Resonant multiphoton ionization of caesium atoms

FÉVRIER 1979Tome 40 ? 2
LE JOURNAL DE PHYSIQUE
Classification
AbstractsPhysics
32 . 80K
Resonant ionization of caesium atomsmultiphoton
G. J. Morellec and D. NormandPetite,
Service de Centre d’Etudes Nucléaires de Saclay,Physique Atomique,
B.P. n° 91190 Gif sur France2, Yvette,
le 24 19 octobre août le (Reçu 1978, accepté 1978)
2014 Résumé. de cet article est l’étude du d’ionisation résonnante L’objet phénomène multiphotonique (IMPR)
de l’atome de césium soumis au intense d’un laser au verre au Une estchamp dopé néodyme. première partie
consacrée à d’une théorie récente de sous une forme en tirer les informationsl’exposé l’IMPR, simplifiée, pour
essentielles sur la de l’IMPR. Nous ensuite deux d’IMPR du césium : ionisationphysique présentons expériences
à de l’atome de césium dans son état avec résonance à trois sur le niveau fondamental, 6F ;quatre photons photons
ionisation à trois de l’atome de césium dans son état avec à deux sur le niveauphotons photons 62P3/2
12F. Dans la on résout la structure fine de la transition ce de mettrepremière expérience, résonnante, qui permet
en lumière et l’effet des formes et des conditions de focalisation sur nos résultatsd’analyser important d’impulsions
Nous donnons des de certains aussi récentes résultats expérimentaux. interprétations publiés auparavant [1].
Dans la deuxième on mesure la structure fine du niveau est trouvée à cm-112F, expérience, qui égale (0,016 ± 0,008)
et on montre nous arrivons aux limites l’effet Les résultats de ces sont enimposées que par Doppler. expériences
bon accord les et de avec considérer comme satisfaisante prévisions théoriques, permettent l’image physique que
nous donnent de l’IMPR les récents travaux à ce sujet.
2014 This studies the resonant ionization in the case of caesiumAbstract. paper multiphoton (RMPI) phenomenon,
atoms with the intense field of a laser. In the first we a recent ofneodymium-Glass part, present theory interacting
in to the main informations on the of RMPI. Then we twoin a form order obtain RMPI, physics present simplified
of RMPI : ionization of the caesium atom in its with a experiments four-photon ground state, three-photon
resonance on the 6F level and ionization of the caesium atom is its state with a three-photon two-photon62P3/2
is resonance on the 12F level. In the first the internal structure of the resonant transition resolved,experiment,
effect of conditions on our us to out and the and enabling point analyse important pulse shapes focusing experi-
mental which are discussed in detail. We also some new of results results, give interpretations published previously
2014 In the second we measure the 12F fine structure which is found to be ± cm-1 2014experiment, (0.016 0.008) [1].
we have reached the limits the effect. These results are in and show that imposed by Doppler experimental good
with the theoretical that the of RMPI recent worksagreement predictions suggesting physical picture given by
on this is subject satisfactory.
- Introduction. The aim of this is to tal results and the theoretical present predic-paper corresponding
results obtained in our on the an ensemble of tions will allow us to decide whether laboratory physical
resonant ionization of caesium of RMPI the is (RMPI) multiphoton image given by theory satisfactory
atoms. or not.
of the recent theories andIn the first we one We recall the results of a previous paper [1] part, present
most in order to for the first time the theoreticalof in its form, RMPI, simplified give corresponding
in theseoutline the main ideas contained physical interpretations.
results of two toformalisms. Then we the Our main in these has been expe- experiments present purpose
of caesium atoms : as as the conditions of theriments on RMPI match four-photon closely possible
stateionization of the caesium atom in its in to make theoretical order ground calculations, comparison
resonance on the 6F between theoretical and results realistic.with a three-photon experimental (62Si12)
ionization of the caesium atom This will result in one of the most featureslevel ; three-photon original
in with a resonance on of our which is its there state, two-photon experiments, being performed62P 3/2
the 12F level. The between the with a transverse and mode Nd-comparison experimen- single longitudinal
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphys:01979004002011500116
such that eliminate the influence of the the effect of states + Glass so we By as i, n 1)laser, neglecting
off n + we make here the common R.W.A.statistics which is well understood only or j, 2 >, light
resonance approximation.[2].
- whose in the ionization The resonant 3 A occurs ), is,resonance multiphoton state r, n - energy
due to the to be much closer when the of an number of toresonance, processes energy integer supposed
that of the initial state than that of of the aboveis to that of an allowed atomic transi- any photons equal
which schematizes non-resonant states.like in the case of tion, 1, figure
- - resonant ionization In order to the effect of non-resonant contri-a study four-photon three-photon
chosen as an in the butions to the resonant ionization a third setprocess, process, example following theore-’
of non-resonant 3 tical is astates k, n - >, where 1 k) survey. atomic state with the same asparity
- 1. the recent theories of RMPIOne of Theory. can be introduced.1 r ),
makes use of the resolvant formalism to[3], applied - Initial and resonant states are embedded in a
the dressed atom model It has been in[4]. developed continuum of final states constituted an ionizedby
our Gontier and and Trahin, laboratory by applied atom and a field 4 ofpopulated by n - photons,
caesiumto the case of the ionization of four-photon + energy (E (n - 4) co’).
a treatment of the[5]. By using very sophisticated The Hamiltonian JC of our is the sumsystem
are able to derive exact forproblem they expressions
the resonant ionization andmultiphoton probability
other related with which we will quantities, compare
our results. The aim of the of the atomic Hamiltonian the field Hamiltonianexperimental present Jea,
theoretical is to a form ofsurvey present simplified
this if for accurate numericalwhich, theory improper
all the ofcontains nonetheless calculations, physics Hamiltonianand the atom field interaction
RMPI.
It follows from 1 that the readily figure following
in the four-states of our dressed atom will appear
- - ionization resonant pro-photon three-photon
chosen for an cess we have example. which can be taken in its common electric form,dipole
- The initial of an atom creation and annihilationstate g, n >, composed where a+ and a are the
bein its and a to field, of one of the mode the ground state 1 g > supposed photon pola-operators cvp, ip
the laser of fre-reduced to a mode of cavity, rization vector of the same r the single mode, position
its number n.described theby occupation of the electron and L3 the volume of quency cop, operator
The of this state is + all box.energy (throughout (Eg nwp) quantization
= = this we take h c that the states are thepaper, 1). Assuming only populated
- andTwo sets of intermediate fundamental and the resonant the ionizationstates i, n - 1 ) states,
whose + and at a time t is 1 2 ), energies (n - 1) j, n - (E; 0153?) probability given by [6]
+ since these states are are, (n - 2) supposed(Ej cop)
to be different from + non-resonant, very (Eg nwp).
where and are the at the time tp,,(t) populations pgg(t)
of the fundamental and the resonant states. From the
of the ionization it expression (1) probability, appears
that our is that of the of twoclearly problem decay
unstable L. Mower has shown howstates. coupled [7]
the use of Green’s function can techniques provide
a and direct to this If simple approach problem. U(t)
is the evolution of our (1)operator system, expression
can be in the formput
with of the resolvantis then calculated help U(t)
operator
of our the system, by following integral
- 1. Resonant ionization scheme.Fig. multiphoton process 117
know the matrix elements ofand C _ are shown on 2 we need to where the contours C + figure just
and where the contribution foronly non-vanishing
abovetimes is that of the contour C+, lying positive
the real axis.
where
- 2. Contour for the of C+ and C- lie and where the describes the effect(4). Fig. integration eq. shift operator R(z)
near the real axis. The contribution of C- vanishes forinfinitely on our of all the states outside process gp*
times.positive and are calculated with of thehelp Ugg(t) Urg(t)
matrix elements and means of by equa-Ggg(z) Ggr(z)
tion These are calculated the method(4). integrals by that thethe fact (2) Expression clearly emphasizes of and we thus need to calculate the residues, poles
can be in a calculation concentrated subspace gp of and it follows from Moreover, expres-Ggg(z) Ggr(z). the initial and the resonant states. It isby spanned sion that these have a (3) poles deep physical meaning,therefore convenient to use the technique ;projector the of the since are Hamiltonian J~they eigenvalues
that ifis, of our and we can from their evolutionsystem, expect,
under the influence of the to obtain someinteraction,
modifiesinformation about the this interaction way
the states of our the matrixand system. By inverting
one shows that andJeo - PR(z) P] Ggg(z) [z -
have the following expressionsGgr(z)
matrix smallthat the elements are Assuming of R(z)
and functions of it can be shownslowly varying z,
that and can to a very good approxima-Ggg(z) Ggr(z)
tion be the represented by following expressions
ionization the of (EI: atom).potential where
to in we havethe Corresponding principal part (10),
which is but one half of the are the of the dressed fundamental and reso- nothing photoionizationenergies
nant of the resonant state the laser field ofstates modified the probability by by intensity dependant quan-
I and tities is the laser intensity frequency (I intensity) wp.118
fun- of Z ± and wethe between the the real and imaginary parts separate, represents three-photon coupling
havedamental and the resonant states. In the expressions
of the elements of we have restricted our-matrix R(z),
inselves to a third order in which is, expansion Jeaf,
this the lowest order rise to case, non-vanishinggiving
ionization contributions to the Therefore,probability.
does not exhibit a to thepart corresponding Rgg(I)
direct with the continuum via the three setscoupling
to theof non-resonant states i >, 1 k) 1 1 j ), (similar
in and for the samepart expression principal (10)), which shows that the effect of the interaction on our
no a width of the fundamentalreason, representing iT g, fundamental and resonant states is the following :state due to non-resonant ionization processes, appears Their have been in two (i) energies changed ways :
in our The effect of these non-resonantexpressions. first the common laser induced a.c. stark shift,by ionization on ionization willthe probability processes and which are includedrepresented by R,,(I) Rgg(I) thus not be taken into account but we willhereafter, in second the and and by three-photon couplingE,, Eg see later how can be introduced.they between these two states whose influence inappears
From the it can be seen that expressions (7), Ggg(z) the third term of E ± .
the com-and have two which are poles, simply Ggr(z) These have now an and(ii) energies imaginary part, roots of the plex equation
we will see in the of the ionization probabilitystudy
is related to the factthat this imaginary part closely
that these states are no but= states, whose if Li longer stationary expressions are, Er - Eg
are in the continuum.decaying
lieit can be shown that these Furthermore, poles
the second Rieman sheet of the lower half in plane,
due to the fact that of a Hermitiancomplex eigenvalues the Introducing quantities Hamiltonian are the method ofTherefore, unphysical.
residues has to be but it can becarefully applied,
- shown that for times not too that is far[7] long
- from the saturation of the this can beprocess point
in the calculation of the ionization ignored probability,
which is found to be :
This similar to that derived the of the is case, complicated expression, expression poles simply
different authors in the by [5, 8] can, general case,
be handled with of accurate numerical cal-only help
culations. it must be noted that it containsHowever,
terms of two kinds :
- on the of the underwith constants terms, and, depending sign expression exponential decay equal
to the T ± of Z the two situations occur :radical, imaginary parts =t ,
- which oscillate at atcrms, damped oscillating
to the difference E + - E - of thefrequency equal the resonant is more In this state case, strongly
of our fundamental and resonant states.energies to the fundamental state than to the conti-coupled
There are some cases where theimportant physical nuum. We have
of the ionization isanalytical expression probability
much one of them is the case of the exactsimpler ;
= characterized = resonance, Li 0 or In thisby F/. Eg 119
which shows even at the exact which is and is resonance, but thethat, intensity dependent nothing
E + # this kind of resonance is characterized in this case of the Rabi nutation E - ; by equivalent frequency,
an The ionization takes modified the term anticrossing point. probability by damping F,.
the form :following
... c-.
In the resonant state is on the this case, contrary
more to the continuum than to thestrongly coupled
fundamental state. We have
which presents essentially damped oscillating terms,
at a That this resonance is oscillating frequency, characterized is, crossingby a
= = where E + E - - the ionizationpoint, Er ; Eg
takes the form :probability
which series ofexhibits terms.only decaying power exponentially
There is a third case were the of the ioni-expression
zation can be and which cor-probability simplified,
to a situation that we will meet later. Whenresponds
the between the resonant state and the conti-coupling and we have
nuum is much than between the resonantstronger
and the fundamental that is when states, ,F,12 » I, Rgr
the of Z ± and can be inexpressions P(t) expanded
The last three terms of this are It is that this ionization rate is expression damped noteworthy nothing
with time constants r - ~ which are much but the one which we would calculate a standard1/2 1/2 rr’ by
smaller than that of the first time term such as the Fermi dependent perturbation argument golden rule,
r +. As soon as the condition 1 > is if we the influence of the non-resonant 1 j2 F, t fulfilled, neglect pro-
we can the effect of these terms on the ioniza- cesses on the ionization resonant neglect proba-multiphoton
tion and write rate Note that the of this probability bility. single approxi-validity
t mation is submitted to the condition » 1,(SRA) F,
which the saturation of the resonantclearly express
--+ the ioniza-state continuum transition. In this case,
tion rate is but the transition rate from thenothing and if we are far from the saturation of theenough fundamental to the resonant that isstate, ionization that we have1, process, is if yt «
P(t) - y t
and our can in this case be described anprocess by
states. Due where is the of resonant top(E,) density ionization rate
the with the this continuum, strong coupling density
is no a ô but can be alonger function, represented by
Lorentzian of half width centred at the F,, position120
that with suitable of our SRA - on a of the shifted resonant is, state, parameter
normalization
since both and à are linear in the laserwhich, Tr
is a atomic Far of the fromIt follows account of the shift intensity, pure parameter. that, taking
K is to the net numberresonance, fundamental we find simply equal Ko state,
of absorbed in the ionization At thephotons process.
= resonance d the K variations exhibit(around 0)
a classical The effect of an dispersion profile. increasing
- of the ionization width that is of the parameter p
- which is ioniza- is to this but the of the (25) damp dispersion profile.nothing expression
In a tion rate. Under the above there is a the case where such rate single conditions, approximation
is not all these calculations have to be noticeable between the resolvant for- carriedvalid, convergence
out the are theand the standard Thismalism, numerically. Qualitatively, predictions perturbation theory.
same as those made with the but there are somehas be noted Beers and SRA, convergence already by
in a different case noticeable différences ; Armstrong slightly [8]. quantitative physical quanti-
- With of this ionization calcula- ties such as the width of the resonance exhi-help rate, analytic peak
-bited the ionization for instance tions are The of the ionization by probability, easy. dependence pro-
-are no related to atomic the laser a Lorentzian longer simply quantities bability upon frequency displays
reso-such as the of the of width 2 and centred at aprofile, (FWHM), photoionization probability F,
nant state. Such calculations have been carried outto one third of the of thefrequency equal energy
Gontier and Trahin in the case of the resonant modified the laser transition, by four-photonby intensity
induced states. As an ionization of with a resonanceshifts of the atomic other caesium, three-photon energy
on the 6S -> 6F transition their results will bewe show on 3 the of the and [5], example, figure dependence
our results. One of theeffective order of non to compared experimental linearity :
differences between the of SRAstrong predictions
and that of a more concerns the evo-general theory
- lution of the maximum ionization atprobability
- the resonance as a function of the laser intensity.
It can be seen from of the ioni-easily expression (25)
zation rate at the the ionization resonance, that, pro-
is to the of the laserbability proportional square
the case of inthat (in SRA) is, represented intensity
coordinates a line with 2.log-log by straight slope
Gontier and Trahin in the behaviour of thisstudy [9]
slope
the in the case where SRApredicted by theory general
is not as a function of the laser valid, pulse duration,
for a set of different laser intensities. The correspond-
4in are on curves, ing published [9], reproduced figure
need some comment. If we follow aand physical
- 3. Evolution of the effective order of non of thelinearity Fig. curve to a laser corresponding given intensity
the as a functionresonant ionization around resonance, process for for dura-(108 W/cm2 instance) increasing pulse = = of where d and ô aI is theJ/5 E’r (dynamic detuning) Eg -
= tions we find :resonance shift. The is a atomic successively parameter p F,lô pure parameter
- = in the value of that is thecase of our SRA. A first at a plateau, PM 4,
net number of absorbed in the ionizationphotons
This coincidence is not accidental and is mostprocess.
to the fact that none of the transitionsrelated probably where is ihe number oi ions creaieû uneNi uuring
- to the ionization that is the
- process participating the interaction whereupon parameter (4/à) ;
fondamental - resonant and the resonant conti-
- nuum transitions is and thus cansaturated, they
be with of handled transition rates.help
- is the shift of the resonant transition for a laser For durations around 100 the energy pulse ps, product
-
- I. Such in the frame which is but the 0 introducedintensity profiles depend only F, t nothing parameter 121
the where SRA is valid.rizing presaturated regime,
x For intensities than 2 108 these twoW/cm2, higher
cannot be inconditions simultaneously fulfilled ;
the follows theother saturation words, immediately
presaturation.
Before this theoretical we will recallending survey,
how the contribution of non-resonant toprocesses
the RMPI can be taken into account : In Gontier[5],
and Trahin have used a similar to the onetheory
described but where are resummed all above, the terms
of the series to ionization withperturbation leading
a net of to an absorption four-photons, up arbitrary
order. In so introduce a high doing, they quantity Tg,
similar to which like a width of the funda-r r’ appears
- mental state due to a direct non-coupling through
- resonant states with the continuum.
An alternative to this method has been proposed by
Beers and Feneuille theArmstrong, [11 ], involving
of all the between the fun-representation couplings
resonant and final states effective Hamil-damental, by
tonians. Non-resonant states are removed in this way
from the calculation as we have done just by using
the The results of such formalismsprojector technique.
-
- hereafter referred to as ABF formalisms are
identical to those of that the effective[5], provided
- Hamiltonians are calculated to the convenient order4. Evolution of = ô as a functionFig. PM Log P(t)max Log I,
- of and that all the relevant effectiveof thé duration for different laser intensities in pulse t, perturbation, W/cm2 -
- from circle cross reproduced [9]. Experimental points : [18] ; are introduced Hamil-[17] ; including shift
the work.triangle : present tonians the fundamental and resonantconnecting
states to for instance. These formalismsthemselves,
have been within the framework of thedeveloped
- M. Crance and S. Feneuille takes values resolvant formalism or to ionization rateby [10] [8] applied
around to decrease. This calculations and the connections between these0.1, PM begins [11] corresponds
-to the of saturation of the resonant two theories are the same as those described state appearance above,
continuum which is when that is that rate are valid in the transition, complete approximations pre-
> 10. To remove all this saturated Moreover these formalismsrr t possible ambiguities, regime only [8].
first saturation will have been used in semi-classical calculations hereafter be referred to as [10],pre-
saturation. where laser intensities are allowed to depend on time,
- For durations between 170 ns and 2 and we will see later the of such calcula-pulse us, importance
we find a new in at a value of tions. An idea contained thesetwo, plateau corresponding important physical
to the of which is formalisms is the the ionization coherent with theprediction SRA, probabilityfollowing :
fact that for the laser both conditions is the sum of two given intensity, amplitude terms, corresponding
for the of SRA are fulfilled in this to the resonant and non-resonant necessary validity respectively pro-
of durations. cesses. The of the resonant term whenrange pulse changes phase
- For durations than 2 the resonance is which is not the case of the non-condi-pulse higher us, crossed,
tion 1 is no and the decrease resonant term. Therefore these two contributions fulfilled, yt longer
of side of thedown to 0 characterizes the saturation of the exhibit constructive interferences on one PM
ionization hereafter on the otherreferred to as the resonance and destructive interferences process, simply
saturation. side. The result is an of the resonance asymmetry pro-
It must be noted that these which were first file characteristic of the well known Fano Theeffects, profile.
introduced as time effects are of the influence of non-resonant processes[10] strongly dependent importance
on the laser This is Fanothe fact on the resonance is characterized intensity. by the emphasized by profile
that there is an x 108 in the case the of the reso-to ratio intensity (2 W jcm2 parameter q [8,10,11], equal
of above which no at the value of 2 nant to the non-resonant contributions to the resonantFig. 4) plateau
is observed. is to the This due fact that and ionization values rr y depend probability amplitude. High of q
to a different order 1 and on the laser lead to weak effects of the non-resonant terms.(respectively 2)
and an increase of the laser obvious- ABF formalisms have been to the case ofintensity, intensity applied
leads to the of decrease simultaneous ionization of with a three-ly range caesium, validity four-photon
of the two conditions 1 1 6F > characte- resonance on the 6S --+ rr t and yt « transition, byphoton 122
M. Crance and her results will be to an atomic of 6 x 101° [12], compared density atoms/cm3. Depending
our results. on the the caesium atoms are either inexperimental experiment,
We conclude this theoretical their the state or in their statesurvey by recalling ground pumped 62P 3/2
main of RMPI we the C.W. field of a H.I.T.C. the the laser predictions theory : expect by dye operated
ionization to a when the laser at the of 8 521 Á ions The createdprobability present peak wavelength [15].
is matched to the resonant the interaction are accelerated a D.C.wavelength wavelength ; during by
of the width and this are electric a time field, position, amplitude peak separated by of flight spectrometer
to on the laser I. We and collected on the cathode of an electron expected intensity expectdepend multiplier
variations of the effective order of non- 50 P 3 whose current is measuredimportant (RTC R) output
of the ionization when the laser on an In order to avoid D.C.linearity process oscilloscope. large
crosses the resonant Stark shifts due to the collection the collectionwavelength.wavelength field,
is about 100 ns after the ion voltage applied creation,
- results. In the 2. Expérimental expérimental part
a by using pulsed accelerating voltage triggered byof this we will two of RMPIpaper experiments present our Nd laser pulse.of caesium atoms a Nd3 +-Glass laser : four-by
2.2 FOUR-PHOTON - THREE-PHOTON RESONANT -ionization of caesium in its state,photon ground
- IONIZATION OF CAESIUM. The of this resonance the 6S -+ 6Fwith a on principle expe-three-photon
riment is schematized on 6 : thé caesium atomintransition and ionization of caesium figure
excited the intense field of a Nd3 +-Glass laserits with a resonance on the by state, two-photon 62P3/2
a ionization which12F undergoes four-photon process, transition.6p3/2 -+
exhibits a resonance on the 6S --+ 6Fthree-photon
- 2.1 EXPERIMENTAL APPARATUS. Our experi- 10 589.6 Á.transition for laser around wavelengths
mental is schematized on the 5. set-up figure Basically,
it is of a transverse and composed single longitudinal
mode tunable Nd3+-Glass a caesiumQ-switched laser,
and different devices to control andtarget, necessary
measure the characteristics of the laser field,
and the created the interaction.number of ions during
The different of this have been describedparts set-up
in full details elsewhere and we will13, 14, [1, 15],
limit ourselves to a brief review of the characteristics
of the different devices.
- 6. The ionization scheme of the caesium atom,Fig. four-photon
transition.with resonance on the 6S ~ 6F three-photon
As can be seen on this resonant transitionfigure 6,
is in fact of four due to a 0.3 cm-1composed lines,
structure of the 6S state and to ahyperfine ground
0.1 cm-1 fine structure of the 6F resonant level. The
the behaviour offollowing quantities characterizing
this resonance have been whencalculated, except
Gontier and Trahin noted, by [16].
For x a laser of 2 10’ we haveintensity W/cm2,
- 5. Fig. Experimental set-up.
is in The laser andoperated single longitudinal
transverse mode conditions It delivers a 37 ns[13].
where s-1 are it follows thatunits, optical frequency and can be tuned from 10 510 A to 10 610 A,pulse
= 2.3 x which shows that this reso-r 21I 10 + 5, MHz. MW Rflr 12 with a bandwidtb of 15 Peak to 80 power up
nance is of the and moreover that thecrossing type, Its andcan be obtained. can be measured wavelength
first condition of of SRA is thereforefulfilled, validity with an better than 2 x 10-2 A-1controlled accuracy
= we calculate for t 40 ns (our pulse duration)for absolute measurements x 10- 3 À,wavelength (2
for relative The laserwavelength measurements) [14].
in caesiumbeam is focused a where the pyrex cell,
is in saturated withconditions, placed vapour vapour 123
is created the interaction as a function of theWe have seen 4 and that SRA comments) during (Fig.
for values of laser for three different values of the laservalid in only, wavelength presaturated regime
> 10. It follows that for an of The curves obtained in this fourF, t intensity intensity. way present
2 x 10’ we are not in a case where we can resonance which as peaks are, enhanced,W/cm2, expected,
reso- shifted and broadened the increase of the such an The width of the laserby apply approximation.
to one this thenance single component intensity, broadening being emphasized by peak corresponding
of the resonant transition must therefore be calculated fact that the internai structure of the resonant transi-
tion is for the lower with of the form of the ionization resolved laser help general pro- intensity only.
= --+ We have on 8 the and for the evolution ofis, (F 3) represented figure bability 62F5/262S1/2
the maximum number of ions collected after thecomponent
interaction as a function of the laser Inintensity.
the three tocoordinates, log-log points corresponding
the three curves of 7 fall on a line offigure straight
On the other the a hand, parameter characterizing that is than 2.± slope (2.5 0.2), undoubtedly greater
the shift the of resonant has been calculated peak by
different authors in and [5, 12], they found, good
agreement
The Fano the effect of theparameter characterizing
non-resonant on the resonance hasprocesses profile
M. is been calculated Crance and found to be[12] by
= 5 x 10’ for a laser of 109 Thisq intensity W/cm2.
is the maximum with which RPMIintensity
have been carried on with nanosecondexperiments
a functionpulses [17]. Therefore, q being decreasing
of the laser we do not intensity, expect important
effects due to these non-resonant in ourprocesses
experiments.
In the we the resonancefirst experiment report here,
- - . - .-is studied the laser andconstant, by keeping intensity
- its across the resonance wave- 8. Maximum number of ions created at the as aFig. resonance, scanning wavelength
of the laser The three function is corresponding intensity. pointsThe result of such an shown onlength. experiment
to the three curves 7. The of this line is thecorrespond of figure slope 7 where we have the number of ionsfigure plotted "
PM. quantity
This underlines the fact as we are notthat, expected,
in the conditions where SRA is valid. The cor-point
to this has been onresponding experiment reported
the curves of and for our 4, falls, figure pulse duration,
on a curve to an ofcorresponding intensity
x 4.3 10’ in with the inten-W/cm2, good agreement
sities used in this with ourexperiment. Together
we have on 4experimental point, represented figure
two to points corresponding experiments by Lompre
= = et al. for t 15 and I 109 [18], ps W/cm2 (circle
on and Grinchuk et al. forFig. 4) by [17],
I = 2 x 109 and a duration which isW/cm2 pulse
uncertain but in falls the of somedefinitely range
on These are threetens of nanoseconds (cross 4). Fig.
obtained in different experimental points, physical
which are in withconditions, very good agreement
theoretical expectations.
The shift of the centre of our resonance energy peak
has been on 9 versus the plotted figure corresponding
If the intensitieslaser on (circles Fig. 9). intensity
too accountused in this are weak, taking
- experiment 7. Number of ions created the interaction as aFig. during
of our measurement touncertainties, function of the laser for three values wavelength of the laserwavelength,
of theallow an accurate determination intensity. experimental 124
in in 1 to thethese results to be the coefficient, good theory developed applies only appear agree- part
ment both with resonance shifts measured in case of laser intensities constant in and the cal-time, [1]
an on and with those culations have been made assuming intensity(triangles Fig. 9) by
All these constant in the whole volume where the ions areal. on (crosses 9). Lompre et [18] Fig. expe-
rimental results are in with theoretical created. These conditions are far from ourgood agreement enough
has results of and as is the result of conditions : the laser [5] [12], experimental experimental pulse roughly
a Gaussian in the focal Grinchuk et al. obtained with intensities too and the intensity region[17] high shape,
of our lens varies from 0 to the maximumto be on 9.given continuously figure
I which has been as our laser intensity quoted intensity.
created under It follows that the ions are different
laser and thus under différent resonantintensities,
this must like awavelengths. Experimentally, appear
broadening.
Semi-classical theories which can handleeasily
time intensities have been dependent developed [6, 10]
but no of these theories to our application experiment
has been made until now.
will these from Therefore we consider anquestions
of view.experimental point
We will consider the time since oneeffect, only
can consider that and time inhomo-reasonably space
the same role and cumulate theirgeneities play simply
effects.
In the we introduce thediscussion, following
parameter
- 9. Shift of the resonance transition as a function ofenergy Fig.
the laser the circles are obtained the centreintensity : by measuring
of the of the are from 7 ; triangles reproduced [1] ]energy peaks figure
theoreticalalso the crosses are from Full-line : (see 2.4), [18]. known as the static that is the differencedetuning [1],
results [5, 12]. between the resonant transition for energy vanishing
laser intensities and the of energy three-photons.
We have seen above if for low laser intensitiesthat, 10a shows the variations of the resonanceFigure
the whole internal structure was when thisresolved,
is we no fineobserve the intensity increased, longer
structure of the 6F level. This shows that there is an
of the resonanceintensity dependent broadening
from which was the Thepeaks, expected theory.
arises if this is the one whichquestion
has been calculated the The by theory. experimental
width of the to thepeak corresponding
transition leftmost one on is(the Fig. 7)
which has to be with the theoretical valuecompared
= x I 2.2 x of 4.4 10-4 cm-1 for 10’ ThereW/cm2.
which must be some experimental broadening explains
this It cannot be the width of thedifference. Doppler
transition which is of 10-2 cm-1 and above all,only
does not on the laser It will depend intensity. appear
that there is an intensity dependent broadening arising
fact that the with which the ionsfrom the intensity
- Effect of the time of the underFig. 10. inhomogeneities intensity are created the interaction is not during homogeneous
which the ions are created at the resonance. 10a : Variations of the
either in time or in But this is space. point important resonant transition with to the smoothenergy time, corresponding
be discussed to separately. variations of our laser lOb : ofenough intensity. Experimental broadening
the resonance from these effects. A lOb ison resulting point figure
2. 3 EFFECT ’OF SPACE AND TIME INHOMOGENEITIES connected to the to tune the resonancedirectly intensity necessary
- which can be read on OF THE LASER INTENSITY. It must be noted that 10a.figure