Excitation dynamics during the multiphoton absorption in SF6.pdf

8/13/2019 Excitation dynamics during the multiphoton absorption in SF6.pdf

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Journal of Quantitative Spectroscopy &

Radiative Transfer 76 (2003) 8599

www.elsevier.com/locate/jqsrt

Excitation dynamics during the multiphoton absorption inSF6+buer-gas mixtures

D.D. Markusheva ;, J. Jovanovic-Kurepaa, M. Terzicb

aInstitute of Physics, P.O. Box 57, 11001 Beograd, Serbia, YugoslaviabFaculty of Natural Sciences and Mathematics, Trg Dositeja Obradovica 4, 21000 Novi Sad, Serbia, Yugoslavia

Received 21 November 2001; accepted 19 March 2002

Abstract

A detailed analysis of the total average number of absorbed photons ntotal during Infrared multiphotonabsorption processes in mixtures of SF6Ar, N2 and CH4 buer gases is presented. The results for ntotalare deduced using pulsed photoacoustic technique in collisional regime. Complete analysis is based on the

theoretical generalized coupled two-level model (GCT) and its application to dierent gas mixtures. Evaluation

of partial ncoll: values is presented too, obtained using the results from time-resolved optoacoustic (TROA)and time-resolved absorption (TRA) methods for VT relaxation times (VT) and the saturable absorber (SA)

method for R,RT relaxation times (rot:rel:), and applying them directly to the GCT model. All methods

(TROA and SA) and the GCT model use the same photoacoustic results from our experiment under identicalexperimental conditions. ? 2002 Elsevier Science Ltd. All rights reserved.

Keywords:Multiphoton excitation; Photoacoustic spectroscopy; Collisional relaxation

1. Introduction

It is well known that polyatomic molecules in the gas phase, irradiated with infrared laser radiation

eld, could be highly vibrationally excited from their ground state, absorbing more than one radiation

eld photon. Actually, this will happen only if the frequency of the radiation eld is coincident withone of molecular absorption line frequency, and if the laser uence is high enough to induce direct

moleculeeld interaction. Such an absorption process is called laser-induced infrared multiphoton

absorption process (IRMPA). Investigation of IRMPA in polyatomic molecules gives very important

information concerning physical properties of absorbing molecules, such as enhanced absorption cross

sections (e) as well as dierential absorption cross sections (d), parameters of molecular vibrational

structure, dissociation level and also vibrational and rotational relaxation parameters. However, the

Corresponding author. Tel.: +381-11-31-60-260; fax: +381-11-31-62-190.

E-mail address: [email protected] (D.D. Markushev).

0022-4073/02/$ - see front matter? 2002 Elsevier Science Ltd. All rights reserved.

P I I : S 0022- 4073(02)00047- X


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D.D. Markushev et al. / Journal of Quantitative Spectroscopy & Radiative Transfer 76 (2003) 85 99 87

methods (GCT, TROA, TRA and SA) use the same basic photoacoustic results obtained in our

experiment under the given (and identical) experimental conditions. Finally, it will be shown that

this type of analysis can be used in dierent gas mixtures, not only with atomic but also with

molecular buer-gas species (N2 and CH4 for example).

2. Experimental apparatus and methods

Our experimental apparatus was specially designed to satisfy the criteria for simultaneous use

of PAS and TRS techniques with the parallel laser beam. The detailed description of this appa-

ratus is given elsewhere [14,15,22]. All our investigations are performed in medium uence range

0.10:5 J=cm2, with 10P(16)CO2 laser line (FWHM 45 ns) characterized with the top-hat pro-

le, in 10100 mbar buer gas (Ar, N2 or CH4) pressure range and a constant SF6 pressure of

0:47 mbar, at room temperature. To obtain the average value of needed experimental quantities, foreach experimental point, typical 60180 laser pulses were used.

As mentioned in the previous paragraph, the main experimental parameter obtained and analyzed in

this work is the total average number of absorbed photonsntotal for the SF6 molecule surrounded byAr atoms (or N2 and CH4 molecules) used as buer-gas species. The measurements were performed

using PAS technique, which means that the experiment directly gives only relative data. However,

to obtain quantitative PAS IRMPA results, calibration of the experimental apparatus was done using

simultaneously taken results of absolute spectroscopy technique (TRS in our case). Details of the

calibration procedure with TRS are given in Ref. [14].

The equation used to evaluate ntotal values from the experimental PAS parameters, valuable forall types of gas mixtures, has the form [14,15]

ntotal =

hNlmln

1

S(p;;T)Pa

Ei

; (1)

where h is laser photon energy, N is concentration of investigated gas mixture, lm is length of

photoacoustic microphone (detector) mounted inside the experimental cell, used to detect acoustic

waves, Ei is incoming laser energy and S(p;;T) is calibration sensitivity factor. S(p;;T) i s a

function of gas sample pressure (p), characteristics of gas particles (= cp=cV) and temperature

inside the experimental cell (T). This equation has two important characteristics which must be

pointed out. First it shows, because Eq. (1) is obtained from the LambertBeer law, that ntotalcorresponds to the average energy (E) absorbed in the irradiated volume during the laser pulse

(E =hntotal). We must note that the value (E) is not always equal to the average energyalready stored in vibrational modes of absorbing molecules (E), especially when working withlong-tail pulses. Second, in the case of the top-hat prole of the laser pulse, this equation gives

the same value for ntotal all over the irradiated volume, for constant pressure of the investigatedgas mixture during the laser pulse.

The base of the GCT model is a coupled two-level absorber model described in detail in Ref.

[6]. This model contains the following features [6,10]. A nite bandwidth radiation eld interacts

with one of several rotational states of a vibrational level of a molecule to promote transitions to an

upper vibrational state. This interaction was considered in a rate equation approximation, resulting

from direct spectral overlap of radiation eld and the absorbing transition of the molecule. Other


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88 D.D. Markushev et al. / Journal of Quantitative Spectroscopy & Radiative Transfer 76 (2003) 85 99

rotational states that are not coupled directly to the radiation eld constitute a set of reservoir states

that may be indirectly coupled to interacting rotational levels through collisions. Other vibrational

levels that are coupled to the interacting states either by collisional or collisionless intermodal VV

transfer process are also included in the reservoir states.An approximate solution of dierential equations which describes the optical and collisional tran-

sitions among the four levels of the model (two absorber levels and two reservoir levels) is given

[6] in the form

n()

f = 1 exp

0

f

; (2)

which gives the relationship between the average number of absorbed photons per molecule n() and

three variables: (uence), 0 (small-signal absorption cross section) and f (the eective fractionof the population for a given vibrational transition which is coupled to the radiation eld because of

collisional relaxation process). n() in this equation is not a spatial average, but a local value thatone can relate to the experimental values ntotal through Eq. (1) in the case of the top-hat spatial

prole of the used laser beam (our case). The approximate expression for f has the form [6]

f = dfi

1 exp

fr

1 fr

p

1 +

frfi

0

p

1 exp

p

+dfrfiexp

p

; (3)

where fi is the fraction of molecules in the absorbing (usually ground) vibrational level (fi =0:3 for

SF6 at 300 K), and fr is the fraction offi molecules in the initial distribution that interacts directlywith the radiation eld. fr can be obtained theoretically using the simple relation fr=LF(),

where L is laser line width and F() is the absorption distribution function for a given absorbing

molecule and dened experimental conditions [6]. The quantity d is dened as

d=

1 +; (4)

where is the ratio of degeneracy of the upper and lower vibrational levels, p is laser pulse length

and is equilibration time of the absorber level and reservoir level, usually taken as rotational

relaxation time in the previous investigation [6,10].

This model is valid in three limiting cases: (1) weak coupling (collisionless), when (p=) 1;(2) strong coupling (collisional) when p= 1 and ux is low (0=(fpfip) 1); (3) strong

coupling (collisional) when p= 1 and ux is high (0=(fpfip) 1). However, this model,

because of such normalization procedure, is not valid in the case of IRMPA processes when s,

where s is an IRMPA starting uence. Then the two-level approximation breaks down. The problem

lies in the fact that Eq. (2) predicts that n() approaches a constant value at high uence. Experimen-

tal results show that n() continues to increase in large polyatomic molecules. Knowing these prob-

lems, the generalization of a coupled two-level model was done [6]. Briey, if one assumes that the

dynamics of the molecule-radiation eld is, in rst approximation, controlled by the lower vibrational

level of the absorbing transition, then the generalized Eq. (2) can be written in normalized functional


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form, taking the limit , as [6]

n()

f

=G0

f ; (5)

which is valid for (0=f) 1, and approaches the two-level result in Eq. (2) for (0=f) 1.Experiments show that, in the case of SF6; G(0=f) (0=f)

2=3 in the high-uence regime,

e.g. when (0=f) 1. Knowing this, for the collisional and high-uence regime Eq. (3) can bewritten in the form [6]

f =fi

1 exp

fr1 fr

p

; (6)

while Eq. (5), in our case, is

ntotal(pbu:; ) = f1=3

(0)

2=3

=

fi

1 exp fr

1 fr

p

1=3

(0)

2=3

; (7)

where, concerning our experimental conditions e.g. top-hat prole and quality of our laser beam,

n() in Eq. (5) is equal to ntotal in Eq. (1). Eq. (7) is the main equation obtained with the GCTmodel which will be utilized in our investigation.

Let us analyze the IRMPA processes during the laser pulse in collisionless and collisional regime.

Generally speaking, if there is no collision between absorbing molecules (or absorbing molecules and

buer-gas particles) only the laser uence is responsible for the excitation level of the absorbing

molecule, and one can write that ntotal= n. But collisions play a very important role in IRMPAprocesses. They can repopulate preferentially pumped rovibrational states, broaden the absorption

lines of the absorbing molecule (mainly through rotational relaxation) and also deactivate excited

molecules (mainly through VT relaxation), allowing them to absorb more photons during the laserpulse. Knowing this, it is possible to write a simple expression for ntotal in the form

ntotal = n+ ncoll: (8)

or

ntotal = n+ nrot:+ nVT+ nVV; (9a)

assuming that ncoll:= nrot:+ nVT+ nVV nrot:; nVT and nVV represents partial valuesofncoll: originating from collisionally induced rotational relaxation (R, RT), vibrational to transla-tional (VT) and intermolecular vibrational to vibrational (VV) relaxation of absorbing molecules

(SF6) respectively, during the laser pulse. When we talk about rotational relaxation, we assume,so-called positive relaxation in the manner of its inuence on photon absorption. Such a process,

keeping the absorbed photons inside the rovibrational modes of a molecule, is rotation to rotation

(RR) relaxation. The rotational to translational (RT) process is present too, but, according to our

experimental conditions, its inuence on multiphoton absorption is much lower in comparison with

RR processes. Possible intermolecular VV relaxation processes occur only in the case of molecular

buer gas, and its existence strongly depends on experimental conditions. In the case of atomic and

most molecular buers, this process can be neglected, and Eq. (9a) can be written in the form

ntotal = n+ nrot:+ nVT (9b)


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or, knowing that E =hn,

E = Etotal = E+ Erot:+ EVT= E+ Et; (9c)

where E = E + Erot: represents the average energy stored in the vibrational modes of theabsorbing molecule (real level of excitation), and Et =EVT represents the average energyreleased from the absorber stored in the translational modes of gas mixture colliding partners (mostly

buer-gas species).

The main goal of this work is to show that, using the GCT model (Eq. (7)), it is possible to

obtain all physical quantities appearing in Eqs. (8) and (9ac) directly, or using some PAS results

(obtained by TROA, TRA and SA methods), as functions of laser uence, buer-gas pressure and

small-signal absorption cross section 0.

The basic idea consists of the following. Using pulsed PAS technique it is possible to obtain,

experimentally, ntotal values using Eq. (1), as a function of the buer-gas pressure at constant laseruence . Now these results can be tted using the nal result of the GCT model, with functional

form based on Eq. (7), given as

ntotal(pbu:; ) = {[1 exp(apbu:)]b}1=3f

1=3

i (0)2=3; (10)

assuming that fi; 0 and are already known. However, a and b are tting parameters. Analyzing

this equation, it is obvious that it consists of two parts which represent dierent inuences on the

multiphoton absorption process: the rst part {[1exp(apbu:)]b}fi presents the pressure inuenceof investigated gas mixture (in most cases pressure of the buer gas, because this pressure is much

larger than the pressure of absorbing molecules), and the second part presents the inuence of laser

uence (0). Comparing Eqs. (6) and (10) it is obvious that

apbu:= fr

1 fr

p

: (11)

Because not only RR and RT but also VT relaxation is responsible for the nally obtained value

ofntotal, we must take that = coll: where coll: (1coll:= Ztotal number of collisions per second)

includes all average lifetimes of all possible collisional processes between molecular absorber and

buer-gas species. Then all types of collisions have an inuence on ntotal value.On the other hand, if one wants to obtain partial values of ntotal depending only on buer-gas

pressure, the GCT model can be used substituting with one of the relaxation times correspond-

ing to dominant collisional process for given experimental conditions. These relaxation times mustbe obtained with some other spectroscopy technique. In our case we have obtained, independently,

relaxation times for all possible collisional processes, such as rotational to rotational (rot:), vibra-

tional to vibrational (VV) and vibrational to translational (VT) relaxation, dependent on the type

of buer-gas species and pressure of absorbing molecules. In the case of low molecular absorber

partial pressure and atomic types of buer-gas species, it is enough to know only rot: and VT,

while only these processes are present. In such a case we adopt some PAS methods, using the

obtained PAS experimental results. These methods are TROA and TRA for VT relaxation time

determination (VT), and the SA method for rotational to rotational relaxation time determination

(rot:). They give the needed relaxation times directly. Knowing these parameters ( VT and rot:),


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Eq. (10) can be written in the general form suitable for nrot: or for nVT:

nk(bu:; ) = 1 expacoll:

tkbu: b

1=3

f1=3

i (0)2=3; (12)

where k subscript corresponds to rot. or VT, indicating which process one would like to analyze.

Concerning the tting parameter b, it is connected with the maximal fraction of absorbing

molecules (SF6 in our case) which are directly coupled with laser radiation eld inside the ir-

radiated volume, due to collisions between absorbing and nonabsorbing gas-mixture species. We

will denote this parameter as fcoll:max. Then we can write that the fraction of the molecules, in-

side the laser beam volume directly coupled to the radiation eld because of the collisions, is

{[1 exp(apbu:)]b}fi =fcoll: and, concerning Eq. (6), fcoll: f. On the other hand, value1 fcoll:max is equal to f representing the fraction of absorbing molecules which are coupled withradiation eld due to the inuence of laser uence. Now using Eqs. (12) and (8) it is possible to

calculate all partial values of ntotal, which allows one to understand the details and dynamics ofIRMPA processes inside the irradiated volume during the laser pulse.

3. Results and discussion

As mentioned before, PAS technique gives relative IRMPA data and, if someone wants to have

absolute values of investigated parameters, some of the absolute techniques (i.e. TRS) must be

used for calibration purposes. If one wishes to analyze IRMPA processes, concretely their important

physical quantities as a function of laser uence and pressure of the buer gas, it is suitable to adopt

the GCT model as a powerful tool for such purposes. To apply this method, some parameters must

be known (from the literature or previous measurements) or preset. (i) the number of collisions persecond (Z) in the investigated gas sample (Z pbu: in the case of small partial pressure of theabsorbing molecules); (ii) the number of molecules interacting directly with the laser radiation eld

(f; it is known from the literature) [23], uence () and the laser line width (L) (L =0:13 cm1

in our case) of used laser source. Quantity f is a function of laser uence and laser line width

L. Our investigations show that f signicantly changes as a function of , which is expected,

and is approved by dierent authors [23].

Using our PAS experimental set-up, Eq. (1), and measuring relevant experimental data, the number

of absorbed photons in SF6 + Ar mixtures, ntotal values, can be obtained (Fig. 1) as a functionof Ar buer-gas (pAr) pressure and laser uence . Solid lines are obtained with GCT model

tting procedure with the functional dependence given in Eq. (10). It is obvious from these results(Fig. 1) that the GCT model satises the criteria for IRMPA analysis for all investigated pressure

and uence ranges.

Generally speaking, these results can be analyzed separately for two dierent pressure ranges: low

( 50 mbar) and high ( 50 mbar). These two ranges are of interest because of dierent roles by

which the collisional eects inuence IRMPA processes.

The lower pressure range ( 50 mbar) of the gas mixture is characterized as a range where the

highest collisional inuence on molecular absorption eciency is present. This inuence is followed

by rapid growth of ntotal values, which means that on raising the pressure of the buer gas, moreabsorbing (SF6) molecules inside the irradiated volume are directly coupled with the laser radiation


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-20 0 20 40 60 80 100 120 140 1600

20

40

60

SF6+Ar

= 0,198J/cm2

/[p

hotonspermolecule]

pAr

/ [ mbar ]

0

20

40

60

SF6+Ar

SF6+Ar

= 0,314J/cm2

0

20

40

60

= 0,486J/cm2

0 20 40 60 80 100 120 140

0

20

40

60

SF6+Ar

= 0.198J/cm2

/[photonspermolecule]

pAr

/ [ mbar ]

0

20

40

60

SF6+Ar

SF6+Ar

= 0.314J/Cm2

0

20

40

60

= 0.486J/cm2

Fig. 1. Average number of absorbed photons ntotal inSF6 + Ar mixture during the laser-induced IRMPA pro-

cesses obtained with PAS using TRS calibration proce-

dure, as a function of Ar buer-gas (pAr) pressure and

laser uence .

Fig. 2. Functional dependence ntotal = f(p) in thepressure range pbu: 50 mbar can be given in the

form f(p)(apAr)1=3. Functional dependence in the

pressure range pbu: 50 mbar can be written as

ntotal= f(p) = const:

eld. In this pressure range functional dependence (GCT model) ntotal = f(p) is given in the formf(p)(apAr)

1=3 (Fig. 2). Such results are in accordance with the GCT model and they are predicted

by Eq. (10), knowing that exp(apAr)(1 apAr) if apAr1 (a102 mbar1). The dominant

collisional process responsible for such ntotal behavior is rotational to rotational relaxation, whichincludes all (allowed and forbidden) rovibrational transitions and eliminates so-called rotational holelling eect. This fact allows us to use Eq. (12), substituting obtained rot: values instead ofk and

evaluating nrot: partial values.The higher pressure range ( 50 mbar) is characterized by the saturation eect of ntotal values

(see Fig. 2). This saturation does not mean that collisions are not present, but they reach their

maximum regarding their inuence on IRMPA processes. It means that all absorbing molecules ( fi)

in the irradiated volume are directly coupled with radiation eld due to laser uence and collisions

inside the given gas mixture. Functional dependence can then be written as ntotal= f(p) = const:(for constant ), because term exp(apbu:) in Eq. (10) is near zero (0).


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We must note here that experimentally obtained values ofntotal are not only the consequence ofabsorption processes during the laser pulse. Relaxation processes play a very important role in this

type of molecular excitation, too. The following example will demonstrate the complexity of IRMPA

processes. Our results for = 0:486 J=cm2 show that ntotal was larger than 34, while n = 34 isthe dissociation level for SF6. The only logical explanation in the case when dissociation is not

present or low enough (our case) is that this large number of absorbed photons is a consequence not

only of IRMP absorption but also of molecular relaxation processes during the laser pulse. Namely,

collisional relaxation processes, in this case vibrational to translational (VT) relaxation, decrease the

vibrational excitation level of the absorbing molecule. It has great inuence on the IRMPA process

allowing VT deexcitation of the molecule and then its possibility to absorb more laser photons

during the moleculeeld interaction. This relaxation process can increase the absorption level (total

number of absorbed photons) in irradiated molecules signicantly. So, ntotal, due to VT relaxationprocesses, does not represent the vibrational excitation level of the excited molecule, but the total

average absorbed energy E per molecule irradiated by one laser pulse in the investigated gasmixture. It consists of the amount of average energy primarily absorbed by the molecule Ep atthe beginning of laser pulse, due to laser uence and RR relaxation, and the amount of average

energy released from this molecule Er due to VT relaxation as a consequence of collisions withbuer-gas species. During further analysis it will be proved that Ep corresponds to the averageenergy stored in vibrational modes of excited molecule E, and Er corresponds to the averageenergy stored in translational modes of the excited molecule Et.

To analyze the IRMPA processes and to distinguish collisional and laser uence inuence, the

GCT model was used. Evaluation of collisional inuence, parameterfcoll:, was directly obtained from

tting procedure (Eq. (12) and Fig. 1). From Eq. (10) it is obvious that [1 exp(apAr)]b = fcoll:,while this part of the equation represents the collisional inuence on ntotal values. This is valid for

the whole buer-gas pressure range. For pAr 50 mbar we can write that [1 exp(apAr)]bb,because, as mentioned in previous paragraphs, exp(apAr) 0. Knowing this, tting parameter bcan be understood as the maximum number of absorbing molecules involved in IRMPA processes,

and one can write that b= fcoll:max: (0 fcoll:6 b 1). In Fig. 3a pressure dependence of fcoll:,

obtained using the experimental data and GCT model analysis from Fig. 1, is presented as a function

of Ar pressure (pAr) for dierent laser uence values . From this gure it can be seen that fcoll:values are lower for higher uence values and higher for lower uence values. This is in accordance

with the results obtained earlier [6,12], approving that collisional inuence was stronger in the weaker

radiation elds and vice versa.

Knowing the tting parameterb=fcoll: it is possible to obtain f values (Fig. 3b) as a function of

laser uence in the investigated buer-gas pressure range. This follows from the simple relation thatf+ fcoll:max:= ftotalmax:= 1. This means that, for constant ; f has a constant value independent

of the pressure of buer gas (pressure of absorber must be constant, too). As mentioned before,

obtained results for f did not change signicantly from previous results ( 5%) obtained with

dierent L values, and identical other experimental conditions. Our results also show that values

of f are increasing when laser uence increases, and they must be in the range 0 f 1.

In Fig. 3c our results for ftotal as a function of the Ar pressure (pAr) are presented, for dierent

laser uences , too. According to the conclusions given in the previous paragraph, ftotal ftotalmax:when pAr 50 mbar, which means that all molecules, which are in proper vibrational state at room

temperature (fi), in irradiated volume interact directly with radiation eld. Also, ftotal has higher


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0 40 80 120 160 200 2400.0

0.2

0.4

0.6

0.8

1.0

f, = 0.486J/cm

2

f, = 0.314J/cm

2

f, = 0.198J/cm

2

SF6+Ar

pSF

6

= 0.46mbar

f/[a.u.]

pAr

/ [mbar](b)(a)

(c)

0 40 80 120 160 200 2400.0

0.2

0.4

0.6

fcoll.

, = 0.486J/cm2

fcoll.

, = 0.314J/cm2

fcoll.

, = 0.198J/cm2

SF6

+Ar

pSF

6

= 0.46mbar

f/[a.u.]

pAr

/ [mbar]

0 40 80 120 160 200 2400.0

0.2

0.4

0.6

0.8

1.0

1.2f

total= f

+ f

coll.

ftotal

, = 0.486J/cm2

ftotal

, = 0.314J/cm2

ftotal

, = 0.198J/cm2

SF6+Ar

pSF

6

= 0.46mbar

fmax

f/[a.u.]

pAr

/ [mbar]

Fig. 3. (a) fcoll: values, characterized with functional form [1exp(apAr)]b, presented as a function of Ar pressure (pAr)for dierent laser uence values . (b) f values as a function of laser uence obtained with f +fcoll:max =ftotalmax =1.

f has (for constant ) a constant value independent of the pressure of buer gas. (c) results for ftotal as a function of

Ar pressure (pAr) for dierent laser uences . It is obvious that, for the investigated uence range, ftotalftotalmax.

values for higher uence , which is in accordance with earlier conclusions that f, in this case,

has greater inuence on ftotal than fcoll:.

Considering ntotal values obtained in our experiment, they represent the total average energyE absorbed by one molecule during the laser pulse. But, this amount of energy must not bealways equal to the average energy stored in the vibrational modes of excited molecule E, dueto collisional deexcitation processes (VT relaxation) inside the excited volume. Knowing f and

fcoll:max: it is possible to obtain

n=fntotal and ncoll:=fcoll:max:ntotal; (13)

as the partial values of ntotal (Eqs. (8) and (10)). In Fig. 4, ntotal is presented as well as theirpartial values for three dierent laser uences: n and ncoll:.


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0 40 80 120 160 200 240

0

10

20

30

40

50

SF6+Ar

= 0.486J/cm2

pSF

6

= 0.46mbar

total

coll.

/

[photonspermolecule]

pAr

/ [mbar]

0 40 80 120 160 200 240

0

10

20

30

SF6+Ar

= 0.198J/cm2

pSF

6

= 0.46mbar

total

coll.

/


pAr

/ [mbar]

0 40 80 120 160 200 240

0

10

20

30

40

SF6+Ar

= 0.314J/cm2

pSF

6

= 0.46mbar

total

coll.

/


pAr

/ [mbar](b)(a)

(c)

Fig. 4. ntotal and partial values for dierent laser uences: (a) =0:198 J=cm2; (b) =0:314 J=cm2; (c) =0:486 J=cm2.

In the case of atomic buer gas (Ar in our case), only rotational to rotational (RR) and vibrational

to translational (VT) relaxation processes have signicant inuence on IRMPA processes. Then

Eq. (9b) represents the ntotal and its partial values in gas mixtures for atomic buer gases ingeneral. On the basis of the results obtained for VT with TROA and TRA methods (Fig. 5) and

rot:rel: (Fig. 6) obtained with the SA method for SF6Ar mixtures, using Eq. (10) we obtain the

partial values for nVT and nrot:rel:.Now, the real excitation level of the absorbing molecule (E) can be characterized byn = n + nrot:rel:, and then E = hn. On the other hand, the value of nt = nVTgives Et= hnt, so called energy stored in the translational modes of the excited molecule.

The results of our average number of absorbed photons in SF 6Ar mixtures are given in Fig. 7.

In this gure our results for the total and partial values of n are given as functions of buer-gaspressures (pAr) and laser uences () for irradiated SF6Ar mixtures, using Eqs. (12). The results

presented here (Fig. 7) show that n is larger than ncoll: e.g. laser uence has a much largerinuence on the IRMPA process in comparison with collisional eects for our investigated uence

range. Also, regarding the collisional eects, it is obvious that rotational to rotational (RR) relaxation


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0 20 40 60 80 100 120 1400

5

10

15

20

Ref. [16]

Ref. [5]

V-T

/[s]

pAr

/ [mbar]

-20 0 20 40 60 80 100 120 1400

10

20

30

40

SF6+Ar

= 0.198J/cm2

rot

/[10-8s]

pAr

/ [ mbar ]

0

10

20

30

40

SF6+Ar

SF6+Ar

= 0.314J/cm2

0

10

20

30

40

50

60

= 0.486J/cm

2

Fig. 5. Results obtained for VT with the TROA method

[16,5] for SF6Ar mixtures.

Fig. 6. Results obtained for rot:rel: with the SA method

for SF6Ar mixtures and dierent laser uences .

is the dominant relaxation process in comparison with vibrational to translational (VT) relaxation.

Concerning n, these values are not larger than 34 (for the SF6 molecule) even for the highestuences, which means that we are near the dissociation limit (3335) but not above it. This means

that, for our experimental conditions (laser temporal and spatial characteristics), dissociation does

not have signicant inuence on our results.

All GCT analysis was provided for Ar atoms as the buer gas. But, what will happen if we

have a molecular colliding partner, which means that vibrational to vibrational (VV) relaxationprocesses between absorbing and nonabsorbing gas-mixture species could have a signicant inu-

ence on IRMPA processes. In the case of diatomic or small polyatomic buer-gas molecules, one

can expect that the VV process could be present, but, in general, its inuence can be neglected in

comparison with other collisional processes mentioned before. However, in the case of large poly-

atomic buer-gas molecules such a VV process cannot be neglected. For most of the molecular

buer gases, no signicant changes in ntotal values are reported due to VV transfer, which meansthat the (VV)AB process between absorber (A) and buer-gas (B) molecules does not contribute

to the IRMPA as much as RR or VT relaxation processes. Our investigations show that such

type of molecular buer gas is, for example, N2, and results of GCT analysis of IRMPA processes


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0 40 80 120 160 200 2400

10

20

30

40

v

V-T

rot.

SF6+Ar

= 0.486J/cm2

pSF6

= 0.46mbar

total

coll.

/


pAr

/ [mbar]

0 40 80 120 160 200 2400

10

20

V-T

rot.

vSF

6+Ar

= 0.198J/cm2

pSF

6

= 0.46mbar

total

coll.

/


pAr

/ [mbar]

0 40 80 120 160 200 2400

10

20

30

v

V-T

rot.

SF6+Ar

= 0.314J/cm2

pSF

6

= 0.46mbar

total

coll.

/

[photonspermole

cule]

pAr

/ [mbar](a) (b)

(c)

Fig. 7. Results for the total and partial values of n given as functions of buer-gas pressures (pAr) and laser uences() for irradiated SF6Ar mixtures, using Eqs. (10).

in SF6N2 mixtures are presented in Fig. 8. However, our investigation also shows that there is a

molecular buer gas, in gas mixtures with SF6 as the absorber, which contributes signicantly to

the ntotal values with VV relaxation process.

4. Conclusions

In this contribution, both the GCT model and its application for the complete analysis of laser-

induced IRMPA processes in gas mixtures consisting of molecular absorber and atomic or molecular

buer-gas species in the high-uence regime 0.10:7 J=cm2 are presented. Using this model together

with data obtained from other spectroscopy methods (TROA, TRA and SA), it is possible to analyze

obtained ntotal values, and evaluate all physical parameters of IRMPA that appear in Eqs. (8), (9)and (12): ncoll:, n, nrot: and nVT. They allow one to understand completely the dynamicsof IRMPA processes in investigated gas mixtures. Also, this model was used to determine the real

level of excitation n in the absorbing molecule.


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0 40 80 120 160 200 240

0

10

20

30

V-T

rot.

v

SF6+N

2

= 0.223J/cm2

pSF

6

= 0.46mbar

total

coll.

/


pN

2

/ [mbar]

Fig. 8. Results of GCT analysis of IRMPA processes in SF6N2 mixtures presented as functions of buer-gas pressures

(pN2 ) and constant laser uence ().

Using the results given in previous paragraphs, it is possible to understand the details of IRMPA

mechanisms. First, at the time t0, when the laser pulse started, part of the irradiated moleculesinteract directly with the radiation eld and they absorb some of the laser photons. That number is

characterized by value n. After a short time period (nearrot:rel:108 s), rotational to rotational

(RR) relaxation processes allow some of the absorbing molecules (SF6 in our case) to interact

with the radiation eld if they have not been in proper rovibrational states, and prepare already

excited molecules in such rovibrational states to absorb some more photons during the laser pulse.

That number of absorbed photons is nrot:rel:. Later on, VT relaxation processes are occurring too(VT10

6 s), but decreasing the level of molecular excitation and allowing the SF 6 molecule to

absorb more photons during the laser pulse (not only FWHM but also pulse tail). That number of

photons then is nVT. It is obvious (see Fig. 4) that the main contribution to ntotal is n con-tribution in comparison with contribution due to collisional processes. The dominant process which

contributes, however, to ncoll: is rotational to rotational relaxation process in the case of atomicand some simple diatomic buer gases (see Fig. 10). It is obvious, too, from the results presented

here, that collisions play a very important role (not negligible) during the IRMPA processes, and

that the GCT model is a powerful tool for their basic investigations.

Also, it is demonstrated that there are some important characteristics of the GCT model. First, it is

applicable for gas mixtures with the molecular buer-gas type, if one is sure that VV intermoleculartransfer does not occur (N2 buer-gas molecules, as example). But, this model can be used to predict

the possible VV energy transfers and even evaluate VV relaxation contribution to IRMPA, when

such VV transfers are allowed (SF6CH4 mixture, for example).

This work shows how one can analyze ntotal using the GCT model, to obtain directly not onlyfunctional dependence ntotal= f(pbu:) but also its partial values dependent on laser uence n,and collisions between gas-mixture species ncoll:, for all investigated laser uences and buer-gas

pressure range. Also, it was shown that, using the results from the TROA and TRA methods for

VT relaxation times (VT) and the SA method for RR relaxation times (rot:rel:) determina-

tion, inside the GCT model, it is possible to evaluate partial values of ncoll:, such as nVT and


15/15


nrot:rel: Knowing these quantities, it is possible to understand more precisely the dynamics ofIRMPA processes during the laser pulse.

Acknowledgements

This research was supported by the Ministry of Science, Technologies and Development of the

Republic of Serbia.

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Excitation dynamics during the multiphoton absorption in SF6.pdf