (auxiliary lasers, optics, and probes) are described omitting those based onplasma own radiation. A short review is provided on image-based diagnostics (shadowgraphy, schlieren, andinterferometry), absorption and fluorescence, Langmuir probe, and less frequently used cavity ringdown andThomson scattering methods.

shkin).

l rights reserved.

© 2010 Elsevier B.V. All rights reserved.

Contents

1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3452. Phenomenology of laser-induced plasmas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3463. Laser ablation models: general overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3464. Models of radiating laser-induced plasma . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 347

4.1. Collisional-radiative (CR) models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3484.2. Collisional-dominated (CD) models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 349

5. Calibration-free models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3505.1. Calibration-free LIBS based on the Boltzmann plot method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3505.2. Other calibration-free models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3515.3. Comparison between CF methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 352

6. Plasma visualization: shadowgraphy, schlieren, and interferometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3526.1. Shadowgraphy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3536.2. Schlieren . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3546.3. Interferometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 354

7. Laser-induced fluorescence (LIF) and absorption spectroscopy (AS) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3547.1. Laser-induced fluorescence (LIF) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3547.2. Absorption . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 355

8. Other diagnostics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3568.1. Cavity ringdown spectroscopy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3568.2. Langmuir probe . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3568.3. Thomson scattering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 356

9. Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 356Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 357References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 357

346

mailto:[email protected]

http://dx.doi.org/10.1016/j.sab.2010.03.021

http://www.sciencedirect.com/science/journal/05848547

346 I.B. Gornushkin, U. Panne / Spectrochimica Acta Part B 65 (2010) 345–359

1. Introduction

Numerous papers including books [1–3] and voluminous journalreviews [4–7] have been published in recent years on laser-inducedbreakdown spectroscopy (LIBS). This reflects a tremendous affection ofthe analytical community to this seemingly simple technique. Highexpectations continue to be supported by new technological break-throughs and steady improvements in instrumentation: better lasers,better spectrometers, and better detectors. However, the analyticalperformance of LIBS does not improve that rapidly as grows the numberof publications; the sensitivity remainsmodest—partspermillion at thebest, precision mediocre (5–10% RSD), and matrix dependence strong.Needless to say that LIBS has not yet arrived in the community as ananalytical method.

Further progress can only be expected from deeper understandingof a variety of plasma processes whose relative contributions to thekey plasma parameters (temperature, density, velocity, and theirgradients) are not precisely known and should be determined in orderto improve the analytical performance of LIBS. Understanding canonly be gained through meticulous theoretical modeling and scru-pulous plasma diagnostics, the latter providing the valuable experi-mental feedback for theory.

The goal of this review is to provide the reader with generalinformation on past and present efforts in laser-induced plasmamodeling as well as to overview some plasma diagnostics carried outby pump-probe techniques. It is our intention to collect in the samereview theoretical models and diagnostics to make the paperattractive for both theoreticians and practitioners. We regret thatwe do not draw direct parallels between particular models andparticular experiments; this would significantly dilute otherwiseconcentrated material. We, therefore, leave this work to the reader.

On the account of existingplasmamodels, the emphasiswill begivento models relevant to spectrochemical analysis, i.e. models of radiatingplasma. Special attention will be paid to so-called calibration-free (CF)modelswhichhave the potential for achieving standardless analysis, theholy grail of analytical spectroscopy. In the diagnostic part, onlymethods based on the use of additional diagnostic tools (auxiliarylasers, optics, and probes) will be considered omitting those based onplasma own radiation. A comprehensive review of the latter methodscan be found in Ref. [7].

2. Phenomenology of laser-induced plasmas

We start from a short phenomenological description of laser-induced breakdown to make evident the complexity of the phenom-enon and challenges for modeling and diagnostics.

During laser-induced desorption or ablation the energy of excitedfree electrons, vibronic and electronic states is converted into heatwhich allows removing atoms, ions, molecules, and clusters from thesurface. Typically, laser desorption does not involve a mesoscopicmodification of the surface and the yield of species is a linear functionof the number of locally excited vibrational and electronic states [8]. Incontrast, laser ablation is accompanied by the formation of an ionizedexpanding plasma. For solid materials, the observed modification ofthe surface is beyond a monolayer and non-linearly related to thenumber of excited states. Also, a certain threshold energy is requiredto initiate laser ablation.

The initiation and evolution of a laser-induced plasma (LIP) stronglydepend on the analyte–matrix combination, environment, laserwavelength, and rate of energy deposition. Material bulk properties(e.g. melting and boiling temperatures, thermal and electric conductiv-ities, absorptivity, reflectivity, elasticity, compressibility, etc.) play animportant role as they determine themechanisms of energy depositionand dissipation. Thesemechanisms are different in differentmatrices. Inaddition, the plasma dynamics itself additionally influences the ablation

(crater morphology, amount of ablated mass etc.) in contrast to otherbeam techniques utilizing electrons or ions.

In gases, the breakdown starts from a production of initial electronsvia cascade ionization, multiphoton ionization or via the tunnel effect athigh irradiances (N1012 W cm−2). Electrons gain energy via inversebremsstrahlung [9] and initiate the ionization cascade which results inan exponential growth of the number of electrons. Multiphotonionization is only important for short laserwavelengthsas the ionizationenergies of most gases are high (N10 eV).

In liquids, the processes leading to breakdown are less theoreti-cally understood. Liquids are often treated as amorphous solids witheffective conduction and valence bands. The formation of seed elec-trons is described by the cascade and multiphoton ionization, thesame as in gases and solids. The plasma initiation follows a “moving-breakdown” model assuming that multiple plasmas are ignitedindependently along the optical axis, typically within the Rayleighdistance inside the focal volume where the critical electron density isreached [10,11]. With increasing laser pulse energy during the pulse,the breakdown moves in the direction of the laser resulting in arapidly expanding plume. Once created, the plasma is heated farbeyond the vaporization point of a surrounding liquid. This causes theexplosive nucleation and cavitation. A dense vapor-cavity zone isformed in the subsurface region followed by the violent vapor-plumeejection and formation of the shock wave. The upward vapor-plumeejection imposes the recoil momentum on the liquid surface causingits deformation. In this stage, the bulk-liquid ejection occurs mainlydue to collapsing of cavitation bubbles [12].

In metals, the nearly free conduction-band electrons absorb laserphotons via inverse bremsstrahlung and heat the electron gas.Electron–lattice coupling (the degree to which ion motion followselectron motion in a solid) is essentially zero; the electrons providedielectric screening to ions of the lattice and prevent them from directinteraction with light. The excitation induced by the laser dissipatesvia collisions between excited electrons and the lattice, i.e. thermalconductivity.

In semiconductors and insulators, both electrons and ions contrib-ute to the excitation because there are no free conduction-bandelectrons in insulators and only a few in semiconductors. Laserradiation is absorbed via multiphoton band-to-band transitionsleading to a creation of electron–hole pairs rather than direct electronheating. Strong electron–lattice coupling plays a definitive role inenergy dissipation; the relaxation mechanisms include the electron–hole recombination and the response of the lattice to the creation andmotion of free charges and electron–hole pairs [8].

Plasma formation and expansion is resulted from absorption of laserlight by a material. The hot matter in the form of electrons, ions,atoms, and clusters expands at a supersonic velocity and continuesabsorbing the laser energy. At some point during the laser action theplasma becomes opaque and shields the material from laser light. Forexpansion into an ambient gas, the plasma slows down via collisionswith ambient species and can even reverse the direction of expansion.Internal and external shocks form as a result of high pressure in theplume and propagate inside and outside the plasma. As the plasmaloses its energy due to expansion and radiation, it recombines, decaysand condenses into particles and clusters.

The exact physical portrait of laser-induced breakdown stronglydepends on the material, laser used, and surrounding medium.Femtosecond ablation, for example, is markedly different from nanosec-ond ablation (especially in a part of laser–matter interaction); similarly,the expansion in atmosphere is different from the expansion in vacuum.Different models describe different interaction–expansion regimes.

3. Laser ablation models: general overview

A recent review on plasma models and methods of numericalsimulations [13] provides a clear picture of the current state-of-the-

347I.B. Gornushkin, U. Panne / Spectrochimica Acta Part B 65 (2010) 345–359

art in the field. The majority of modern plasma models is based on the19th century achievements by Fourier, Navier, Stokes, Maxwell, andBoltzmann with relatively modest addition from later physics. Thegreatest challenge for constructing a self-consistent plasma model isthe necessity to deal with many physical concepts and theoriessimultaneously.

Many laser-induced plasma models were developed in view ofspecific applications: pulsed laser deposition (PLD), laser ablation-inductively coupled plasma-mass spectrometry (LA-ICP-MS), laser-induced breakdown spectroscopy (LIBS), nano-fabrication, lasermachining and welding etc. Although describing the same phenom-enon, the models differ in many ways with emphasis given to aprocess or processes that are most relevant to a consideredapplication. For example, models for PLD are focused on laser–matterinteraction and plume expansion; models for LA-ICP-MS usuallyinclude cluster and particle formation; models for LIBS always containthe radiation theory.

The majority of models are continuous models based on fluiddynamics supplemented by radiation transfer or chemical kinetics[14,15]. Many of the models include laser–matter interaction whichoccurs via either thermal or non-thermal energy transfer. Dependingon the duration of a laser pulse, either heat conduction [16,17] or two-temperature (electron–phonon) [18,19] approaches are employed.Continuous models break down or experience difficulties when theconcept of continuity becomes questionable, e.g. in highly dilutedplasmas or at large gradients. For example, artificial viscosity isintroduced in atmospheric models to cure the rupture at a shockinterface.

The other group of models is called discrete models and based onMonte Carlo (MC) or molecular dynamics (MD) simulations. In MCmethods [20,21] many particles, each of which is tracked separately,are allowed to interact. This occurs at random times but with afrequency matching the real one. Bulk properties of the system arethen reconstructed from the raw population data. As noted in [13], thistechnique rather mimics the nature than explains it. In MD models[22,23], particle behavior is studied on the molecular scale that allowshandling matter in the condensed state. This is particularly importantfor the study of laser–matter interaction and the mechanisms ofmaterial removal. Both techniques are computationally expensive andcan provide data only on a short time scale (∼picoseconds) and for alimited number of particles (∼b108).

Yet another group of models are hybrid models [24,25] where theoutput of one model is used as an input for the other. For example, in[25] the expansion of a laser plume was modeled by gas dynamicswhich was followed by the direct MC simulation. This modelexplained the formation of a shock wave and described the reactiveinteraction between the plume and gas species.

In the following sections, we overview only a specific group ofmodels, those which are based on the concepts of collision-dominating and collisional-radiative plasmas and bear relevance tolaser-induced breakdown spectroscopy, or LIBS. Also, the discussionwill be limited to the ns time scale as mainly ns-laser pulses areutilized in LIBS. We fully acknowledge that our review is far frombeing complete if such a task is at all possible. We regret omittingmany important publications and recognize that other selection ofpapers might have been equally valid.

4. Models of radiating laser-induced plasma

Every plasma model assumes a certain type of equilibrium. Typesof equilibriums depend on the balance between micro processes:

X� ↔ X + hν Spontaneous decay=excitation ð1aÞ

X + e−↔ X� + e− Collisional excitation=de� excitation ð1bÞ

Xα+ e−↔Xα + 1+ e− + e− Impact ionization=3� body recombination

ð1cÞ

Xα + hν↔Xα + 1 + e− Photoionization=Radiative recombination:

ð1dÞ

In complete thermodynamic equilibrium (TE), every single interac-tion process is balanced by its reverse process. The TE is rarelyachieved in laboratory plasmas due to misbalance of radiativeprocesses: the plasmas are optically thin at most frequencies.

A state which frequently occurs in laboratory plasmas is the stateof local thermodynamic equilibrium (LTE) that is the equilibriumwith adiluted radiation field. This state is realized at high electron densitiesat which collision processes — induced transitions and reactions aremore frequent than radiative ones. In LTE, the detailed balancing ofthe processes (1b) and (1c) holds while the balancing of the processes(1a) and (1d) is destroyed since the number of emission processesexceeds the number of photoabsorption processes on account of thediluted radiation field. The population of atoms and ions in the variousbound states is controlled entirely by electron collisions and alldistribution functions with the exception of that of the radiationenergy are given by Boltzmann distributions. Such plasma is referredto as a collisional-dominating plasma (CD) and corresponding modelsare called CD models. The McWhirter criterion [26] is commonly usedas a quick test for a CD plasma and LTE,

ne ≥1012T1 = 2e ðEk−EiÞ3 cm−3

; ð2Þ

where Te is the electron density in K and Ek−Ei is the energy gap in eVbetween atomic levels. This criterion, however, may not be applicableas a proof of LTE in transient laser-induced plasmas. Cristoforetti et al.[27] have demonstrated that even though the condition (2) issatisfied, the plasma can still be in a non-equilibrium state due to itshigh degree of ionization after the breakdown that may cause themisbalance between the ionization and recombination processes(Eq. (1c) in the above diagram), the latter prevailing. A fast expansionand fast diffusion with rates close to a plasma relaxation rate mayavert laser-induced plasmas from reaching the LTE.

In contrast to CD plasmas and LTE, the radiation field plays animportant role in collisional-radiative plasmas (CR) because it affectsthe population densities of bound states. CR plasmas are the denseplasmas in which electron densities are often sufficiently high tosatisfy the condition (2). The corresponding models are called CRmodels; here atomic processes and radiation transport are consideredtogether. None of the micro processes (1a)–(1d) is neglected and,generally speaking, none is balanced. CR plasmas are, therefore, non-equilibrium plasmas. To build a successful model, atomic cross sec-tions and transition probabilities relevant to the processes (1a)–(1d)must be known. For atoms with many levels this problem is toocomplicated for general solution. This is a great difficulty that does notoccur in the treatment of plasmas in LTE.

Some simplifications are possible to solve a CR plasma. One ofthem is the concept of partial thermodynamic equilibrium which relieson the fact that only low atomic levels are strongly affected byradiation trapping, while higher levels are still in LTE, i.e. controlled bycollisions. This steams from the different dependence of rates ofspontaneous emission Aki (process (1a)) and collisional population/depopulation Xki (process (1b)) upon the energy gap ΔEki=Ek−Ei[27]:

Aki∝ΔE2ki and Xki∝ΔE−1ki : ð3Þ

For the sake of generality, we also mention a plasma state withcorona equilibrium (CE) which is realized at very low densities. Here,the spontaneous emission (process (1a)) prevails over collisional de-excitation (process (1b)) while the photoabsorption (inverse process


(1a)) is unlikely to occur due to the optical thinness of coronaplasmas. So, the detailed balance does not apply. Instead, the balanceexists between collisional excitation and spontaneous radiative de-excitation (processes (1a) and (1b)) as well as between collisionalionization and radiative recombination (process (1d)). CE models arerarely applied to laser-induced plasmas. More information on plasmatypes and equilibriums can be found in Refs. [28,29].

The collisional-radiative (CR) and collisional-dominated (CD) plasmamodels are by far the most usable models to describe radiating plasmas.We review them both because of their relevance to spectroscopy.

4.1. Collisional-radiative (CR) models

In recent years, the trend became noticeable in plasma modelingtoward more attention to non-equilibrium conditions in laser-induced plasmas. The most rigorous approach for describing non-equilibrium plasmas is probably that proposed by Capitelli et al. [30].Unlike equilibrium plasmas where population densities are describedby the Boltzmann law with only one parameter — temperature, non-equilibrium plasmas require a solution of a CR model where densitiesof excited states are treated separately in a so-called state-to-stateapproach. This helps to more precisely describe plasma transportproperties which depend upon the excitation states of atoms andmolecules.

A system of kinetic equations is composed for population densitiesof a maximal possible number of levels:

dni = dt = ∑Rrad + ∑Rcol; ð4Þ

where Rrad and Rcoll denote all possible radiative and collisionalexcitation–de-excitation events, and solved simultaneously with theBoltzmann equation for the electron energy distribution function fe(EEDF):

∂fe = ∂t = ð∂fe =∂tÞE + ð∂fe =∂tÞcol + S; ð5Þ

where the first and second terms describe variation of the EEDF due tothe electric field (index E) and collisions (index col) and S is the sourceterm describing inelastic losses and superelastic gains. In equilibrium,the EEDF is given by the Maxwellian distribution function. Obviously,the state-to-state approach is a formidable problem as it requires fullinformation about cross sections of different excited states and theirdependence upon internal energy of a relevant system. These dataexist for only a limited number of levels and elements.

A proof-of-principle work with an implication for LIBS was per-formed by Colonna et al. [31] on the example of a hydrogen plasma. Atime-dependent CR model was coupled to the Boltzmann equation forthe EEDF. Different non-equilibrium conditions were tested. Althoughplasma expansion dynamics was not a part of themodel, the conditionsapplied in themodel roughly approximated thoseusually found in laser-produced plasmas during the recombination phase. The results impliednon-equilibriumpopulationdensities andnon-equilibriumEEDFduringevolution of the system to stationary conditions.

The plasma dynamics was included in the CR model proposed byCasavola et al. [32]. The model confirmed the existence of non-equilibrium conditions during the plasma plume expansion. Mass,momentum and energy conservation equationswere coupled to kineticequations for ionization/recombination in a multi-level atomic system.Themodel predicted time-dependent concentrations of Ti (themodeledelement) at different heights above the target. More generally, non-equilibrium problems in laser-induced plasmas were considered byCapitelli et al. [33] who linked the development of non-equilibriumeffects (i.e. the deviation from Boltzmann/Maxwell distributions) to thecloseness of time scales on which plume expansion and ionization/recombination occur. It was concluded that the equilibrium state mustbear a recombining character whenever τion≥τexp, τion and τexp are

being the characteristic times for ionization and plume expansion,respectively.

Several modifications to the model [31–33] were proposed by thesame researchers aimed at elucidation of mechanisms of thin filmdeposition by ablation at reduced pressure [15,34,35]. In [34],chemical reactions under LTE were coupled to one-dimensionalfluid dynamics to describe the expansion of a TiO plasma. Themodel was able to predict the temperature and time-dependentprofiles of mass density. It also implied that chemical reactionsoccurring in the recombining regime produce an enormous amount ofenergy that reduces the rate of temperature decrease and acceleratesthe plasma plume. In [35], a CR model was developed to study thetime and space evolution of the plasma generated by a UV laser on theTi surface. The model included one-dimensional Euler equationscoupled to ionization/recombination kinetic equations. It was shownthat during the plume expansion the ionization/recombination equi-librium was shifted toward recombination thus explaining a spatialseparation between atoms and ions observable in time-of-flightexperiments. The influence of initial conditions such as temperatureand material production rate on the plume evolution was alsoinvestigated.

In [15], fluid dynamics was omitted; only ionization/recombina-tion kinetic was employed based on the state-to-state approach.Plasma expansion was incorporated into the model by introducingexperimentally measurable terms in the kinetic equations. Evolutionof atom, ion, and electron densities was predicted for ablation fromTiO and TiO2 targets. The authors emphasized the deviation from LTEgiven the difference between the kinetic temperature of atoms andthat of ions, while the temperature of ions and electrons was thesame. The difference was explained by radiative processes actingdifferently on atoms and ions. More details on this and other similarplasma models can be found in the review by Capitelli et al. [36].

Kinetic modeling of a laser-induced plasma was used by Babushoket al. who studied physical and chemical factors responsible for a LIBSsignature of lead [37,38] and explosives (e.g. cyclotrimethyenetrini-tramine and RDX) [39]. In [38], a computational fluid dynamic modelcomplemented by chemical kinetics was used to describe chemicalspecies and reactions between them. In later works [38,39], onlychemical kinetics was investigated; a temporal temperature profiletypical for LIBS was incorporated into the model mechanically. It wasfound in all studies that reactions proceeded in two steps. During thefirst stage (∼1 µs) species reached the quasi-stationary concentra-tions, while during the second stage the concentrations changed inaccordance with the decreasing plasma temperature. It was argued[39] that a type of the initial compound, an explosive, was not relevantduring ∼1 µs of plasma evolution thus allowing the detection ofenergetic materials via their unique C/N/H/O emission line ratios.

A state-to-state kinetic approach was used by Mazhukin et al. [40]who simulated a time-dependent energy distribution of atoms andions following the breakdown in an Al vapor. The transient CR modelwas developed which included the non-equilibrium laser heating,stepwise collision ionization, and photo-processes in laser radiationfield and continuum: photoionization, resonance, and non-resonancephotoexcitation. Analysis of basic mechanisms of non-equilibriumionization of Al vapor showed the dominant effect of photo-processeson the distribution of plasma species.

In other papers [14,41,42], Mazhukin et al. modeled laser plasmasinitiated at the interface between different media. The laser–targetinteraction was avoided by assuming a thin plasma layer pre-existingabove the target surface. In [41], plasma dynamics at the air–waterinterfacewasdescribed by the systemof gas-dynamic equations and theradiative transfer equation. It was shown that the plasma evolutionstrongly depended on the laser wavelength and that the plasmaradiation contributed significantly to the redistribution of plasmaenergy. In [14,42], the effect of radiative transfer on gas dynamics ofthe Al laser plasma at low ambient pressure was studied. The


mathematical description included two-dimensional radiation gasdynamics and the multi-group diffusion approximation for plasmaradiation transfer. Calculation of the plasma spectrum was performed[14] forwide (0–100 eV) andnarrow, optical (2–5 eV) energywindows.

A CR model of laser-induced aluminum plasma was developed byTravaillé et al. [43] to assess the validity of the concept of LTE anddiagnostics based on it. The calculations were carried out forstationary, isothermal and homogeneous aluminum plasma involving220 energy levels in three ionization states: Al0, Al+, and Al++.Synthetic spectra were generated and then used for constructing aBoltzmann plot from which the plasma temperature was obtained.The model outputs served as a test for physical accuracy of theBoltzmann temperature used in plasma diagnostics and calibration-free LIBS (see Section 5). The deviationwas found ranging between 10and 30% between the measured Boltzmann temperature and thetemperature set in the model signifying the importance of multi-levelionization/recombination kinetics.

A simplified analytic CR model incorporating non-LTE and opticaldepth effects was developed by Pomarico et al. [44] relevant to LIBSapplications. A four-level model was proposed with seven collisionaland radiative mechanisms responsible for the levels population/depopulation. The effects of the temperature, electron density, andoptical thickness on line intensity ratios were investigated andcompared to the equilibrium plasma state. A similar reduced quasi-stationary kinetic CRmodel was proposed by Gordillo-Vázquez [45] topredict the spatial and temporal evolution of five levels of Li atoms innon-equilibrium laser-generated plasmas.

Le et al. [46] developed a hydrodynamic CRmodel which describednon-equilibrium conditions for ionization and recombination andassumed two temperatures for electrons and heavy particles. Themodel was applied to a Si laser-induced plasma expanding into argonand helium. Plasma initial conditions were obtained using a one-dimensional model of laser–solid interaction. A full Navier–Stokesmodel including ambipolar diffusion, heat conduction, and viscositywas compared to a simpler Euler model. The results indicated that theEuler model could adequately describe only the earliest stage ofplasma expansion, whereas the Navier–Stokes model was capable tosimulate adequately the overall plasma behavior. The model demon-strated a crucial influence of a type of the background gas and ambientpressure, however, it failed to explain the observable difference inexpansion velocities of atoms and ions.

It should be emphasized that CR plasma models are used for notonly low-temperature spectrochemical laser plasmas but also (andmainly) for highly energetic plasmas produced in laser fusionexperiments and various technologies. Highly sophisticated codeslike the SPECT3D [47], HELIOS-CR [48], etc. were developed capable ofperforming non-LTE atomic kinetic calculations with up to ∼103–105

atomic discrete levels. The codes were used, for example, forcalculating properties of laser-produced plasmas at conditionsrelevant to extreme ultraviolet lithography [49] or X-ray lasing [50].

4.2. Collisional-dominated (CD) models

The detailed CR models based on the full Navier–Stokes, kinetic,and radiative transfer formulation require a large amount ofcomputational time as well as the knowledge of a large number ofthermodynamic and spectroscopic parameters that are not readilyavailable. It is difficult to use such models for fast evaluation oflaboratory plasmas as needed, for example, in spectrochemicalanalysis or thin film deposition. A number of simpler analyticalmodels have been developed for these purposes which included allessential physics necessary to correctly predict the properties ofinterest. A few examples of such models are given below based on theconcept of CD plasma.

Yalçin et al. [51] studied the influence of ambient conditions on thelaser air spark with simple Saha–Boltzmann analysis that was valid for

uniform isothermal CD plasmas. They found evidence in support of alaser-supported radiation wave model.

Hermann et al. [52] developed a model of a non-uniform plasmadivided into two uniform zones of different densities and tempera-tures to describe self-absorption of the plasma radiation.

Tallents [53] solved the radiative transfer equation and used theassumption of a linear (with respect to coordinate) plasma expansionvelocity to determine plasma conditions from shapes of optically thicklines. A synthetic spectrum was calculated for the 3.4 nm C(VI) line.Model parameters, such as plasma emissivity, absorption coefficientand ion velocity were adjusted until a close fit was obtained betweenthe computed and measured line profiles.

A simplified theoretical approach was developed by Gornushkinet al. [54] for optically thick inhomogeneous laser-induced plasmaunder LTE. Themodel was able to predict the time evolution of plasmacontinuum and line emission as well as the distributions of atoms,ions, and electrons.

An analytical CD model was developed by Arnold et al. [55] for aspherical expansion of the plasma plume into an ambient air. Themodel described different regimes of plume evolution: almost freeinitial expansion, strong shock propagation, and plume stopping.An internal shock wave was included in the model and responsiblefor the heating of the plume edge and plume splitting. The resultswere applied to analysis of ablation of steel and high temperaturesuperconductor in argon.

A similar analytical model for expansion dynamic of the copperplasma with a counter-propagating internal shock wave wasproposed by Wen et al. [56]. The plasma evolution was divided infour stages depending on a position of the internal shock wave. Foreach stage, integral conservation equations were solved to obtaintrajectories of the shockwaves and contact surfaces and the distribu-tions of plasma density, pressure, and temperature. Efficiency ofconversion of laser energy and the amount of sample vaporized weredetermined by comparing the simulated trajectories with experi-mental ones. The model was verified experimentally in [57] and wasused to study the radiative plasma cooling [58] and ionization [59].

Models which we reviewed until now included only descriptionsof plasmas omitting laser–matter interaction (except for [46]). Thelatter was substituted by a good guess of plasma initial conditionsafter the laser pulse had terminated. Meanwhile, there is a group ofmodels in which both the laser–matter interaction and plasma stageare considered together, the former providing initial conditions forthe latter. Most of these models are based on the concepts of CD andLTE plasmas. Many suggest a thermal mechanism of energy transferwhich is valid for ns ablation and which implies the use of the heatconduction equation and single thermodynamic temperature.

Ho et al. [60] simulated a dynamic of a laser plasma produced by anexcimer laser on an Al target. A one-dimensional model of targetheating was combined with two-dimensional radiative gas dynamics.The vapor phase consisting of neutrals, ions and electrons wasapproximated as a one-component ideal gas. The radiative transferequation was solved simultaneously with the gas dynamic equationsand the resulting radiation source term was incorporated into theenergy balance equation. LTE was assumed for each computationaltime step. The authors discussed in detail plasma radiation effects.

A model by Gusarov et al. [61,62] described a one-dimensionalsurface vaporization (through a Knudsen layer) followed by two-dimensional gas dynamic of the ablated plume. The model wasapplied for vacuum and low pressure ambient atmosphere. It wasnoted that the distribution of vapor inside the plume was markedlydifferent for vacuum and atmospheric conditions; while in vacuumthe vapor filled the entire plume volume, in atmosphere it wasaccumulated near the plume boundary.

Liu et al. [63] modeled laser ablation into vacuum and ambientgas based on thermal laser–surface interaction and one-dimensionalCR hydrodynamics. The model revealed the following phenomena:


formation and propagation of shockwaves, shock heating and ioniza-tion, strong effects of the initial velocity distribution on subsequentplasma expansion and transport, and confinement of the plasma by abackground gas. The model was further extended to investigate a self-similar plume expansion near the target surface [64] and the interactionof plume particles with the deposition substrate [65].

Mazhukin et al. [66–68] studied dynamics of vacuum ablation of Alby using a two-dimensional model that included heat transfer in thecondensed phase and radiation gas dynamics in the plasma. Energyexchange between the target and plasma occurred through a Knudsenlayer. It was found that surface evaporation was controlled by thesurface temperature and plasma back pressure. The evaporation hadthree characteristic stages: sonic evaporation in the beginning,condensation during the plasma formation, and subsonic evaporationduring the plasma expansion. Mass removal was greater in theperiphery of the laser beam than in the beam center due to the smallerplasma counter-pressure [66]. Mass removal was also affected by alaser wavelength [67,68].

Bogaerts et al. [69–72] proposed a model for nanosecond laserablation of a Cu target into vacuum and ambient gas. One-dimensionalenergy transfer and heat conduction equations were used to modellaser–solid interaction and material vaporization. The output of thismodel was coupled to a one-dimensional fluid dynamic modeldescribing the expansion of the plasma plume. The model predictedthe temperature distribution inside the target, depth of melt, amountof material vaporized, vapor density, velocity and temperaturedistribution in the plume, and the degree of ionization. The modelwas used to study effects of plasma shielding [69], laser parameters[70], and a type of the ambient gas [71] on plasma density,temperature, and expansion velocity. Recently, this model wasexpanded to a double-pulse (DP) ablation mode [72]. The resultswere compared to a single-pulse (SP) ablationmode provided that theoverall laser energy in both modes was the same. The calculationsshowed the 2-fold lesser laser energy absorbed by the plasma in theDP mode than in the SP mode. The target in the DP mode remainedlonger in molten phase resulting in more material supplied to theplasma by vaporization and liquid splashing. This could explain theenhancement of plasma specific emission in the DP configuration. Itwas noted that the one-dimensional descriptionwas adequate for firstfew hundreds of nanoseconds only.

A similar model was proposed by Wu et al. [73] for the one-dimensional thermal heating/vaporization of Al, Ni, and Si targetsincluding re-condensation, vapor transport through a Knudsen layer,and hydrodynamic plume expansion into an ambient gas. It was foundthat the plasma formation and laser–plasma interaction had signif-icant effects on laser-induced vaporization. The model was valid forlaser–target interactions without phase explosion, i.e. when the targettemperature did not reach or exceeded the material criticaltemperature. For the phase explosion regime, the model was refined[74] and included one-dimensional hydrodynamics over the entirephysical domain including the target surface. It was assumed that thesharp interface between the condensed and gaseous phases dis-appears when the target temperature exceeds the critical tempera-ture; then the substrate contributes mass to the plasma region mainlythrough hydrodynamic expansion instead of vaporization.

Regretfully, relatively few publications can be found in theliterature on modeling spectrally-resolved plasma emission, theproperty which is easy to measure and which provides a goodmeans to verify a validity of a model. There are only several researchgroups who model plasma specific radiation (some have already beenmentioned: [14,43,48,52–54]).

Ershov-Pavlov et al. [75] developed a model which described aradiation dynamic of an aluminum plasma in air. The model was usedto simulate emission spectra in single- and double-pulse (SP and DP)ablation regimes. Thermal heating and evaporation through aKnudsen layer were considered followed by two-dimensional

expansion dynamics and “line-by-line” approximation of the radiativetransfer. The model calculated time and spatial profiles of thermody-namic functions and their dependence upon the excitation mode.Based on simulations, signal enhancement in the DP mode wasexplained by creation of the larger plasma containing more materialas compared to the SP mode. The complex character of the spatialdistributions of temperature, pressure and density was demonstratedand their effect on shapes and intensities of spectral lines was studied.Qualitative agreement with experiment was achieved. The cautionwas issued that neither half-widths, nor relative intensities ofintegrated emission spectra can be directly used for measurementsof plasma electron density and temperature, respectively.

Aghaei et al. [76] used a one-dimensional model to describeablation of copper in 1 atm helium. The model closely followed thatdescribed in Ref. [69] except for the calculation of spectrally-resolvedplasma radiation. The temporal evolution of three copper lines andnon-specific radiation background was calculated. It was emphasizedthat the model could be important for LIBS as it is capable ofpredicting the optimal detection times and spectral line positions.However, no comparison with experiment was offered.

In summary, it seems quite obvious that non-equilibriumCRmodelsprovide more adequate description of laser-induced plasmas comparedto equilibrium CDmodels. This stems from the clearer realization of thefact that laser-induced plasmas may significantly deviate from LTE,especially during early stages of evolution. Unfortunately, the largedeficit of data required for CR models including transition probabilitiesand transport coefficients of excited states narrows a scope of theirapplications. On the other hand, equilibrium CDmodels can be entirelyadequate for many practical needs, e.g. thin film deposition, spectro-chemical analysis, etc., as numerous examples show. For practice, thechoice of a model should be dictated, among other factors, by thesignificance of an effect that the deviation from equilibrium (or from anassumed plasma symmetry) imposes on the modeled property (e.g.plasma spectrum, shape, thickness of a deposition film, etc.). Besides,different applications may correspond to different degrees of deviationfrom LTE or from a convenient symmetry. Some models are intention-ally designed to work within only a certain set of experimental con-ditions (e.g. vacuum)or a certain timewindow(e.g.first 100s of ns) thusmaking simple descriptions satisfactory. Concerning the modeling ofspectrochemical plasmas, where spatially-, time-, and spectrally-resolved plasma emission is simulated, the both CD and CR approacheslook promising.

5. Calibration-free models

As mentioned in the Introduction, we expect modeling to solvepractical problems, namely, problems existing in spectrochemicalanalysis. One of the problems is the standardization in LIBS. Thissection gives, in our opinion, a good example of usefulness ofmodeling for practice.

A group of models described here was developed specifically forLIBS. By design, they allow a back-calculation of plasma compositionbased onmeasured emission spectra. No calibration is required to linkline intensities to concentrations thus providing calibration-freeanalysis. The development of calibration-free algorithms for LIBS hasa strong rationale. If successful, it will eliminate tedious calibration,allow for single shot analysis, and open up wide perspectives fordistant monitoring in harsh environments.

5.1. Calibration-free LIBS based on the Boltzmann plot method

A recent review on the calibration-free LIBS (CF-LIBS) by Tognoniet al. [77] covers nearly all instances of application of this methodduring the past decade. In comparison with [77], our review of CFmodels is given in a broader context of plasma modeling and is not


limited to just the Boltzmann plot models. Other CF models are alsoincluded which did not receive enough attention in [77].

About a decade ago, Ciucci et al. has demonstrated that the BPmethod can be used not only for plasma diagnostic but also forquantitative analysis by LIBS [78,79]. An underlying theoretical modelwas that of a static, homogeneous, isothermal, and optically thinplasma under LTE. For such plasma a simple relation exists betweenthe line integral intensity, atom number density and plasmaequilibrium temperature. Considering a certain instrumental arrange-ment with a response factor F, a measured emission signal is given by

Ik→iλ = FCa

gkAki

UaðTÞexp −Ek

.kBT

� �; ð6Þ

where gk, Aki, and Ek are the statistical weight, transition probability,and energy of the emitting level k, Ca and Ua(T) are the concentrationof species a and its partition function, kB is the Boltzmann constant,and T is the plasma temperature. By simple algebra this equation istransformed into y=mx+q, where the slope (m) is inverselyproportional to the temperature and the intercept (q) is proportionalto the logarithm of the concentration. Finding the intercept q one findsthe concentration Ca provided that all other terms in Eq. (4) areknown or measured. The temperature is measured from theBoltzmann plot slope (several spectral lines from the same elementare used). The experimental factor F is found from the condition of aunit total concentration; knowledge of total sample composition istherefore necessary. The latter requires full qualitative analysis andmeasuring intercepts for all elements. The contribution from ionizedspecies is accounted for by solving the Saha equation.

Preliminary results marked by the high accuracy were obtained byapplying CF-LIBS to analysis of metal alloys and atmospheric air [78].The claim for “matrix-free” analysis had, however, insufficient ground.A key assumption of themethodwas the assumption of stoichiometricablation. If ablation is not stoichiometric (e.g. due to matrix effects),the CF-LIBS method cannot fix this.

A refinement of the CF algorithmwas proposed by Bilajic et al. [80]who took into account line self-absorption. Curves of growth wereconstructed for working lines of all elements; linear parts of thecurveswere extrapolated to determine fictitious line intensitieswhichthe lines would exhibit if they were not self-absorbed. Ratios ofobserved line intensities to the fictitious ones provided a value for aso-called self-absorption parameter which span the range between 1(full transparency) and 0 (full opaqueness). This correction resulted insignificant improvement of the method bringing the concentrationsfound from the Boltzmann plot closer to certified values. The methodwas tested on steel standards and ternary alloys.

To further improve the method, Tognoni et al. [81] investigatednumerous factors that could affect the precision and accuracy of theCF-LIBS procedure. It was found that the most influential ones werethe spectral irreproducibility, erroneous spectral response function,and uncertainties in spectroscopic parameters. The question of plasmanon-ideality was, however, left open. Over the years, the same groupapplied CF-LIBS to many objects: metals [78–80], combustionproducts [81], biological tissues [83], soils [84], and cultural heritagesamples [85,86].

The method became popular; several groups used it for analysis ofvarious solid materials. Burakov et al. [87–89] employed CF-LIBS foranalysis of brass, glass, crystalline and archaeological samples. Theaccuracy within 10% of certified values was achieved for majorconstituents and within 100–500% for minor ones. This result wasattributed to the possible absence of LTE and line re-absorption. DeGiacomo et al. [90] proposed a modification to the CF-LIBS proceduresuggesting an approach to determine the “experimental factor” (termF in Eq. (4)). Instead of the normalization of BP intercepts by unity asin [78], it was suggested that the experimental factor F is determined

from the blackbody equation which was used to approximate theplasma background continuum.

Fornarini et al. [91] studied theoretically and experimentally theablation of bronze samples. Amodel included laser–target interaction,heat diffusion, phase transformations, and sample vaporizationthrough a Knudsen layer. The composition of the plasma wascalculated and compared to that of the solid bronze. Differenceswere detected manifesting the non-stoichiometric ablation. CF-LIBSwas further applied to determine the plasma composition experi-mentally. The composition agreed well with that predicted by theablation model and, logically, did not agree with that of the solidbronze. This example shows that the assumption of stoichiometricablation may not always hold.

The same group applied CF-LIBS to analyzeMartian rock analoguesunder the simulated Martian atmosphere [92]. Volcanic and sedi-mentary rocks and NIST soil standards were used. Alternatively, thesame samples were analyzed by the energy dispersive X-raytechnique (EDX). The results obtained implied that, similar to theresults from other groups (see above), the CF-LIBS was capable ofsemi-quantitative analysis with an accuracy of 20–30% for majorelements and 60% for minor elements. However, CF-LIBS performedbetter than EDX and was found feasible for planetary exploration.

Sallé et al. [93] also reported on CF-LIBS analysis of Martialsimulates (minerals) under the simulated Martian atmosphere. Theaccuracies reported were anywhere between 1% and 1700%, the worstnumbers being related to minor constituents. Large errors wereexplained by uncertainties in spectroscopic parameters.

5.2. Other calibration-free models

Gornushkin et al. developed a relatively simple model of a post-breakdown plasma expanding into vacuum [94–97] and ambientatmosphere [98] under the assumptions of spherical [94,95,98] andellipsoidal [96,97] plasma symmetries. The model implemented thecoupled solution of the Euler, state, and radiative transfer equations topredict spatial and temporal evolution of plasma temperature, numberdensities, and emission spectrum. The model solved a two-fold taskillustrated in Fig. 1. First, it calculated plasma radiation dynamics (andsynthetic spectra) under arbitrarily chosen initial conditions. Second,throughmultiple iterations, it determined the initial plasma conditions,i.e. solved the initial value problem. Namely this feature of the modelprovided the possibility for standardless analysis. Monte Carlo optimi-zation was used to find plasma parameters which corresponded tothe best possible match between synthetic and experimental spectra.The model inputs were the plasma emission spectrum, initial plasmasize and initial temperature. The potential for standardless analysiswas demonstrated on the binary SiC sample and multi-componentaluminum samples. The agreement between determined and certifiedconcentrations was within 10–70% thus providing a semi-quantitativeresult.

Yaroshchyk et al. [99] proposed a calibration-free algorithmwhichcombined the idea of a static homogeneous plasma as in [78] with theidea of synthetic spectra generation and optimization as in [95]. In thisapproach, a full emission spectrum was modeled based on thesolution of the radiative transfer equation for a homogeneous layer

IνðlÞ =2hν3

c21− expð−κ′ðνÞlÞðgkni = ginkÞ−1

; ð7Þ

where κ′(ν) is the absorption coefficient and l is the layer length. Incontrast to [78], self-absorptionwas inherently included in themodel;no special refinement was necessary. The synthetic spectrum wasoptimized via multiple iterations providing the best least-square fitto the experimental spectrum. This procedure was applied to analysisof mineral samples, brass, and air. For many major elements the

Fig. 1. Monte Carlo (MC) LIBS model proposed in [94–98].


accuracywas within 10–50% except for a few cases where a correctionfactor was needed based on the one-point calibration.

A similar approach was used by D'Angelo et al. [100] whodetermined concentrations of elements in the plasma by the least-square fit of experimental and theoretical spectra. New here was theattempt to account for plasma non-homogeneity. The plasma wasassumed consisting of two zones with two different temperatures andoptical thicknesses.

5.3. Comparison between CF methods

Herrera et al. [101] made a direct comparison between CF-LIBS[78] and the standardless approach based on Monte Carlo optimiza-tion (tabbed as MC LIBS) [95]. The experiment was carried out invacuum as the MC LIBS model was fine-tuned for characterization ofvacuum plasmas. It was found that both methods worked reasonablywell for high concentrations while often failed for concentrationsbelow 1% (Fig. 2). The results from both approaches were classified assemi-quantitative with 30–200% of accuracy. From the practical pointof view, it was noted that the CF-LIBS approach was laborious in-cluding much decision making, whereas the MC LIBS approach waseasier to use but it required long computational time.

To conclude this section, the following remarks should be made.Based on our current knowledge of laser-induced plasmas, thedescribed plasma models for calibration-free LIBS seem oversimpli-fied. No surprise that they have quite a poor predictive capability. Asnoted by Colonna et al. [34], the success of calibration-free approachheavily relies on the accurate knowledge of the parameters and thevalidity of assumptions made. For example, the assumption of a static,isothermal and homogeneous plasma as in models [78–93,99] is onlyapproximately valid. Many studies (e.g. [102]) showed that theplasma is neither homogeneous nor isothermal, nor static. The laser-induced plasma has steep temperature and concentration gradients.The assumption of single ionization during the measurement time

may also not be true; the plasma can be multiply ionized with possi-ble uneven spatial distributions of neutral and charged species [103].From this perspective, the calibration-free models based on ana-lytical solutions of gas dynamic equations as in [94–98] look morepromising as they include the plasma dynamic, non-uniformity, andnon-isothermality.

6. Plasma visualization: shadowgraphy, schlieren,and interferometry

We nowmove to the diagnostic section and start from visualizationtechniques which provide a very simple and yet powerful tool forunderstanding laser-induced plasmas. There are several methodscommonly used: shadowgraphy, schlieren technique, and interferometry.They are all dependent on plasma refractive properties and used tovisualize temperature gradients, shock waves, non-homogeneousplasma regions, convection patterns, particulate ejection, etc. Whileshadowgraphy and shlieren serve mostly qualitative purposes, inter-ferometry allows for direct quantitative measurements of plasmarefractive indexes and electron densities [104].

Shadowgraphy is the simplest of the threemethods as illustrated inFig. 3a. It uses a plane parallel beam transmitted through a plasma.Shadow pattern is produced behind the plasma and recorded.Shadowgraph systems are sensitive to the second spatial derivativeof the refraction index; the change in the image intensity ΔI withrespect to the initial intensity distribution I is given by

ΔI = I = Lðd2x + d2yÞ∫Ndl; ð8Þ

where L is the distance between the plasma and image plan, dx2 and dy2

are the second spatial derivatives taken in the x–y plan normal to theprobe beam, N is the local refractive index, and l is the pathlengththrough the plasma. Shadowgraphy is not very sensitive to small

Fig. 2. Relative concentration values obtained using MC LIBS and CF-LIBS comparedwith certified values (solid bars). Adapted from [101] with permission.

Fig. 3. Schematics of plasma imaging methods: a) shadowgraphy; b) shlieren; andc) interferometry.


variations in plasma density but capable of detecting large densitygradients.

In schlieren systems (Fig. 3b), the similar parallel beam illuminatesthe plasma but now a knife edge is placed in the focal point of the lensthat partially obstructs the deviated light rays. For this system, thedeviation of light rays is proportional to the first spatial derivative ofthe refraction index:

ΔI = I = Ldy∫Ndl: ð9Þ

Here, the notations are the same as above and y-axis is perpendicularto the knife edge. Typically, schlieren methods are more sensitive thanshadowgraphy, although the shadowgraphy can handle larger phaseshifts [104,105].

Interferometry is even more sensitive toward small phase shiftsallowing in addition simple quantitative measurements. By measur-ing the ratio of the observed fringe shift to fringe spacing Δ one findsthe electron density ne by solving

Δ = ð2λLncÞ−1∫nedl; ð10Þ

where λL is the probe wavelength, nc is the critical electron density,and l is the path length through the plume. The most popular is theMach–Zehnder configuration shown in Fig. 3c. From interferograms,one can measure electron densities at points where fringes appear.The quantity of information is thus limited by the number of fringes ortheir deformation. In contrast, schlieren and shadowgraphy generateinformation at every pixel of the image but, as mentioned, they aredifficult for quantitation.

6.1. Shadowgraphy

Shadowgraphy combinedwith space- and time-resolvedmeasure-ments was used by Corsi et al. [106] to reveal two zones in the plasmaassociated with characteristic emission: the outer zone involvingcontinuum and ambient elements emission and the inner zoneinvolving ablated species emission. The first zone was attributed toheating and excitation of the medium by the shock wave. The sameresearchers used time-resolved emission and shadowgraphy to studythe orthogonal double-pulse (DP) ablation of brass in air [107]. Theshadowgrams revealed that the emission enhancement (compared toa single-pulse LIBS) was caused by the complex interplay between thepre-ablation and ablation plasmas and their associated shockwaves. Agenerally accepted view was confirmed that the enhancement was

due to the rarefaction of the ambient gas by the first pulse thatprovided better ablation conditions and less plasma shielding for thesecond pulse.

Choi et al. [108] used shadowgraphy to study the DP femtosecondablation of silicon with a picosecond pulse separation. The increasedablation efficiency was explained by the change in surface conditionafter the first pulse.

Borchert et al. [109] investigated the expansion dynamic of thenano- and picosecond laser-excited plasmas. The shadowgramsrevealed that the nanosecond plasma was driven by the laser-supported detonation. Incident laser radiation was absorbed by anarrow layer on the plasma front which expanded supersonicallytowards the laser source. A different type of plasma was observed inthe picosecond regime. Here a dense, hot and intensely radiatingplasmawas created near the target surface. Shadowgrams showed theappearance of the radiation-induced ionization towards the end of orimmediately after the laser pulse. It was concluded that thepicosecond plasma was driven by the radiative energy transport.The finding was supported by hydrodynamic calculations.

Hauer et al. [110] investigated the shock propagation for plasmasinduced on a polymer by lasers with different wavelengths. Thisresearch was relevant to laser plasma thrusters. The shadowgraphicimages showed that the shock propagation speed and, hence, theexplosion energy had increasedwith decreasing the laser wavelength.This behavior was attributed to the increase in light penetration depthwith increasing the wavelength. At longer wavelengths, the largervolumewas heated but to the lower temperature thus resulting in lessefficient material decomposition.

Russo's group [111–114] used femtosecond-resolved shadow-graphy to investigate processes in early ablation plasmas. A hightemporal resolution was adequate for studying highly dynamic laserplasmas whose typical expansion velocities are ∼106 cm/s. In [111], acomparison of femto- and nanosecond UV ablations of silicon wascarried out with both shadowgraphy and spectroscopic measure-ments. It was observed that in early times (∼1 ns) the femtosecond


plasma expanded in one dimension while the nanosecond plasmaexpanded in three dimensions as predicted by the Sedov–Taylor pointexplosion theory. In later times, the expansion of the both plasmaswas three-dimensional. In [112], the femtosecond shadowgraphy wasused to study the mechanism of particle ejection during ablation of Siand Cu with a ns UV laser. It was assumed that early particle ejectioncould be related to the interaction of an internal shockwave with amolten pool of material. The internal shock was clearly seen onshadowgrams traveling several times between the plume boundaryand sample surface. In [113], the transmittance of the early Cu plasma(∼1–40 ns) was measured using the 100 fs-resolved shadow images.The technique allowed for the evaluation of plasma temperature andelectron density during very early ablation times. In [114], fs-resolvedshadowgraphy was used to study the propagation of laser-inducedshocks originating from ablation inside glass cavities.

Gornushkin et al. [115] applied resonance shadowgraphy forimaging laser-induced plasmas. The shadowgrams were obtainedwith a laser tuned in resonance with atomic transitions of targetelements, Sn and Pb. The photodecomposition of lead and tin dimersand larger clusters was visualized.

Okano et al. [116] used electron shadowgraphy to study the spatialseparation of electric charges in laser-induced plasma. The electronbeam was able to “see” the charge separation (impossible for opticalmethods) because of the effects of plasma electric andmagnetic fields.The same group used also X-ray shadowgraphy for imaging ofaluminum plasma [117]. Time resolution of ∼50 ps was achieved,however, advantages of X-ray shadowgraphy before optical shadow-graphy were not discussed.

6.2. Schlieren

A combined schlieren–interferometric method was used by Iwaseet al. [118]. The method provided the information on plasma electrondensity and the shock propagation.

Englert et al. [119] used schlieren technique to study temporal andspatial evolution of electron density in the air plasma at low pressure.A second harmonic of a Nd:YAG laser was used as a probe beam. Themeasurements helped to explain self-focusing of the laser beam andlobe structure of the plasma.

Ventzek et al. [120] used pulsed schlieren photography to visualizeplasmas induced on polymers. Two-dimensional time-resolvedimages showed the shock propagation, plume turbulences andasymmetries. A threshold value for laser fluence was determined bymonitoring the transition from sound to shock wave.

Wang et al. [121] employed the high speed schlieren system toinvestigate laser-induced ignition of the H2/O2/Ar mixture on amillisecond time scale. This work was relevant to combustion studies.Time-resolved schlieren images revealed the plasma shape transfor-mation and formation of vortexes and instabilities.

Precise characterization of ablation plumes is crucial for medicalapplications. An elaborated shlieren technique was used by Vogelet al. [122,123] to study ablation processes of biological tissues. Allstages of the plume evolution were visualized, starting from phasetransitions and material removal during the action of the laser pulseand ending by complex hydrodynamic processes including recoilwaves and post-pulse ablation. Such visualization was very useful inexplaining the plume dynamic.

6.3. Interferometry

Doyle et al. [124] used a Mach–Zehnder interferometer to measureelectron number density in early (25–85 ns) laser-induced plasma.The plasma was induced on a Mg target in vacuum; the interferencefringes were detected with a gated ICCD with a 2 ns temporalresolution. It was found that the electron number density linearlydecreased with increasing the distance from the target and linearly

increased with the increase of the laser irradiance. It was emphasizedthat light–material interaction was strongly dependent on thethermo-physical properties of the material.

Schittenhelm et al. [125,126] used a Michelson interferometer toimage the distribution of the refractive index in the Cu laser plume. A500 ps time resolution was achieved by using a short-pulse dye laser.The images revealed a steep decrease in the refraction index behindthe shock front. Two-wavelength interferometry was later applied tocalculate the values of electron densities [126]. It was demonstratedthat the change of an ambient gas had a drastic effect on the electrondensity but the ablation efficiency remained the same.

Fast streak camera coupled to aMach–Zehnder interferometer wasused by Noll et al. [127] for comparative diagnostic of plasmas ignitedon a metal surface by a single laser pulse and collinearly orienteddouble pulses. Time-resolved plasma photographs revealed differentexcitation dynamics for the single and double-pulse plasmas andallowed measurements of plasma propagation velocities. The veloc-ities were compared to those predicted by the strong explosion theoryby Sedov. It was found that short after the plasma ignition (∼25 ns)the single-pulse plasma propagation obeyed the relation for aspherical explosion, whereas the double-pulse plasma propagationcorresponded to a planar explosion. Interferometry also revealed thevalues for refraction indices and plasma electron densities. It wasfound that the electron densities and temperatures of single- anddouble-pulse plasmas were similar while the size of the double-pulseplume was 3-fold of that of the single-pulse plume. It was thusconcluded that the enhancement of the emission signal observed inthe double-pulse configuration was due to the larger mass ablated.

7. Laser-induced fluorescence (LIF) and absorptionspectroscopy (AS)

These two techniques offer an excellent possibility for spatial andtemporal diagnostics of laser-induced plasmas. High temporal, spatial,and spectral resolutions are inherent to both of them with the use ofpulsed lasers as an excitation source. Spectral narrowness andtunability of lasers typically used in LIF and AS allow for the directprobing of population densities of atoms and ions in different energystates. In addition to density measurements, the techniques can alsobe used for determining temperatures and energy transfer rates. Thisis achieved by measuring relative intensities of lines originating fromlaser-excited levels or from levels collisionally coupled to them.Compared to optical emission diagnostics, LIF and AS are moresensitive and capable of providing information long after the emissionfrom a plasma has ceased. An important advantage of AS over opticalemission spectroscopy (OES) is that only relative intensities need bemeasured for determining absolute concentrations, thus avoidingproblems with calibration. The inconvenience is that both thetechniques are single-element techniques that reduces the amountof information and limits its collection speed.

7.1. Laser-induced fluorescence (LIF)

Sdorra et al. [128–130] used LIF to measure temporal and spatialdistributions of atoms and ions in laser-induced plasmas (LIP) createdon solid samples. A strong spatial non-uniformity was detected withmaxima located in the plasma center. The effects of ambient pressurewere discussed; the optimal pressure (∼140 hPa of Ar) was found thatprovided maximal densities for both atomic and ionic species. Thepotential of LIP-LIF for sensitive microanalysis and plasma diagnosticswas demonstrated including the determination of collision transfercross sections [130].

Fluorescence measurements were used by Margetic et al.[131,132] to investigate hydrodynamic expansion of femtosecondlaser-produced microplasmas and to assess the validity of the pointblast model proposed in [55]. It was argued that the point blast model


is especially relevant to femtosecond plasmas as no interaction occursin this case between the laser and the plasma plume. Spatially-resolved fluorescence of elements in the plume was measured atdifferent delay times up to hundreds of microseconds. The measure-ments revealed plasma segmentation similar to that described in [55]where two independent shockwaves were predicted propagatinginside and outside of the plume–air interface.

Chemical reactions and mapping of plasma species by LIF werestudied in [133,134]. Burakov et al. [133] investigated chemicaldynamics in laser-produced plasmas of metallic (Ti and Al) andgraphite samples using LIF. The main focus was on mechanisms offormation of metal oxides and dimers. Many LIF measurements wereperformed on atoms, ions, and molecules to attain populationdensities, electron, vibrational, and rotational temperatures andspace–time distributions of species. The studies showed that metallicoxides originated from chemical reactions in the recombining plasmarather than from thermally activated surface vaporization. It wasconcluded that oxidation reactions governed the ablation plumedynamics after 10 µs of plasma evolution.

Dutouquet et al. [134] studied the oxidation and nitridation of Al, Ti,and C plasmas in lowpressure N2 or O2. LIFwas used tomeasure groundstate absolutenumberdensities of atomsandmolecules after calibrationof the spectrometer by additional absorptionmeasurements. A series ofLIF images (Fig. 4) was obtained at resonance frequencies of Ti and AlOshowing strongly non-uniform distribution of species inside the plasmaplume. The authors concluded that laser ablation lead to strong gasphase oxidation inO2, whereas no nitride formation (except for carbon)was detected in N2 atmosphere. The observations also confirmedtheoretical predictions of the snow plough effect resulting from acompression of the ambient gas by the expanding plasma plume(Fig. 4a) and the turbulent flow behavior (Fig. 4b).

The formation of gaseousmetallic dimers in laser-produced plasmasby LIFwas earlier investigated by Bondybey et al. [135–137]. The dimers(Pb2, Sn2, Cr2, and Be2) formed in the expanding plasma plume wereguided through a small orifice into vacuum where molecular fluores-cence was excited. The values of internuclear distances and vibrationalfrequencies were derived from the spectra.

Two-dimensional LIF imaging was employed in [138–140]. Pure-tzky et al. [138] studied the dynamic of ablation products desorbed bylow energy lasers (30–70 mJ/cm2) from organic crystals commonlyused in MALDI. Molecular images revealed a two-component plumewith non-uniform velocity field. Matsuo et al. [139] used one- andtwo-dimensional LIF to measure velocities and spatial distributions ofatoms and ions resulted from femtosecond ablation of samarium. Thehigher velocities and narrower distribution were found for ions thanfor atoms, the result similar to [128]. Watarai et al. [140] studied laser

Fig. 4. Spatial distribution of AlO ground state population densities for laser ablation in O2 at pposition. Spatial scaling is plotted in millimeters. The color scale is adjusted from zero up to tfrom [134] with permission.

ablation in reactive gas atmosphere of C4F8 by two-dimensional LIF.The density distributions of C2 and CF2 were visualized. The studyshowed thatmixing between ablated species and ambient gas was notsignificant; chemical reactions important for synthesizing newmaterials occurred mainly on the interface between the ablationplume and ambient gas.

An original imaging technique was proposed by Okada et al. [141]for diagnostics of particle dynamics during thin film deposition bylaser ablation. The technique was tabbed as re-decomposition LIF orReD-LIF and based on additional laser vaporization of nanoparticlesformed in the post-ablation plume. The technique was investigatedboth theoretically and experimentally. Three lasers were used: one forablation (Nd:YAG), one for particle vaporization (XeCl), and one forfluorescence excitation (OPO). The technique was applied todiagnostics of Si plasma in 10 Torr He atmosphere. The formation ofsilicon nanoclusters was clearly visualized at times of about 300 µsafter the plasma ignition pulse. The imaging diagnostics helped toestablish the relationship between the deposition conditions and filmproperties and provided information for further optimization of theprocess.

7.2. Absorption

Hirsch et al. [142] developed a photoabsorption imaging systemfor vacuum ultraviolet (VUV) plume diagnostics. The illuminationsource was a laser-generated gold plasma. The system was used tomeasure time-resolved images and spatial distributions of photo-absorption/photoionization of Ba+ in expanding laser plasma on anabsolute basis. The system was also used to measure velocities ofelements in different ionization states (Ca, Ca+ and Ca2+). It wasfound, for example, that the expansion of Ca+ ions proceeds fasterthan that of Ca, the result similar to that in [128,139].

Gornushkin et al. [143] used molecular absorption technique tostudy a production of ozone and nitrogen oxides during multiple laserbreakdown in oxygen–nitrogen mixtures. The light source for absorp-tionmeasurementswas the continuum radiation emitted by the plasmaitself. It was found that in oxygen-dominating atmosphere the ozonewas the dominating reaction product, whereas the production of NOx

species lagged behind. As the amount of N2 increased, the production ofnitric oxide also increased, ozone was rapidly consumed producingnitrogen dioxide. At higher partial pressures of nitrogen the “ozonephase” disappeared completely from the absorption spectra, whereasthe production of NO, and especially NO2, increased dramatically.

The possibility of detection of isotopes by AS in laser-inducedplasmas was demonstrated in [144,145]. Narrowband CW lasers andreduced pressure Ar atmosphere were used in both cases. King et al.

ressures of 70 Pa (a) and 7 Pa (b) and 8 µs delay time. The black bar indicates the targethe maximum ground state density which is given on each image in 1013 cm−3. Adapted


[144] measured the isotope ratio of 85Rb/87Rb at 100 µs delay after theablation pulse, and Quentmeier et al. [145] was able to measure theisotope ratio of 235U/238U.

Gornushkin et al. [146] used AS to study line broadening mechan-isms in a low pressure laser-induced plasma using Rb isotopes. It wasshown that for a trace element (Rb in CaCO3 matrix), the broadeningwas due to the Doppler effect, whereas for a major matrix component(Ca) the broadening was due to the resonance broadening. It was alsofound that the plasma was non-equilibrium as the difference betweenthe kinetic and excitation temperatures was detected. The numberdensities of Ca atoms in the ground state were derived from the ab-sorption spectra.

8. Other diagnostics

There are few other diagnostic techniques worth mentioning thatare applicable to laser-induced plasmas.

8.1. Cavity ringdown spectroscopy

Cavity ringdown spectroscopy (CRDS) is a variation of atomicspectroscopy which employs a multiple passage of the probe beamthrough an absorbing medium. This is achieved by placing anabsorbing object inside the cavity constructed from two highlyreflective mirrors. The probe beam bounces back and forth betweenthe mirrors passing every time through the object. A fraction of thebeam leaking through the cavity mirror is detected. The signal decayrate, β(ν), is proportional to the medium opaqueness via

βðνÞ = cL½ j lnR j + κðνÞl�; ð11Þ

where c is the speed of light, L is the cavity length, ν is the frequency ofthe probe beam, l is the single pass absorption length, κ(ν) is theextinction coefficient, and R is the mirror reflectivity.

Labazan et al. [147] used CRDS to study evolution of lithium atomsand dimers in the laser-induced lithium plasma in vacuum. Thetunable probe laser was scanned across resonance transitions of Li andLi2 with the simultaneous measurement of the cavity loss signal(Eq. (11)). Arrival times (the travel time between the target and probebeam) were measured providing the values for expansion speeds of Liand Li2. It was found that dimers are 3-fold slower than atoms. It wasshown that the dimers mostly result from surface desorption ratherthan from condensation.

Krstulović et al. used CRDS to study characteristics of a titaniumplasma in vacuum in a single- [148] and double-pulse [149] ablationmodes. Absorption profiles were studied and compared to atheoretical model accounting for the plume anisotropy and velocitydistribution inside the plume. The dual-pulse ablation showed higherabsorption losses and greater line splitting as compared to the single-pulse ablation. The double-pulse plume had also higher density andlarger angular spread.

8.2. Langmuir probe

The technique relies on measuring the current induced by plasmaions and electrons on a thin metallic electrode placed in the vicinity ofthe plasma. Plasma temperature and electron density can be derivedfrom the Langmuir probe signal using the Boltzmann-like rela-tions [150]:

ln IP = lnð1 = 4⋅neveeAPÞ−eVP−VPL

kTeð12Þ

and

ne =IPðVPLÞ

1= 4⋅veAPe; ð13Þ

where IP is the probe current, VP and VPL are the probe and plasmapotentials respectively, AP is the probe area, k is the Boltzmannconstant, ve, e, and Te are the mean electron velocity, electron chargeand electron temperature, respectively. Plasma electron temperatureis found from the slope of a semi-logarithmic plot defined by Eq. (12),whereas the electron density (Eq. (13)) is found from the interceptwith the ordinate axis at VP=VPL.

In work by Wild et al. [151], electron temperature of a plasmainduced on the Bi–Sr–Ca–Cu–O target in vacuum was directlymeasured by the Langmuir probe placed at a short distance (∼mm)from the target surface. Themeasurement yielded temperature valuesbetween 1 and 2 eV corresponding to the delay times between 0.5 and1 µs, the typical values for laser-induced plasmas.

Hansen et al. [152] used Langmuir probes to monitor vacuumexpansion of the silver ablation plume. Eight probes were arranged ina circle around the plasma. Angular and temporal distributions of ionsand electrons were determined with the help of time-of-flightmeasurements and found to be in good agreement with the modelof self-similar adiabatic expansion. A similar experiment with theLangmuir probe and femtosecond laser ablation in vacuum wasperformed by Williams et al. [153] and Mannion et al. [154] to studysurface contamination effects.

8.3. Thomson scattering

In this technique, a probe laser is elastically scattered by freecharged particles (mostly electrons) inside the plasma. Importantplasma properties can be inferred from the scatter signal including theelectron number density, temperature, and electron energy distribu-tion function (EEDF). The technique is non-intrusive, spatiallydiscrete, and does not require additional assumptions about plasmasymmetry or LTE. Although Thomson scattering (TS) is the routinetool for diagnostics of high temperature plasmas (e.g. nuclear fusionplasmas), it is used quite rarely for diagnostics of analytical plasmas. Areason is the weakness of the TS signal due to its very low crosssection (∼10−25 cm2) and severe spectral interferences. Demandinginstrumentation and high level of expertise are required for thesemeasurements. Nevertheless, the technique was shown to be suitablefor analysis of low-temperature plasmas; examples are given in thecomprehensive review by Warner and Hieftje [155].

Delserieys et al. [156] used TS for direct measurements of electrontemperature and density in Mg laser-induced plasma. Clear TS featureswere observed for collective and non-collective scattering regimes (onecorresponding to scattering fromgroups of electrons and the other fromindividual electrons) during the plasma evolution. The character of thedecay curves for both the electron temperature and electron densityimplied that theplasmawas strongly recombining, i.e. non-equilibrium;the result similar to that reported in [33,133].

Diwakar et al. [157] applied the TS technique for diagnostic of earlylaser plasma induced in atmospheric air. Significant Thomsonscattering was observed during the initial plasma evolution that alsosuggested the deviation from LTE. Regretfully, no analysis wasattempted based on the intensity or shape of the TS signal; theplasma electron density was routinely determined from the Stark-broadened nitrogen ion line.

9. Conclusion

Laser-inducedbreakdownspectroscopy, or LIBS, continues to remaina tremendously popular technique due to its simplicity and disregardof material types and ambient conditions. However, this visible


operational simplicity hides great complexity of underlying physicalprocesses which need to be better understood in order to improve thetechnique.We hope that the current reviewhas provided the importantinformation on the diversity of plasma processes and means of howthese processes can be modeled or derived from experiments.

It is important to note that the laser-induced plasma is not aswewant itto be; simplifying concepts like LTE, or Maxwell–Boltzmann distribu-tions may not be applicable throughout the entire range of changingplasma conditions. In fact, the collisional-radiative (CR) plasmamodelsdescribed in Section 4 clearly demonstrate that deviations from LTE canoccur and, therefore, the Boltzmann distribution for populationdensities and Maxwell distribution for electron energy distributionfunction (EEDF) are not fully accurate approximations.

Another question remains whether LIBS as an analytical methodwill benefit from the inclusion into plasma models the early laser–matter interaction. In our opinion, the resulting uncertainties inevaluation of the mass input into the plasma are today equivalent tostarting a radiative model with an educated guess of initial conditions.

For further progress of LIBS as a quantitative analytic technique,the knowledge is indispensible of what we measure and how weinterpret the measurements. That is where plasma modeling anddiagnostics should help; especially diagnostics with high spatial andtemporal resolutions are needed urgently. In this case, active methodssuch as laser-induced fluorescence and absorption are the mostpromising and simple tools highly compatible with the transientnature of the plasma. Laser diodes will probably be the sources ofchoice in this case. While shadowgraphy and schlieren imaging offer asimple experimental approach to refractive-index measurements,Thomson scattering, although experimentally challenging, is the verypromising absolutemethod for gaining detailed information about thedistribution functions of electrons.

Acknowledgements

Financial support from the DFG-NSF grant GO 1848/1-1 and NI185/38-1 (USA, Germany) is gratefully acknowledged.

References

[1] D.A. Cremers, L.J. Radziemski, Handbook of Laser-induced Breakdown Spectros-copy, John Wiley & Sons, London, 2006.

[2] A.W. Miziolek, V. Palleschi, I. Schechter, Laser-induced Breakdown Spectroscopy,Cambridge University Press, New York, 2006.

[3] J. Singh, S. Thakur, Laser-induced Breakdown Spectroscopy, Elsevier, Amsterdam,2007.

[4] W.B. Lee, J.Y. Wu, Y.I. Lee, J. Sneddon, Recent applications of laser-inducedbreakdown spectrometry: a review of material approaches, Appl. Spectrosc. Rev.39 (2004) 27–97.

[5] J.D. Winefordner, I.B. Gornushkin, T. Correll, E. Gibb, B.W. Smith, N. Omenetto,Comparing several atomic spectrometric methods to the super stars: specialemphasis on laser-induced breakdown spectrometry, LIBS, a future super star,J. Anal. At. Spectrom. 19 (2004) 1061–1083.

[6] C. Pasquini, J. Cortez, L.M.C. Silva, F.B. Gonzaga, Laser-induced breakdownspectroscopy, J. Braz. Chem. Soc. 18 (2007) 463–512.

[7] C. Aragon, J.A. Aguilera, Characterization of laser-induced plasmas by opticalemission spectroscopy: a review of experiments and methods, Spectrochim.Acta Part B 63 (2008) 893–916.

[8] R.F. Haglund Jr., Mechanisms of laser-induced desorption and ablation, in: J.C.Miller, R.F. Haglund Jr. (Eds.), Laser Ablation and Desorption, ExperimentalMethods in Physical Sciences, 30, Academic Press, 1998.

[9] G.M.Weyl, Physics of laser-induced breakdown: an update, in: L.J. Radziemski, D.A.Cremers (Eds.), Laser-induced Plasmas and Applications, Marcel Dekker, Inc, NewYork, 1989.

[10] A. Vogel, J. Noack, K. Nahen, D. Theisen, S. Busch, U. Parlitz, D.X. Hammer, G.D.Noojin, B.A. Rockwell, R. Birngruber, Energy balance of optical breakdown inwater at nanosecond to femtosecond time scales, Appl. Phys. B 68 (1999)271–280.

[11] P.K. Kennedy, D.X. Hammer, B.A. Rockwell, Laser-induced breakdown in aqueousmedia, Prog. Quant. Electron. 21 (1997) 155–248.

[12] D. Kim, M. Ye, C.P. Grigoropoulos, Pulsed laser-induced ablation of absorbingliquids and acoustic-transient generation, Appl. Phys. A 67 (1998) 169–181.

[13] J. van Dijk, G.M.W. Kroesen, A. Bogaerts, Plasma modelling and numericalsimulation, J. Phys. D: Appl. Phys. 42 (2009) 190301.

[14] V.I. Mazhukin, V.V. Nossov, G. Flamant, I. Smurov, Modeling of radiation transferand emission spectra in laser-induced plasma of Al vapor, J. Quant. Spectrosc.Radiat. Transf. 73 (2002) 451–460.

[15] A. De Giacomo, V.A. Shakhatov, O. De Pascale, Optical emission spectroscopy andmodeling of plasma produced by laser ablation of titanium oxides, Spectrochim.Acta Part B 56 (2001) 753–776.

[16] Z. Zhang, Z.-X. Han, G.S. Dulikravich, Numerical simulation of laser-inducedplasma during pulsed laser deposition, J. Appl. Phys. 90 (2001) 5889–5897.

[17] A. Bogaerts, Z. Chen, Nanosecond laser ablation of Cu: modeling of the expansionin He background gas, the comparison with expansion in vacuum, J. Anal. At.Spectrom. 19 (2004) 1169–1176.

[18] J. Jandeleit, G. Urbasch, H.D. Hoffmann, H.-G. Treusch, E.W. Kreutz, Picosecondlaser ablation of thin copper films, Appl. Phys. A 63 (1996) 117–121.

[19] S. Sonntag, J. Roth, F. Gaehler, H.-R. Trebin, Femtosecond laser ablation ofaluminium, Appl. Surf. Sci. 255 (2009) 9742–9744.

[20] F. Garrelie, A. Catherinot, Monte Carlo simulation of the laser-induced plasma-plume expansion under vacuum and with a background gas, Appl. Surf. Sci. 138–139 (1999) 97–101.

[21] S.R. Franklin, R.K. Thareja, Monte-Carlo simulation of laser ablated plasma forthin film deposition, Appl. Surf. Sci. 177 (2001) 15–21.

[22] B.J. Alder, T.E. Wainwright, Studies in molecular dynamics: I. General method,J. Chem. Phys. 31 (2009) 459–466.

[23] K. Gouriet, T.E. Itina, L.V. Zhigilei, Molecular dynamics study of nanoparticleevolution in a background gas under laser ablation conditions, Appl. Surf. Sci.255 (2009) 5116–5119.

[24] T.E. Itina, J. Hermann, P. Delaporte, M. Sentis, Laser-generated plasma plumeexpansion: combined continous-microscopic modeling, Phys. Rev. E 66 (2002)066406.

[25] T.E. Itina, J. Hermann, Ph. Delaporte, M. Sentis, Combined continuous-micro-scopicmodeling of laser plume expansion, Appl. Surf. Sci. 208–209 (2003) 27–32.

[26] R.W.P. McWhirter, in: R.H. Huddlestone, S.L. Leonard (Eds.), Plasma DiagnosticTechniques, Academic Press, New York, 1965, pp. 201–264, Chapter 5.

[27] G. Cristoforetti, A. De Giacomo, M. Dell'Aglio, S. Legnaioli, E. Tognoni, V. Palleschi, N.Omenetto, Local thermodynamic equilibrium in laser-induced breakdown spec-troscopy: beyond the McWhirter criterion, Spectrochim. Acta Part B 65 (2010)86–95.

[28] W. Lochte-Holtgreven (Ed.), Evaluation of Plasma Parameters in OpticallyThick Plasmas. Plasma Diagnostics, JohnWiley and Sons, New York, 1968, p. 215,42–52.

[29] J. Van der Mullen, Excitation equilibria in plasmas, a classification, Phys. Rep. 191(1990) 109–220.

[30] M. Capitelli, I. Armenise, D. Bruno, M. Cacciatore, R. Celiberto, G. Colonna, O. DePascale, P. Diomede, F. Esposito, C. Gorse, K. Hassouni, A. Laricchiuta, S. Longo, D.Pagano, D. Pietanza, M. Rutigliano, Non-equilibrium plasma kinetics: a state-to-state approach, Plasma Sources Sci. Technol. 16 (2007) S30–S44.

[31] G. Colonna, L.D. Pietanza, M. Capitelli, Coupled solution of a time-dependentcollisional-radiative model and Boltzmann equation for atomic hydrogenplasmas: possible implications with LIBS plasmas, Spectrochim. Acta Part B 56(2001) 587–598.

[32] A. Casavola, G. Colonna, M. Capitelli, Non-equilibrium conditions during a laser-induced plasma expansion, Appl. Surf. Sci. 208–209 (2003) 85–89.

[33] M. Capitelli, F. Capitelli, A. Eletskii, Non-equilibrium and equilibrium problems inlaser-induced plasmas, Spectrochim. Acta Part B 55 (2000) 559–574.

[34] G. Colonna, A. Casavola, M. Capitelli, Modeling of LIBS plasma expansion,Spectrochim. Acta Part B 56 (2001) 567–586.

[35] A. Casavola, G. Colonna, A. De Giacomo, M. Capitelli, A combined fluid dynamicand chemical model to investigate the laser-induced plasma expansion, Appl.Phys. A 79 (2004) 1315–1317.

[36] M. Capitelli, A. Casavola, G. Colonna, A. De Giacomo, Laser-induced plasmaexpansion: theoretical and experimental aspects, Spectrochim. Acta Part B 59(2004) 271–289.

[37] V.I. Babushok, F.C. DeLucia Jr., P.J. Dagdigian, M.J. Nusca, A.W. Miziolek, Kineticmodeling of the laser-induced breakdown spectroscopy plume from metalliclead, Appl. Opt. 42 (2003) 5947–5962.

[38] V.I. Babushok, F.C. DeLucia Jr., P.J. Dagdigian,M.J. Nusca, A.W.Miziolek, Experimentaland kinetic modeling study of the laser-induced breakdown spectroscopy plumefrom metallic lead in argon, Spectrochim. Acta Part B 60 (2005) 926–934.

[39] V.I. Babushok, F.C. DeLucia Jr., P.J. Dagdigian, J.L. Gottfried, C.A. Munson, M.J.Nusca, A.W. Miziolek, Kinetic modeling study of the laser-induced plasma plumeof cyclotrimethylenetrinitramine (RDX), Spectrochim. Acta Part B 62 (2007)1321–1328.

[40] V.I. Mazhukin, V.V. Nossov, M.G. Nickiforov, I. Smurov, Optical breakdown inaluminum vapor induced by ultraviolet laser radiation, J. Appl. Phys. 93 (2003)56–66.

[41] V.I. Mazhukin, V.V. Nossov, I. Smurov, Modeling of plasma dynamics at the air–water interface: application to laser shock processing, J. Appl. Phys. 90 (2001)607–618.

[42] V.I. Mazhukin, V.V. Nossov, I. Smurov, G. Flamant, Modelling of radiation transferin low temperature nanosecond laser-induced plasma of Al vapor, J. Phys. D:Appl. Phys. 37 (2004) 185–199.

[43] G. Travaillé, O. Peyrusse, B. Bousquet, L. Canioni, K. Michel-Le Pierres, S. Roy,Local thermodynamic equilibrium and related metrological issues involvingcollisional-radiative model in laser-induced aluminum plasmas, Spectrochim.Acta Part B 64 (2009) 931–937.

[44] J.A. Pomarico, D.I. Iriarte, H.O. Di Rocco, An analytic collisional-radiative modelincorporating non-LTE and optical depth effects, Eur. Phys. J. D 19 (2002) 65–72.


[45] F.J. Gordillo-Vázquez, Concentration of Li atoms in plasmas produced from laserablation of LiNbO3, J. Appl. Phys. 90 (2001) 599–606.

[46] H.C. Le, D.E. Zeitoun, J.D. Parisse, M. Sentis, W. Marine, Modeling of gas dynamicsfor a laser-generated plasma: propagation into low pressure gases, Phys. Rev. E62 (2000) 4152–4161.

[47] J.J. MacFarlane, I.E. Golovkin, P.R. Woodruff, D.R. Welch, B.V. Oliver, T.A.Mehlhorn, R.B. Campbell, Simulation of the ionization dynamics of aluminumirradiated by intense short-pulse lasers, Proc. Inertial Fusion and SciencesApplications 2003, Amer. Nucl. Soc., 457, 2004.

[48] J.J. MacFarlane, I.E. Golovkin, P.R. Woodruff, HELIOS-CR — a 1-D radiation-magnetohydrodynamics code with inline atomic kinetics modeling, J. Quant.Spectrosc. Radiat. Transf. 99 (2006) 381–397.

[49] J.J. MacFarlane, C.L. Rettig, P. Wang, I.E. Golovkin, P.R. Woodruff, Radiation-hydrodynamics, spectral, and atomic physics modeling of laser-produced plasmaEUVL light sources, in: R.Scott Mackay (Ed.), Emerging Lithographic Technolo-gies IX, Proceedings of the SPIE, 5751, 2005, pp. 588–600.

[50] E. Hajiyev, A. Demir, A collisional-radiative model for simulation of Ne-like andF-like resonance lines emitted from laser produced plasmas, Comp. Phys. Comm.164 (2004) 86–90.

[51] Ş. Yalçin, D.R. Crosley, G.P. Smith, G.W. Faris, Influence of ambient conditions onthe laser air spark, Appl. Phys. B 68 (1999) 121–130.

[52] J. Hermann, C. Boulmer-Leborgne, D. Hong, Diagnostics of the early phase of anultraviolet laser-induced plasma by spectral line analysis considering self-absorption, J. Appl. Phys. 83 (1998) 691–696.

[53] G.J. Tallents, An investigation of the potential of optically thick line profiles fordetermining laser-produced plasma parameters, J. Phys. B: Atom. Molec. Phys.13 (1980) 3057–3072.

[54] I.B. Gornushkin, C.L. Stevenson, B.W. Smith, N. Omenetto, J.D. Winefordner,Modeling an inhomogeneous optically thick laser-induced plasma: a simplifiedtheoretical approach, Spectrochim. Acta Part B (2001) 1769–1785.

[55] N. Arnold, J. Gruber, J. Heitz, Spherical expansion of the vapor plume intoambient gas: an analytical model, Appl. Phys. A 69 (1999) S87–S93 Suppl.

[56] S.-B. Wen, X. Mao, R. Greif, R. Russo, Expansion of the laser ablation vapor plumeinto a background gas. I. Analysis, J. Appl. Phys. 101 (2007) 023114.

[57] S.-B. Wen, X. Mao, R. Greif, R. Russo, Laser ablation induced vapor plumeexpansion into a background gas. II. Experimental analysis, J. Appl. Phys. 101(2007) 023115.

[58] S.-B. Wen, R. Greif, R. Russo, Radiative cooling of laser ablated vapor plumes:experimental and theoretical analyses, J. Appl. Phys. 100 (2006) 053104.

[59] S.-B. Wen, R. Greif, R. Russo, Analysis of laser ablation: contribution of ionizationenergy to the plasma and shockwave properties, J. Appl. Phys. 102 (2007) 043103.

[60] J.R. Ho, C.P. Grigoropoulos, J.A.C. Humphrey, Gas dynamics and radiation heattransfer in the vapor plume produced by pulsed laser irradiation of aluminum, J.Appl. Phys. 79 (1996) 7205–7215.

[61] A.V. Gusarov, A.G. Gnedovets, I. Smurov, Two-dimensional gas-dynamic modelof laser ablation in an ambient gas, Appl. Surf. Sci. 154–155 (2000) 66–72.

[62] A.V. Gusarov, A.G. Gnedovets, I. Smurov, Gas dynamics of laser ablation:influence of ambient atmosphere, J. Appl. Phys. 88 (2000) 4352–4364.

[63] C.L. Liu, J.N. Leboeuf, R.F. Wood, D.B. Geobegan, J.M. Donato, K.R. Chen, A.A.Puretzky, Computational modeling of physical processes during laser ablation,Mater. Sci. Eng. B47 (1997) 70–77.

[64] K.R. Chen, T.C. King, J.H. Hes, J.N. Leboeuf, D.B. Geohegan, R.F. Wood, A.A.Puretzky, J.M. Donato, Theory and numerical modeling of the acceleratedexpansion of laser-ablated materials near a solid surface, Phys. Rev. B 60 (1999)8373–8382.

[65] J.N. Leboeuf, K.R. Chen, J.M. Donato, D.B. Geobegan, C.L. Liu, A.A. Puretzky, R.F.Wood, Computational modeling of dynamical processes in laser ablation, Appl.Surf. Sci. 96–98 (1996) 14–23.

[66] V.I. Mazhukin, V.V. Nossov, I. Smurov, Analysis of laser-induced evaporation of Altarget under conditions of vapour plasma formation, Thin Solid Films 453–454(2004) 353–361.

[67] V.I. Mazhukin, V.V. Nossov, I. Smurov, Modeling of plasma-controlled surfaceevaporation and condensation of Al target under pulsed laser irradiation in thenanosecond regime, Appl. Surf. Sci. 253 (2007) 7686–7691.

[68] V.I. Mazhukin, V.V. Nossov, I. Smurov, Modeling of plasma-controlled evapora-tion and surface condensation of Al induced by 1.06 and 0.248 µm laserradiations, J. Appl. Phys. 101 (2007) 024922.

[69] A. Bogaerts, Z. Chen, R. Gijbels, A. Vertes, Laser ablation for analytical sampling:what canwe learn frommodeling? Spectrochim. Acta Part B 58 (2003) 1867–1893.

[70] A. Bogaerts, Z. Chen, Effect of laser parameters on laser ablation and laser-induced plasma formation: a numerical modeling investigation, Spectrochim.Acta Part B 60 (2005) 1280–1307.

[71] A. Bogaerts, Z. Chen, D. Bleiner, Laser ablation of copper in different backgroundgases: comparative study by numerical modeling and experiments, J. Anal. At.Spectrom. 21 (2006) 384–395.

[72] A. Bogaerts, Z. Chen, D. Autrique, Double pulse laser ablation and laser-inducedbreakdown spectroscopy: a modeling investigation, Spectrochim. Acta Part B 63(2008) 746–754.

[73] B. Wu, Y.C. Shin, Modeling of nanosecond laser ablation with vapor plasmaformation, J. Appl. Phys. 99 (2006) 084310.

[74] B. Wu, Y.C. Shin, H. Pakhal, N.M. Laurendeau, R.P. Lucht, Modeling andexperimental verification of plasmas induced by high-power nanosecondlaser–aluminum interactions in air, Phys. Rev. E (2007) 026405.

[75] E.A. Ershov-Pavlov, K.Yu. Katsalap, K.L. Stepanov, Yu.A. Stankevich, Time–spacedistribution of laser-induced plasma parameters and its influence on emissionspectra of the laser plumes, Spectrochim. Acta Part B 63 (2008) 1024–1037.

[76] M. Aghaei, S. Mehrabian, S.H. Tavassoli, Simulation of nanosecond pulsed laserablation of copper samples: a focus on laser-induced plasma radiation, J. Appl.Phys. 104 (2008) 053303.

[77] E. Tognoni, G. Cristoforetti, S. Legnaioli, V. Palleschi, Calibration-free laser-induced breakdown spectroscopy: state of the art, Spectrochim. Acta Part B 65(2010) 1–14.

[78] A. Ciucci, M. Corsi, V. Palleschi, S. Rastelli, A. Salvetti, E. Tognoni, New procedurefor quantitative elemental analysis by laser-induced plasma spectroscopy, Appl.Spectrosc. 53 (1999) 960–964.

[79] A. Ciucci, V. Palleschi, S. Rastelli, A. Salvetti, D.P. Singh, E. Tognoni, CF-LIPS: a newapproach to LIPS spectra analysis, laser part, Beams 17 (1999) 793–797.

[80] D. Bilajic, M. Corsi, G. Cristoforetti, S. Legnaioli, V. Palleschi, A. Salvetti, E. Tognoni,A procedure for correcting self-absorption in calibration-free laser-inducedbreakdown spectroscopy, Spectrochim. Acta Part B 57 (2002) 339–353.

[81] E. Tognoni, G. Cristoforetti, S. Legnaioli, V. Palleschi, A. Salvetti, M. Mueller, U.Panne, I. Gornushkin, A numerical study of expected accuracy and precision incalibration-free laser-induced breakdown spectroscopy in the assumption ofideal analytical plasma, Spectrochim. Acta Part B 62 (2007) 1287–1302.

[82] M. Corsi, V. Palleschi, A. Salvetti, E. Tognoni, Calibration free laser-inducedplasma spectroscopy: a newmethod for combustion products analysis, Clean Air3 (2002) 69–79.

[83] M. Corsi, G. Cristoforetti, M. Hidalgo, S. Legnaioli, V. Palleschi, A. Salvetti, E.Tognoni, C. Vallebona, Application of laser-induced breakdown spectroscopytechnique to hair tissue mineral analysis, Appl. Opt. 42 (2003) 6133–6137.

[84] M. Corsi, G. Cristoforetti, M. Hidalgo, S. Legnaioli, V. Paleschi, A. Salvetti, E.Tognoni, C. Vellebona, Double pulse, calibration-free laser-induced breakdownspectroscopy: a new technique for in situ standard-less analysis of polluted soils,Appl. Geochem. 21 (2006) 748–755.

[85] L. Angeli, C. Arias, G. Cristoforetti, C. Fabbri, S. Legnaioli, V. Palleschi, G. Radi, A.Salvetti, E. Tognoni, Spectroscopic techniques applied to the study of italianpainted neolithic potteries, Laser Chem. 2006 (2006) Article ID 61607.

[86] I. Borgia, L.M.F. Burgio, M. Corsi, R. Fantoni, V. Palleschi, A. Salvetti, M.C.Squarcialupi, E. Tognoni, Self-calibrated quantitative elemental analysis by laser-induced plasma spectroscopy: application to pigment analysis, J. Cult. Herit. 1(2000) S281–S286.

[87] V.S. Burakov, V.V. Kiris, P.A. Naumenkov, S.N. Raikov, Calibration-free laserspectral analysis of glasses and copper alloys, Russ. J. Appl. Spectrosc. 71 (2004)740–746.

[88] M.V. Bel'kov, V.S. Burakov, V.V. Kiris, N.M. Kozhukh, S.N. Raikov, Spectralstandard-free microanalysis of gold alloys, Russ. J. Appl. Spectrosc. 72 (2005)376–381.

[89] V.S. Burakov, S.N. Raikov, Quantitative analysis of alloys and glasses by acalibration-free method using laser-induced breakdown spectroscopy, Spectro-chim. Acta Part B 62 (2007) 217–223.

[90] A. De Giacomo, M. Dell'Aglio, O. De Pascale, R. Gaudiuso, R. Teghil, A. Santagata,G.P. Parisi, ns- and fs-LIBS of copper-based-alloys: a different approach, Appl.Surf. Sci. 253 (2007) 7677–7681.

[91] L. Fornarini, F. Colao, R. Fantoni, V. Lazic, V. Spizzicchino, Calibration analysis ofbronze samples by nanosecond laser-induced breakdown spectroscopy: atheoretical and experimental approach, Spectrochim. Acta Part B 60 (2005)1186–1201.

[92] F. Colao, R. Fantoni, V. Lazic, A. Paolini, F. Fabbri, G.G. Ori, L. Marinangeli, A. Baliva,Investigation of LIBS feasibility for in situ planetary exploration: an analysis onMartian rock analogues, Planet. Space Sci. 52 (2004) 117–123.

[93] B. Sallé, J.-L. Lacour, P. Mauchien, P. Fichet, S. Maurice, G. Manhès, Comparativestudy of different methodologies for quantitative rock analysis by laser-inducedbreakdown spectroscopy in a simulated Martian atmosphere, Spectrochim. ActaPart B 61 (2006) 301–313.

[94] I.B. Gornushkin, A.Y. Kazakov, N. Omenetto, B.W. Smith, J.D. Winefordner,Radiation dynamics of post-breakdown laser-induced plasma, Spectrochim. ActaPart B 59 (2004) 401–418.

[95] I.B. Gornushkin, A.Y. Kazakov, N. Omenetto, B.W. Smith, J.D. Winefordner,Experimental verification of a radiative model of laser-induced plasmaexpanding into vacuum, Spectrochim. Acta Part B 60 (2005) 215–230.

[96] I.B. Gornushkin, S.V. Shabanov, N. Omenetto, J.D. Winefordner, Theoreticalmodeling of a non-isothermal asymmetric expansion of laser-induced plasma invacuum, J. Appl. Phys. 100 (2006) 073304.

[97] S.V. Shabanov, I.B. Gornushkin, J.D. Winefordner, Radiation from asymmetriclaser-induced plasmas collected by a lens or optical fiber, Appl. Opt. 47 (2008)1745–1756.

[98] A.Y. Kazakov, I.B. Gornushkin, N. Omenetto, B.W. Smith, J.D. Winefordner,Radiation dynamics of post-breakdown laser-induced plasma expanding intoambient gas, Appl. Opt. 45 (2004) 2810–2820.

[99] P. Yaroshchyk, D. Body, R.J.S. Morrison, B.L. Chadwick, A semi-quantitativestandard-less analysis method for laser-induced breakdown spectroscopy,Spectrochim. Acta Part B 61 (2006) 200–209.

[100] C.A. D'Angelo, D.M.D. Pace, G. Bertuccelli, D. Bertuccelli, Laser-inducedbreakdown spectroscopy on metallic alloys: solving inhomogeneous opticallythick plasmas, Spectrochim. Acta Part B 63 (2008) 367–374.

[101] K. Herrera, E. Tognoni, I.B. Gornushkin, N. Omenetto, B.W. Smith, J.D. Wine-fordner, Comparative study of two standard-free approaches in laser-inducedbreakdown spectroscopy as applied to the quantitative analysis of aluminumalloy standards under vacuum conditions, J. Anal. At. Spectrom. 24 (2009)426–438.

[102] J.A. Aguilera, C. Aragon, Characterization of a laser-induced plasma by spatiallyresolved spectroscopy of neutral atom and ion emissions. Comparison of local


and spatially integrated measurements, Spectrochim. Acta Part B 59 (2004)1861–1876.

[103] C.W. An, Y.F. Lu, Y.W. Goh, E. Tan, Observation of species distribution in laser-induced plasma, Appl. Surf. Sci. 154–155 (2000) 269–275.

[104] G.S. Settles, Schlieren and Shadowgraph Techniques: Visualizing Phenomena inTransparent Media, Springer-Verlag, Berlin, 2001.

[105] I.H. Hutchinson, Principles of Plasma Diagnostics, Cambridge University Press,Cambridge, 2002.

[106] M. Corsi, G. Cristoforetti, M. Hidalgo, D. Iriarte, S. Legnaioli, V. Palleschi, A.Salvetti, E. Tognoni, Temporal and spatial evolution of a laser-induced plasmafrom a steel target, Appl. Spectrosc. 57 (2003) 715–721.

[107] G. Cristoforetti, S. Legnaioli, L. Pardini, V. Palleschi, A. Salvetti, E. Tognoni,Spectroscopic and shadowgraphic analysis of laser-induced plasmas in theorthogonal double pulse pre-ablation configuration, Spectrochim. Acta Part B 57(2006) 340–350.

[108] T.Y. Choi, D.J. Hwang, C.P. Grigoropoulos, Femtosecond laser-induced ablation ofcrystalline silicon upon double beam irradiation, Appl. Surf. Sci. 197–198 (2002)720–725.

[109] H. Borchert, K. Darée, M. Hugenschmidt, Plasma formation during the interactionof picosecond and nanosecond laser pulses with BK7 glass, J. Phys. D 38 (2005)300–305.

[110] M. Hauer, D.J. Funk, T. Lippert, A. Wokaun, Time resolved study of the laserablation induced shockwave, Thin Solid Films 453–454 (2004) 584–588.

[111] X. Zeng, X.L. Mao, R. Greif, R.E. Russo, Experimental investigation of ablationefficiency and plasma expansion during femtosecond and nanosecond laserablation of silicon, Appl. Phys. A 80 (2005) 237–241.

[112] C.Y. Liu, X.L. Mao, R. Greif, R.E. Russo, Time resolved shadowgraph images ofsilicon during laser ablation: shockwaves and particle generation, J. Phys. Conf.Ser. 59 (2007) 338–342.

[113] X. Mao, S.-B. Wen, R.E. Russo, Time resolved laser-induced plasma dynamics,Appl. Surf. Sci. 253 (2007) 6316–6321.

[114] X. Zeng, X. Mao, S.S. Mao, S.-B. Wen, R. Greif, R.E. Russo, Laser-inducedshockwave propagation from ablation in a cavity, Appl. Phys. Lett. 88 (2006).

[115] I.B. Gornushkin, M. Clara, B.W. Smith, J.D. Winefordner, U. Panne, R. Niessner,Time-resolved resonance shadow imaging of laser-produced lead and tinplasmas, Spectrochim. Acta Part B 52 (1997) 1617–1625.

[116] Y. Okano, Y. Hironaka, K.G. Nakamura, K.-I. Kondo, Time-resolved electronshadowgraphy for 300 ps laser ablation of a copper film, Appl. Phys. Lett. 83(2003) 1536–1538.

[117] Y. Hironaka, T. Inoue, Y. Fujimoto, K.G. Nakamura, K.-I. Kondo, M. Yoshida, Time-resolved X-ray shadowgraphy experiment of laser ablation of aluminum usinglaser-induced picosecond pulsed X-rays, Jpn. J. Appl. Phys. 38 (1999) L242–L244.

[118] O. Iwase, W. Süß, D.H.H. Hoffmann, M. Roth, C. Stöckl, M. Geissel, W. Seelig, R.Bock, Laser-produced plasma diagnostics by a combination of schlieren methodand Mach–Zehnder interferometry, Phys. Scr. 58 (1998) 634–635.

[119] T.J. Englert, M.A. Beik, Using the second harmonic from a Nd:YAG as a probebeam for determination of free electron density in a plasma induced by thefundamental, Rev. Sci. Instrum. 61 (1990) 3783–3786.

[120] P.L.G. Ventzek, R.M. Gilgenbach, J.A. Sell, D.M.Heffelfinger, Schlierenmeasurementsof the hydrodynamics of excimer laser ablation of polymers in atmosphericpressure gas, J. Appl. Phys. 68 (1990) 965–968.

[121] C. Wang, S. Xu, G. Jia, Laser-induced spark ignition of H2/O2/Ar mixtures, Sci.China E 50 (2007) 797–806.

[122] A. Vogel, V. Venugopalan, Mechanisms of pulsed laser ablation of biologicaltissues, Chem. Rev. 103 (2003) 577–644.

[123] A. Vogel, I. Apitz, S. Freidank, R. Dijkink, Sensitive high-resolution white-lightschlieren technique with a large dynamic range for the investigation of ablationdynamics, Opt. Lett. 31 (2006) 1812–1814.

[124] L.A. Doyle, G.W. Martin, A. Al-Khateeb, I. Weaver, D. Riley, M.J. Lamb, T. Morrow,C.L.S. Lewis, Electron number density measurements in magnesium laserproduced plumes, Appl. Surf. Sci. 127–129 (1998) 716–720.

[125] H. Schittenhelm, G. Callies, P. Berger, H. Hügel, Time-resolved interferometricinvestigations of the KrF-laser-induced interaction zone, Appl. Surf. Sci. 109–110(1997) 493–497.

[126] H. Schittenhelm, G. Callies, P. Berger, H. Hügel, Two-wavelength interferometryon excimer laser induced vapour/plasma plumes during the laser pulse, Appl.Surf. Sci. 127–129 (1998) 922–927.

[127] R. Noll, R. Sattmann, V. Sturm, S. Winkelmann, Space- and time-resolveddynamics of plasmas generated by laser double pulses interacting with metallicsamples, J. Anal. At. Spectrosc. 19 (2004) 419–428.

[128] W. Sdorra, K. Niemax, Temporal and spatial distribution of analyte atoms andions in microplasmas produced by laser ablation of solid samples, Spectrochim.Acta Part B 45 (1990) 917–926.

[129] W. Sdora, A. Quentmeier, K. Niemax, Basic investigations for laser microanalysis:II. Laser-induced fluorescence in laser-produced sample plumes, Microchim.Acta 98 (1989) 210–218.

[130] W. Sdorra, A. Quentmeier, K. Niemax, Measurement of atomic fine structurecollision transfer cross sections in laser produced vapors, Z. Phys. D. Atoms, Mol.Clust. 13 (1989) 95–99.

[131] V. Margetic, T. Ban, F. Leis, K. Niemax, R. Hergenröder, Hydrodynamic expansionof a femtosecond laser produced plasma, Spectrochim. Acta Part B 58 (2003)415–425.

[132] V. Margetic, T. Ban, F. Leis, O. Samek, F. Leis, K. Niemax, R. Hergenröder, Shock-wave velocity of a femtosecond laser-produced plasma, Czech. J. Phys. 54 (2004)423–429.

[133] V.S. Burakov, N.V. Tarasenko, N.A. Savastenko, Plasma chemistry in laser ablationprocesses, Spectrochim. Acta Part B 56 (2001) 961–971.

[134] C. Dutouquet, J. Hermann, Laser-induced fluorescence probing during pulsed-laser ablation for three-dimensional number density mapping of plasma species,J. Phys. D: Appl. Phys. 34 (201) 3356–3363.

[135] V.E. Bondybey, J.H. English, Laser-induced fluorescence of metal clustersproduced by laser vaporization: gas phase spectrum of Pb2, J. Chem. Phys. 74(1981) 6978–6979.

[136] V.E. Bondybey, J.H. English, Laser excitation spectra and lifetimes of Pb2 and Sn2

produced by YAG laser vaporization, J. Chem. Phys. 76 (1982) 2165–2170.[137] V.E. Bondybey, Laser-induced fluorescence and bonding of metal dimers, Science

227 (1985) 125–131.[138] A.A. Puretzky, D.B. Geohegan, LIF imaging and gas-phase diagnostics of laser-

desorbed MALDI-matrix plumes, Appl. Surf. Sci. 127–129 (1998) 248–254.[139] Y. Matsuo, T. Kobayashi, M. Kurata-Nishimura, T. Kato, T. Motobayashi, J. Kawai, Y.

Hayashizaki, LIF observation of neutral atoms and ions produced by femtosecondlaser ablation of Sm on a substrate, J. Phys. Conf. Ser. 59 (2007) 555–558.

[140] H. Watarai, K. Sasaki, Dynamics of laser-ablation plume and ambient gasvisualized by two-dimensional laser-induced fluorescence, Appl. Opt. 42 (2003)6001–6005.

[141] T. Okada, Y. Nakata, M. Maeda, Diagnostics of particle dynamics during opticallyfunctional thin-film deposition by laser ablation, RIKEN Rev. 50 (2003) 29–33.

[142] J.C. Hirsch, E.T. Kennedy, A. Neogi, J.T. Costello, P. Nicolosi, L. Poletto, Vacuum-ultraviolet photoabsorption imaging system for laser plasma plume diagnostics,Rev. Sci. Instrum. 74 (2003) 2992–2998.

[143] I.B. Gornushkin, C.L. Stevenson, G. Galbacs, B.W. Smith, J.D. Winefordner, Measure-ment and modeling of ozone and nitrogen oxides produced by laser breakdown inoxygen–nitrogen atmospheres, Appl. Spectrosc. 57 (2003) 1442–1450.

[144] L.A. King, I.B. Gornushkin, D. Pappas, B.W. Smith, J.D. Winefordner, Rubidiumisotope measurements in solid samples by laser ablation–laser atomicabsorption spectroscopy, Spectrochim. Acta Part B 54 (1999) 1771–1781.

[145] A. Quentmeier, M. Bolshov, K. Niemax,Measurement of uranium isotope ratios insolid samples using laser ablation and diode laser-atomic absorption spectrom-etry, Spectrochim. Acta Part B 56 (2001) 45–55.

[146] I.B. Gornushkin, L.A. King, B.W. Smith, N. Omenetto, J.D. Winefordner, Linebroadening mechanisms in the low pressure laser-induced plasma, Spectrochim.Acta Part B 54 (1999) 1207–1217.

[147] I. Labazan, S. Milošević, Observation of lithium dimers in laser produced plumeby cavity ring-down spectroscopy, Chem. Phys. Lett. 352 (2002) 226–233.

[148] N. Krstulović, N. Čutić, S. Milošević, Spatial and temporal probing of a laser-induced plasma plume by cavity ringdown spectroscopy, Spectrochim. Acta PartB 63 (2008) 1233–1239.

[149] N. Krstulović, N. Čutić, S. Milošević, Cavity ringdown spectroscopy collinear dual-pulse laser plasmas in vacuum, Spectrochim. Acta Part B 64 (2009) 271–277.

[150] J.D. Swift, M.J.R. Schwar, Electrical Probes for Plasma Diagnostics, Iliffe Books Ltd.,London, 1970.

[151] J. Wild, P. Kudrna, T. Gronych, T. Jirsák, P. Kubát, Z. Zelinger, S. Civiš, Langmuirprobe measurement of the electron temperature in the plasma plume formed bypulsed laser deposition of Bi–Sr–Ca–Cu–O, Czech. J. Phys. 53 (2003) 171–177.

[152] T.N. Hansen, J. Schou, J.G. Lunney, Langmuir probe study of plasma expansion inpulsed laser ablation, Appl. Phys. A 69 (1999) S601–S604 Suppl.

[153] G.O. Williams, G.M. O'Connor, P.T. Mannion, T.J. Glynn, Langmuir probeinvestigation of surface contamination effects on metals during femtosecondlaser ablation, Appl. Surf. Sci. 254 (2008) 5921–5926.

[154] P. Mannion, S. Favre, G.M. O'Connor, B. Doggett, J.G. Lunney, T.J. Glynn, Langmuirprobe study of plasma expansion in femtosecond pulsed laser ablation of silver,Proc. SPIE 5827 (2005) 457–466.

[155] K. Warner, G.M. Hieftje, Thomson scattering from analytical plasmas, Spectro-chim. Acta Part B 57 (2002) 201–241.

[156] A. Delserieys, F.Y. Khattak, C.L.S. Lewis, D. Riley, J. Pedregosa Gutierrez, OpticalThomson scatter from laser-ablated plumes, Appl. Phys. Lett. 92 (2008) 011502.

[157] P.K. Diwakar, D.W. Hahn, Study of early laser-induced plasma dynamics:transient electron density gradients via Thomson scattering and Starkbroadening, and the implications on laser-induced breakdown spectroscopymeasurements, Spectrochim. Acta Part B 63 (2008) 1038–1046.

radiative models of laser-induced plasma and pump-probe diagnostics relevant to laser-induced...

Documents