A. C. Stark effect on the 4713 Å line emitted by a helium glow discharge in the field of a multimode T.E.A. CO2 laser

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A. C. Stark effect on the 4713 Å line emitted by a helium glow discharge in the field of a multimode T.E.A.

CO2 laser

B. Dubreuil, P. Pignolet, A. Catherinot, P. Davy

To cite this version:

B. Dubreuil, P. Pignolet, A. Catherinot, P. Davy. A. C. Stark effect on the 4713 Å line emitted by a

helium glow discharge in the field of a multimode T.E.A. CO2 laser. Journal de Physique, 1982, 43

(6), pp.875-881. �10.1051/jphys:01982004306087500�. �jpa-00209465�

A. C. Stark effect on the 4713 A line emitted by ^{a helium} glow discharge

in the field of a multimode T.E.A. CO2 ^{laser (*)}

B. Dubreuil, ^P. Pignolet, A. Catherinot and P. Davy

Groupe de Recherches sur l’Energétique des Milieux Ionisés (**), ^{U.E.R. de} Sciences Fondamentales et Appliquées,

Université d’Orléans, 45046 Orléans Cedex, ^France

(Reçu le 4 novembre 1981, révisé le 1er février ^1982, accepté ^le 10 fevrier 1982)

Résumé.

Nous avons étudié le déplacement ^Stark dynamique de la transition radiative 43S1 ~ ² 3P0,1,2

(03BB

^{4 713} Å) de l’hélium dû à l’interaction non résonnante des états 4 3S et 4 3P avec le rayonnement ^{d’un laser} à CO2 multimode.

Cette étude réalisée en fonction de l’intensité laser dans le domaine IL ³⁵ MW/cm2 ^montre que pour

IL > 2 MW/cm2 ^le déplacement ^Stark dynamique ^de l’énergie du niveau 4 3S ne suit plus ^la dépendance ^linéaire

en IL donnée par la théorie des perturbations ^{au second ordre. Un} modèle à trois niveaux tenant compte de l’inter- action à tous les ordres permet ^{de rendre} compte globalement des résultats expérimentaux. Cependant, pour

IL > 1 MW/cm2, ^{nous obtenons un} élargissement important de la raie 4 713 Å accompagnant ^le déplacement

Stark dynamique. ^Cet élargissement ^{croit avec} IL ^et conduit à la formation d’un pseudo-continuum ^{s’étendant}

sur 50 Å pour IL

³³ MW/cm2.

Nous interprétons ^{cet effet comme étant dû aux} fluctuations d’amplitude ^{et de} phase des modes du champ ^laser pendant l’interaction. L’enregistrement de la raie 4 713 Å nécessitant un très grand nombre de tirs laser, ^le profil expérimental reflète dans ces conditions la distribution statistique ^de l’amplitude des modes du champ ^laser.

Abstract

In a helium glow discharge, the A. C. Stark shift of the 4 3S1 ~ ² 3P0,1,2 transition (03BB ~ ^{4 713} Å)

induced by nonresonant interaction of the 4 3S and 4 3P levels with a multimode CO2 laser field is measured as a function of laser intensity ⁱⁿ the range IL ³⁵ MW/cm2. Departure ^from the linear intensity dependence given by second order perturbation theory is observed for IL > 2 MW/cm2. ^A three-level atom model taking ^{into account}

the interaction with the laser field in a non perturbative way agrees with the experiment. Strong broadening ^is

also detected for IL > 1 MW/cm2. ^This broadening grows with IL ^{until a} quasi-continuum spreading ^{over 50 Å}

is observed for IL

³³ MW/cm2.

This broadening results from amplitude ^and phase fluctuations of the laser field modes during interaction. For

IL

³³ MW/cm2 the recorded 4 713 Å spectral ^line shape reflects the statistical distribution of the mode ampli-

tudes.

Classification

Physics ^Abstracts

32.70J

32.90

1. Introduction.

Nonresonant irradiation of an

atomic system by ^a laser field leads to a shift of the

quasistationary energy values usually ^{referred as}

nonresonant A.C. Stark effect or light-shift [1, 2].

Standard second order perturbation theory gives

the following formula for the _energy shift of a state

I n> :

(*) ^Work partly supported by D.R.E.T. under contract no 79/151.

(**) Equipe ^de Recherche Associ6e au C.N.R.S.

In equation (1), ^{all the} quantities ^{are in atomic}

units except ^for IL, the laser intensity, ^{which is} expressed ⁱⁿ MW/cm2. En, En, ^are respectively ^the

energy of the n ) and n’ > states, hWL ^{is the laser} photon energy and ( n’ E. r I n > is the electric dipole

matrix element with _s, the polarization ^{vector of the}

laser field.

According ^to the definition of light-shift [1, 2], equation (1) ^{is valid} only for laser intensities such that

Calculation of equation (1) ^{for the n}

2,..., ^{7 states}

of helium was performed in reference [3] ^{for the} CO2

laser and the neodymium ^laser wavelengths.

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphys:01982004306087500

876

Particularly ^{the 4 3S and 4 3P states were shown}

to be shifted as much as AE,3s

^{1.95 cm-1 and} AE43p (averaged ^{over the} magnetic quantum ^num-

bers) = -0.64cm’’ ^{for 1} MW/cm2 ^{of the} CO2

laser field (1iWL

944cm-’) ^{due to the} relatively

small detuning (64 3S,43p= ²⁵ cm-1) from the allowed 4 3S --+4 3 P transition (Fig. 1). Experimentally ^the

shift of the 4 713 A line starting ^{from the 4 3 S state}

was investigated ^{in reference} [3] in the laser intensity

range IL ⁵⁰ kW/cm2 ^{and was found in} quantitative agreement with the value deduced from equation (1).

Fig. ^1.

Partial energy diagram ^{of the} 4 3S-43P-2 3p

states of helium.

Extrapolation of these results to higher CO2 ^laser

intensities indicates that, ^for IL > 10 MW/cm2, ð.E43S- > 20 em - 1 so that relation (2) ^{is not fulfilled}

and equation (1) ^{is no} longer ^valid.

In this _case, the A.C. Stark effect on the 4 713 A

fluorescence line (4 Si - 2 3Po,1,2 transition) ^can

be described in the frame of a three-level model

including ^{the 4} 3 S, ^{4 3 P laser} perturbed ^{states and}

the 2 3P detection level. This problem ^{was investi-} gated theoretically using ^the density matrix forma- lism [4, 5]. ^The equations of motion for the off-diagonal

elements in the rotating ^wave approximation ^are given by :

In (3) ^the subscripts 1, 2, ^{3 stand} respectively ^for

the states 4 ’P, ⁴ 3S, ^{2 3p of} helium,

is the Rabi frequency ⁱⁿ the laser field

where E is the polarization ^{vector and} OL(t) a complex

function taking ^{into account} amplitude ^and phase

fluctuation. Furthermore, T, and ₇₂ are the damping

constants of levels 1 and 2 and _W12

(El - £2)/n.

The spectrum of all transitions terminating ^{in level 3}

is connected to the Fourier transform of the dipole

moment operator

where _W23 ⁼ (E2 - £3)/1i ^and d23 ^{is the} dipole

moment of the allowed 2 -+ 3 transition (the ^transition

1 ^- 3 is forbidden).

Resolution of equation (3) ^{in the case of a well-}

stabilized monomode laser field (ØL

0) ^indicated [4, 5] ^{that the} spectrum consists of a doublet centred at W23 ⁺ Am/2 (Am

WL - W12) ^and separated by

-

the one-photon component (emission process)

centred at

-

the two-photon component (two photon process)

centred at

Respective intensities of these two lines are.given by

and

In the low laser intensity regime : (OR, 7 1, 7 2 I Aw 1,

the shift of the one-photon component bw/2 ^{reduces to}

the quadratic Stark shift of the two-level system 1, ² (eq. 1) ^{and the} two-photon component intensity ^is negligibly ^{small. In the} high ^field intensity regime a)R >> I ^ð.w I, ^{T 1, Y 2} ðw /2 WR, the shift of the doublet becomes linear in Eo ^{and we} obtain the well-known

optical Autler-Townes effect [5, 6, 7] ^{in a} three-level

system.

In the more realistic case of multimode lasers under-

going amplitude, phase ^and frequency fluctuations such as free-running high energy pulsed lasers, ^the complex phase OL(t) ^must be taken into account in

equation (3).

Several _papers have dealt with this theoretical

problem ^{in the case of} phase fluctuations in resonance

fluorescence [8], phase ^and amplitude fluctuations in

multiphoton ionization _processes [9, 10] (see ^refe-

rences [11, 12, 13] ^for experimental studies), ^{in double}

resonance and resonance fluorescence [4, 14, 15], ^and

in two-photon transitions [16].

In most of these _papers, the multimode laser with a

large ^{number of} nearly independent ^modes fluctuating

from shot to shot is described by ^a non-monochro- matic chaotic field [9, 10, 12, 14, 15, 16]. ^{In this} model, E(t) ^{is a} stochastic function of time obeying ^Markov

process, ^so that equations (3) ^are stochastic differen- tial equations.

The numerical results for the A.C. Stark effect in double resonance and fluorescence resonance [14, 15]

indicate that the chaotic field tends to broaden the shifted fluorescence lines. This broadening ^{can be}

understood in terms of the amplitude fluctuations of the laser field inducing fluctuations in _DR and in the Stark shift bco/2. ^At high intensities when the two levels 1 and 2 are completely ^driven by ^{the laser field,}

the amplitude fluctuations tend to suppress the

« natural » line structure and determine the spectrum of the fluorescence line. The observed spectral ^line shape reflects the amplitude distribution function of the laser modes. In this regime, the characteristic time of interaction _{’rR -} 2 n/(OR is much shorter than the coherence time of the laser field and the atomic system is _very sensitive to the fast fluctuations of the field,

that is, ^to the instantaneous value of the field amplitude

and not to its mean value as in the low intensity ^case.

The main _purpose of this _paper is to present ^an

experimental study of these effects on the 4713 A (4 Si - 23PO,I,2) ^line (one-photon component) ⁱⁿ

the field of a multimode T.E.A. CO2 laser for time

averaged intensities IL up ^to 35 MW/cm2. ^{In this}

« intermediate » intensity range (transition ^from qua- dratic to linear A.C. Stark shift) [17] intensity ^{of the} two-photon line is smaller by ^{more than one order of} magnitude ^{than the} one-photon ^{line and was not}

detected.

Observation of this two-photon ^{line was} performed

in a helium plasma by ^D. Prosnitz et al. [18] ^with CO2

laser flux in the range 100-500 MW/CM2.

2. Experiment

^The experimental set-up ^{was des-} cribed in a paper dealing with A.C. Stark effect in

hydrogen [19]. ^{Let us} just recall that the partially polarized ^{beam of a} multimode T.E.A. CO2 ^laser operating ^{at 10 Hz and} producing ^{1 J} distributed in a

main peak ^{of 150 ns F.W.H.M. and in a} 3 JlS tail at WL ⁼ 944 cm - 1 (P.20 line) ^is slightly ^focused along

the axis of a helium 20 mm length capillary glow

discharge. The fluorescence light ^is analysed ^{with and}

without laser irradiation by ^{a 1.15 m} grating ^mono-

chromator connected to a photomultiplier. ^The syn- chronization of the detection system with the laser

pulse ^{is monitored} by ^a clock which switches on the

discharge ^{at 20 Hz and} triggers ^{the laser at 10 Hz.}

A two channel (A ^and B) gated integrator synchronized by this clock analyses ^the photomultiplier signal. ^Gate A, ^{100 ns} wide, ^is positioned ^{on the laser} pulse, ^the discharge being ^on; alternately, gate ^{B is} opened only

when the discharge ^{is on} and laser off. Output ^of gate ^A

gives ^the laser-perturbed signal ^whereas gate ^B gives

the unperturbed (reference) signal. Perturbed and reference line profiles ^are displayed simultaneously

on a two channel strip chart recorder by slowly rotating ^the grating ^{of the} spectrometer (speed

0.08 A/min).

In the present experiment, ^the spectral resolution is about 0.05 A in the vicinity ^{of the 4 713 A line. Each} point ^{on the} profile corresponds ^{to a summation over}

100 laser shots, ^{that is an} accumulation time of 10 s

and a scanned spectral range of 0.013 A.

Focusing of the laser beam in the discharge ^is per- formed so that the whole volume inside the capillary

tube is irradiated. Consequently, the available time-

averaged ^laser intensity IL (MW/cm2) depends ^{on the} capillary ^radius. According ^to the desired laser inten-

,

sity range, ^a 4 mm diameter capillary ^{tube for} X ¹⁵ MW/cm2 ^{and a 2.5 mm diameter one for}

IL ³⁵ MW/CM2 ^{are used.}

Measurement of the pulse energy is performed ^at

the output ^{of the} discharge ^tube taking ^{into account}

transmission of the KBr windows, ^whereas temporal

evolution and adjustment ^with respect ^to gate ^{A are}

continuously controlled by ^{a 1 ns time resolution} photondrag detector connected to a 7844 dual beam Tektronix oscilloscope. ^This permits ^{accurate deter-}

mination of IL ^and E(t) ^the normalized temporal

distribution function of the laser pulse. However, the radiation of the multimode T.E.A. C02 ^laser

contains about 30 longitudinal modes in the 3 GHz

spectral bandwidth, corresponding ^{to a} typical ^cohe-

rence time of ;:t 330 ps. Measurement of the time

development of these modes cannot be performed ^and

we observe only interaction (beating) between these modes leading ^{to a} slight modulation of the time-

envelope ^function C(t). ^{The measured} quantity IL

represents ^the averaged intensity

where Em ^{is the} complex amplitude of the mth mode of the field (IL corresponds ^{to the r.m.s.} value of the field amplitude Eo ⁼ JIL) and differs from the actual instantaneous intensity IL(t) o probed » by

atoms. IL(t) ^is given by ^{and can}

be connected to the measured parameters IL ^and E(t)

in the form [11] : IL(t)

7L ^{t(t) m(t) where m(t) is a}

nearly periodic modulating ^function (period - ¹⁰ ns)

878

taking ^{into account the} mode interaction. IL ^and E(t)

are quasi-reproducible ^{within 5} % ^{from shot to} shot,

but as the mode distribution fluctuates in phase ^and amplitude, m(t) ^{is a} quasi-stochastic function which cannot be easily characterized due to the 1 ns detector risetime.

_

Change ⁱⁿ IL ^{values cannot} be achieved by varying

the voltage of the laser discharge ^without large

uncontrolled alterations in the discharge and in the laser pulse. On the other hand, ^{the use} of calibrated neutral filters at 10.6 Jlm with incident _energy of 1 J is rather difficult so that we make use of the possibi- lity ^{to set the} gate ^{A at} different times along ^the

whole laser pulse shape E(t). Defining ^{the mean laser} intensity IL averaged ^over the time duration of the observation gate :

where

is the gate function, ^this experimental procedure permits quasi-continuous tuning ^of IL ^{when the gate A}

is positioned along ^{the 3} ps tail (variation of C(t) ⁵ % during ^{the 100 ns of the} gate g(tl, t)), ^whereas higher IL ^{values are} obtained when gate ^{A is} positioned ^{on the}

main peak (with ^{a variation of E(t) 25} %). ^{With this} operating mode, ^all experiments ^{for a} given capillary

tube are performed ^{in the same} laser irradiation condi-

tions. Particularly, ^{the total laser} energy passing through ^the discharge ^{remains constant.}

3. Results and interpretation.

Figures ^{2 and 3}

show the experimental recordings of the 4 713 A line

Fig. ^2.

Experimental recordings of the laser perturbed

and unperturbed ^{4 713} A line for It

0.1, 0.3, l.1 MW jcm2.

Fig. ^3.

^{Same as} figure ^{2 for} IL

1.9, 2.8, ^6.2 MW/cm2.

obtained for increasing ^{values of} IL. ^As expected ^{[3], the}

shift of the 4 ’S, -+ ² 3P0,1,2 transition towards the blue wavelengths ^increases with IL, ^{but a strong}

broadening ^is also observed for IL > 1 MW/cm2.

As discussed in part 1, ^this broadening results from fluctuations of the phase ^and amplitude of the laser modes, inducing fluctuations in the A.C. Stark shift

bw/2. ^{Due to this} asymmetric broadening, ^{two line}

shifts can be defined : the shift ^{AA’ of the 4 713 A line} peak ^value and the shift ðÀ of the line gravity ^centre.

These two measured shifts are reported ⁱⁿ figure ^{4 as a}

function of 79L. ^{Error bars on} 79L correspond only ^{to the}

measured extreme variations of E(t) g(tl, t) during

the 100 ns of a measurement and do not result from

noisy signal.

Fig. ^4.

Plots of the ⁴ 713 A line A.C. Stark shifts LBÀP, AA as a function of IL : ^M experiment with the 4 mm

inner diameter discharge tube; ^CJ experiment ^{with the}

2.5 mm inner diameter discharge tube, and the theoretical

curves corresponding ^to second order perturbation theory

and to the non perturbative three-level atom model.

The curve AA

f(I[) ^{shows a} deviation from

linearity ^for IL > 2 MW/cm2, (bw/2 ^Am > 0.2) ^and

tends to the square-root limit of the optical ^Autler-

Townes effect at higher intensities. Drawn with these data are also theoretical curves deduced from _equa- tion (1) ^and equations (4-5) taking ^{into account} coupling ^{of the 4 3 S} (M

0) ^{and 4 3p} (M

± 1) magnetic ^sublevels by the laser field propagating along

the quantization ^axis z - with polarization ^vector

e

(x ⁺ y)/, ,,,/2 ^{[3]. For IL9 2} MW/cm2 ^{the fit} by equation (1) is in broad agreement ^with experiment ^so

that second order perturbation theory ^{can be used in}

this intensity range. Fit of the data by equation (4) (non perturbative three-level atom) ^is also rather good

in the whole explored intensity range provided ^the

laser field amplitude Eo ^{is taken as} Eo

To ⁼ JIL.

On the contrary, the shifts of the peak ^{value AA’ are}

found ^{lower in a ratio - 1.2-1.3 than the mean values}

A/L for Ig > 2 MW/cm2, ^{and cannot} be fitted by equation (4) using ^{the mean laser} intensity IL. ^This

effect is indeed connected to amplitude fluctuations of the laser modes and the relevant difficulty ^{of measur-} ing ^the actual laser intensity ^{« seen »} by ^{atoms. Theo-}

retical investigations of the A.C. Stark effect induced

by monochromatic chaotic field [14, 15] ^{discussed in} part ¹ indicate that the Stark shift AA’ caused by ^a strong chaotic field (phase ^and amplitude fluctuations)

is less than that caused by ^a phase-fluctuating ^field

with the same average intensity IL. ^For _higher ^values

of IL, ^{AA’ tends to the limit} AA/,y2 where AA is the

mean Stark shift. This limit corresponds ^{to the ratio}

between the r.m.s. field amplitude value and the most

probable value. The measured ratio AAP A/L/1.25

for IL > 2 MW/cm2 agrees with this theoretical result.

Such an effect was also observed in resonant multi-

photon processes [20].

Recordings of the 4 713 A line for 79L > 6 MW/cm2 (Fig. 2) show that the line structure tends to disappear

in a large pseudo continuum. In this regime (the ^shift

becomes nearly proportional ^{to the} amplitude ^{of the}

laser field) iR 48 _ps is much shorter than the cohe-

rence time of the laser field so that the atoms follow the time development of the mode structure. The

« instantaneous» Stark shift becomes _very sensitive to fluctuations of the mode amplitudes ^and phases.

Experiments ^{were performed in} this direction _up to

h

³³ MW/cm2. As shown in figure 5, ^the perturbed

4 713 A line is now a broad continuum lying ^{on the}

blue side of the unperturbed ^{line and} spreading ^over

-

40 A with a rather flat intensity distribution. For this laser intensity, the atomic line shape ^is certainly completely determined by ^{the mode} amplitude ^distri-

bution function [4, 14, 15].

In order to give ^a quantitative approach ^{to this} analysis, ^we performed ^a numerical simulation of the

experiment using results of the non perturbative approach (eqs. 4-5) ^and assuming ^a Gaussian distribu- tion function of the longitudinal laser mode ampli-

tudes [22] :

where Eo

,,/79L is the main value deduced from measurement and E012 ^the standard deviation.

The 4 713 A line intensity ^{value in a 0.013} A spectral

range is obtained by accumulating contributions of 30 x 100 laser field amplitudes (100 ^laser shots)

distributed according ^to equation (7) ^and assuming

that the transition dipole d23 ^{is constant. Moreover,}

this calculation takes into account the supplementary broadening ^{due to the} temporal variation of the enve-

lope ^function £(t) g(t, to) during ^{the 100 ns accumu-}

lation time.

Some results of this simulation for different 79L ^values

corresponding ^{to the} experimental recordings ^of figure ^{2 and} figure ^{3 are} presented ^{in figure 6. The}

numerical simulation fdr h

³³ MW/cm2 ^{is drawn}

on figure ^{5 with the} experimental recording. ^Broad agreement ^with experiments is observed although equation (7) ^{does not} exactly represent ^the amplitude

distribution function of the actual laser modes. How-

880

Fig. ^5.

Experimental recording of the laser perturbed ^{4 713 A line for} Il

³³ MW/cm2. The laser beam was blocked two times during ^this recording ^{in order to check the} ground ^level.

Fig. ^6.

Results of the numerical simulation of the experiment for different mean laser intensity ^values Ïl corresponding

to the experimental recordings ^of figures ^{2 and 3.}

ever a recent experiment ^on multiphoton ionization of caesium atoms [22] confirms that a 3 GHz bandwidth

neodymium ^{laser field can} be considered as being

Gaussian in the same way ^as chaotic light.

4. Conclusion.

The A.C. Stark effect of the one-

photon component (4 ⁷¹³ A) line of the 4 3P-4 3S-2 3P three-level system ^of helium in the field of a multimode T.E.A. CO2 ^{laser was} investigated in the intermediate

intensity range IL 35 MW/cm2. Departure ^from

second order perturbation theory (quadratic ^Stark shift) ^is observed for IL > 2 MW/cm2. ^At higher

intensities the mean Stark shift becomes a nearly ^linear

function of the laser field amplitude. Fluctuations of the longitudinal ^mode amplitude ^and phase ^distribu-

tion lead to a large broadening of the shifted line. For

IL > 6 MW/cm2, ^{when the} typical interaction time becomes much shorter than the correlation time of the

CO2 ^{laser field, the} o unperturbed » ^{line structure}

tends to disappear ^{in a} broad flat continuum. The

perturbed ^line shape then reflects the statistical distri- bution of the mode amplitudes in the laser averaged

over a large number of shots.

In this form, the observed laser-induced Stark

broadening ^can be connected to the Stark broadening

of spectral lines emitted by plasmas ^where the statistics of electric fields (spatial ^and temporal ^ion distribution)

inside the plasma manifests itself in the line shape [21].

Analysis ^{of this} broadening ^is currently ^{used in} plasma

spectroscopy ^{to determine some} statistical properties

such as averaged ion number density. Laser induced A.C. Stark effect can also be used as an experimental

tool to investigate ^the statistical properties ^{of the}

radiation field [4].

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