Download Electron spectroscopy study of single and double multiphoton

Electron spectroscopy study of single and double
multiphoton ionization of strontium by visible
picosecond laser light
G. Petite, P. Agostini
To cite this version:
G. Petite, P. Agostini. Electron spectroscopy study of single and double multiphoton ionization
of strontium by visible picosecond laser light. Journal de Physique, 1986, 47 (5), pp.795-808.
<10.1051/jphys:01986004705079500>. <jpa-00210263>
HAL Id: jpa-00210263
https://hal.archives-ouvertes.fr/jpa-00210263
Submitted on 1 Jan 1986
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J.
Physique 47 (1986) 795-808’
m
1986,
795
Classification
Physics Abstracts
32.80D - 32.80F - 32.80K
Electron spectroscopy study of single and double multiphoton ionization
of strontium by visible picosecond laser light
G. Petite and P.
C.E.N.
Agostini
Saclay, Service de Physique, Atomes et Surfaces, 91191 Gif
(Reçu le 31
octobre 1985,
sur Yvette Cedex, France
accepti sous forme définitive le 24 janvier 1986)
Les techniques de spectroscopie d’électrons ont été appliquées à l’étude de l’ionisation multiphotonique
impulsions picosecondes de 1011 à quelque 1012 W cm-2, foumies soit
par un laser Nd : Yag doublé en fréquence, soit par un laser accordable (à rhodamine 6G). Les spectres d’énergie
d’électrons montrent que l’ionisation multiphotonique simple laisse l’ion soit dans son état fondamental, par un
processus à trois photons, soit après absorption d’un quatrième photon, dans un des premiers états excités. Des
résonances à deux et trois photons sur des états à un ou deux électrons excités peuvent intervenir dans ces processus
et créer une excitation importante du coeur. L’ionisation double apparaît essentiellement comme un processus
en deux étapes, dont la seconde peut avoir pour état initial un état excité de l’ion.
Résumé.
simple
2014
et double du strontium par des
Multiphoton single and double ionization of strontium was studied using electron spectroscopy
a picosecond, frequency doubled Nd : Yag Laser and a picosecond rhodamine 6G Dye Laser
Both
techniques.
were used, with intensities ranging from 1011 W . cm- 2 to a few 1012 W . cm-2. Single MPI was shown to produce
ions in both the ground state (3 photon) and several low lying excited states, through a four photon process. Two
and three photon resonances were observed, on singly and doubly excited states of the atom, resulting in an important degree of core excitation. Double ionization was shown to be essentially a « stepwise » process which can
involve excited states of the ion as the initial state of the second part of the process.
Abstract.
2014
1. Introduction.
Multiphoton Ionization (MPI-[1] and
therein) has long been studied, because
references
it is the
laser-atom
interaction
dominates
the
which
process
when high laser intensities are used. Most of the
emphasis has been put, in the past few years on the
study of MPI under very high laser intensities
(1011 W.cm-2 and above) for which new processes
can occur.
under such intensities an
of photon
necessary for ionization, in a process known as
«Above Threshold Ionization » (ATI) leading to
the production of hot electrons. ATI was studied in
the case of rare gases [2, 6] and caesium [7]. Both
perturbative [8, 9] and non perturbative [10, 11]
approaches were considered in theoretical work.
In [7] a good agreement between experimental
results and a perturbative calculation was obtained.
In the case of rare gases, which deals with both
higher intensities and more complex atoms, such
comparisons are still out of hand.
It
was
shown
[2] that
atom can absorb more than the number
The study of MPI processes under very high laser
intensities also led to the observation of multiple
ionization of atoms. It was observed in the case of
rare gases [12-15], alkaline earths [16-20] alkalis [21]
and rare earths [13, 22]. In several cases, double
ionization was observed at the same intensity where
simple ionization occurs though being of a much
higher order.
Here again different situations are encountered
depending on the type of atom considered. Rare
gases, with a complete outer shell require very high
laser intensities. They were at the origin of the most
impressive results concerning both the number of
electrons ejected (up to the complete outer shell),
and the number of photon absorptions involved
(a hundred and more). Clearly, for such high order
processes, the perturbative approach is not adequate
and new types of formalisms have to be developed.
A statistical approach of this problem [23] has been
recently proposed and is one of the possible paths
towards a better understanding of these processes.
Alkaline earths on the other hand present a quite
different picture. They are easily ionized, involving
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphys:01986004705079500
796
processes of a lower order. Though the calculation
of ionization probabilities is not easy, one can still
consider the perturbative approach as reasonably fit to
this problem. Moreover, in the case of strontium,
some specific ionization paths leading to double
ionization have been proposed [17, 20] and some
observations seem to indicate that ATI can play an
important role in double ionization. Resonances in
the double ionization signal were observed which
were assigned to transitions in the ion spectrum
whose initial state is an excited ion state which can
only be reached by absorption of extra photons.
However the electron spectra presented in proof
did not show the components implied by this inter-
pretation.
In this paper, we present electron energy spectra,
and their variations with the laser wavelength,
intensity and in some cases, polarization for single
and double ionization of strontium atoms by a
rhodamine 6G picosecond dye laser and a frequency
doubled Nd : Yag Laser. In addition we present
new observations of MPI in situations were multiphoton excitation of either the atom or the ion
yields an excitation energy close to an ionization
threshold. Last, we present new observations concerning electrons which can be unambiguously
assigned to a double ionization process. Besides
providing a decisive proof of the interpretations
given in references [17, 20], we discuss the following
issues.
(i) ATI in a complex atom : how does it differ
from ATI in a single electron atom; are the definitions
and concepts used in a single electron atom still valid
in the case of alkaline earths ? Can ATI lead to the
production of excited ion states ?
(ii) clarify
the
terminology concerning the diffeour experiment.
rent ionization processes involved in
(iii) briefly discuss the issue of double ionization
of strontium (direct or stepwise process).
The first two points of this discussion strictly deal
with single ionization of strontium.
2.1 SINGLE IONIZATION OF STRONTIUM.
Multiphoton ionization of alkaline earth has been the subject
of several theoretical publications these last years,
the emphasis being put on the central question of
autoionization under strong laser field [24-26]. These
models all predict strong modifications of the Fano
auto-ionization profile under high laser intensity.
Both single photon ionization [24] and MPI [25, 26]
were considered and a quite complete calculation in
the case of strontium can be found in [26] in an attempt
to analyse experimental results reported in [27, 28].
However some of the features of our experiment are
not considered in these papers, and will be the subject
of this theoretical part. We use the resolvent operator
formalism, as presented in [24], and later developed
in [25, 26].
The different couplings relevant to our experiment
are shown on figure 1. States of interest are : the
ground stateI g) of energy E8, two continual I c1 )
andI c2 &#x3E; (energies E1 and E2) and one auto-ionizing
stateI a &#x3E; of energy E. lying between the ionization
limits corresponding to continuaI c, &#x3E; andc2 &#x3E;. We
use the dressed atom model and these states will be
dressed respectively by n photons of the laser field
forI g), n - 3 photons fora ) andI c1), and
n - 4 photons forc2 ), etc.
Note that continualI cl &#x3E; andI C2 &#x3E; correspond to
different states of the core. For instance, in strontium,
-
(ii) ATI and double ionization : what are the
relationships between these two « high order » processes ?
(iii) What are the most probable
leading to double ionization.
mechanisms
Section 2 is devoted to a theoretical discussion
of the points mentioned above. Our aim is to give
clear definitions of the concepts to be used in this
paper rather than to present calculations correspondthose are still
ing to the results presented later
out of reach for the moment.
Section 3 will describe our experimental set up.
Our experimental results will be presented and
discussed in section 4 : electron energy spectra,
and their variations with the laser wavelength,
intensity and in some cases, polarization.
-
2.
Theory.
In this part, our goals are the following :
(i) using the simplest possible model,
we obtain
of
our
predictions concerning
aspects
experiment which have not been so far considered in the
literature.
some
Fig. 1. - Schematic representation of the couplings
involved in 3 and 4 photon ionization with a three photon
resonance on an
auto-ionizing state.
797
I ci ) is the continuumSs, E1 ) andI C2 &#x3E; could be
the continuum4d, 82 &#x3E; Energies of the dressed states thus are :
through the
inversion
integral
with
Couplings betweenI g) andI a &#x3E;,I cl &#x3E; orI c2 &#x3E;
Ha is the atomic Hamiltonian and Hf the field
Hamiltonian, these states are eigenstates of :
If
If we use the dipole approximation for the atom
field interaction, the total Hamiltonian of our system
will be :
Where D is the
dipole operator :
involve several photons so that it would be necessary
to complete the atomic spectrum of figure 1 with a
set of non resonant intermediate states, as it was
made in references [25, 26].
Instead we choose to represent the coupling between
the different states by effective interaction Hamiltonian such as :
that
so
in which 8 is the electric field amplitude and E the
polarization vector. V is the Coulomb interaction
responsible for the auto-ionization of)[ a ) and eventually for configuration mixing of other states too.
We can then proceed as in references [24, 26] and
compute the evolution operator U(t) of our system
from the resolvent operator.
our
interaction Hamiltonian writes :
Note that
DC2g
represents the coupling between
I g ) andc2 ) through a set of non resonant autoionizing states such asI a ), but does not include the
I c1 ) continuum. The coupling between the continua
I c1 &#x3E; andc2 ) will be neglected as it was done in [24].
With the above definitions, the equations determining the resolvent operator matrix elements are :
At time t
0, all the atoms are in the ground stateI g &#x3E;, so that the ionization rates in continualI cl &#x3E;
andI c2 ) will be determined byI Ug,,(t) aidI Ug-2(t)
We are thus interested in GClg and G129’ which can be expressed, from equations (9. c) and (9. d) by :
=
12
Using these expressions
in
equations (9. a) and (9. b)
12.
we
get :
798
we
then define :
which represent the shifts of
which
are
which is
a
the widths of
statuesI g &#x3E; andI a &#x3E; due
statesI g &#x3E; and[ a ) due
to their interaction with the continua :
to the same
interactions, and :
modified effective interaction between statesI g &#x3E; andI a &#x3E;, as defined in [24] but with an additional
continuumI c2 &#x3E; which should be small compared to the others because of its higher order in the
term due to
laser
intensity.
System (II)
which
then writes :
yields :
Expressions which are strikingly similar to those obtained in the
of hydrogenic atoms. We then obtain for GCIS and G,,,,, :
From this point on, the calculations have to be
carried out numerically, but the physics of our system
is already apparent in these expressions.
Expression (17. a), which describes ionization in
continuumI c, &#x3E; is made of two terms. The first one
describes direct ionization ofI g &#x3E; inI cl &#x3E;, when the
second one describes the excitation ofI a) followed
by auto-ionization ofI a) inI c, &#x3E;. The interference
between these two terms leads to the well known
Fano profile. This result is identical to the one obtained
in [24]. Because of the use of effective Hamiltonians
it differs from the results of references [25, 261 : Stark
case
of resonant
multiphoton ionization
shift of the ground and auto-ionizing states due to one
photon coupling with intermediate bound states are
not apparent, and also the modification brought to
VaC1 by a two photon coupling via the bound states
is missing. The latter could probably be taken into
account by using a modified VaC1 instead of VaC1’ like
it was done in reference [26].
If we now consider expression (17. b) it is strikingly
identical to (17. a) apart from the fact that ionization
ofa &#x3E; is due to a dipole interaction instead of a
Coulomb interaction. The same result was obtained
in the case of resonant multiphoton ionization
799
with a formalism sometimes referred to as « pseudo
auto-ionization » :: ionization in continuumI C2 &#x3E; is
the result of interference between a resonant amplitude
(Dc2a Dag) and a non resonant one (DC2g) in the same
way as ionization inI cl &#x3E; results of an interference
between a direct channel and the auto-ionizing one.
Considering expressions (17. a) and (17 . b)
remarks
can
a
few
be made.
(i) Expression (17. a), describing ionization to the
first continuum is identical to the one obtained in [24]
when only one continuum is considered.
The only differences are in the position of the poles
which are slightly modified by the presence ofc2 ),
and in one additional term in Dag which should be
small if not negligible.
(ii) Considering ionization in upper continua, as
described by equation (17.b) it appears to be an
usual MPI process, involving a number of bound
transitions and one bound-free transition. Since no
free-free transition is involved, and though absorption
of one photon above the lowest ionization threshold is
necessary to reach continuumI c2), ATI is not
involved, as it has sometimes been stated before [ 17, 20].
In this respect the acronym ATI can be somewhat
confusing in the case of two-electron atoms. It must
be applied only to ionizing processes involving c - c
transitions inside the same continuum (I c1) or
possiblyI c2 &#x3E;), that is without change of the excitation
state of the « core » electron.
As a conclusion to this paragraph, we note that,
apart from the high intensity effects already predicted
in auto-ionization, production of excited ion states
can exhibit resonances on auto-ionizing states lying
between the two ionization limits in a way analoguous
to resonant multiphoton ionization. The same width
should be measured on these resonances and in the
usual auto-ionization in the lower continuum; because
this width is determined by the poles imaginary parts,
which are the same in (17. a) and (17. b) so that the
intensity effects predicted in [25, 26] should be seen
in the production of excited ion states.
Note that because the dipole operator is monoelectronic, only resonances on states with the same
core can appear in excited ion states production.
This is true of course only when configuration interactions are neglected. In the opposite case, interesting
indications can be obtained in this way, on the importance of these interactions.
2.2 DOUBLE IONIZATION.
Multiple ionization has
been repeatedly observed for about ten years now
[12-22, 27-29] and not much is known about the
mechanisms leading to multiply charged ion production. In the framework of perturbation theory, two
apparently different mechanisms can lead to double
ionization which will be discussed here :
(i) direct ionization : two electrons are simultaneously excited and ejected yielding a doubly charged
ion obtained directly from the neutral atom.
(ii) stepwise ionization : a singly charged ion is
obtained first, and a doubly charged ion results from
multiphoton ionization of this ion.
Thus far, the question of the competition between
these two processes has been considered as a central
one. It was recently considered in a paper [30] which
thoroughly discusses this question in view of an
application to two-photon ionization of helium.
The following discussion directly stems from the
conclusions of this paper, and only that part of the
calculations which are necessary to the understanding
of the discussion will be reproduced.
We consider here, as in [30] and for the sake of
simplicity of the expressions, a two-photon double
ionization process, but the discussion can easily be
generalized to a higher order process. We are thus
interested in the case where an atom in its ground
stateg) of energy Eg can be doubly ionized by
absorption of two photons of energy Ep, giving a
doubly charged ion in its ground state192 &#x3E; and two
electrons with energies 81’ and 82 such that :
In the framework of lowest order perturbation
theory, the probability of such a process can be
expressed, by :
where I is the laser intensity, d the atomic dipole
operator and Ii) an intermediate state with energy E;.
In doing this, we of course neglect correlation for the
continuum states.
We then note that d, being a monoelectronic operator, can only coupleg2, E1, G2 ) to states pertaining
to the continuum of simple ionization, that is of the
typeI el, G1 &#x3E;, ourIe1, G2 ) whereI el &#x3E; is one of the
singly charged ion states (ground or excited), so that
(19) yields.
-
This expression clearly describes the interferences
between two series of time ordered two photon interaction diagrams representing the following process :
absorption of one photon by the atom in its ground
state yielding a singly charged ion and an electron of
energy s, (or P2), followed by an absorption of a
second photon resulting in ionization of the singly
800
charged ion, yielding another electron of energy 82
(resp. Ei). This shows that, in this framework, double
ionization is a sequential process, even if there is no
way to decide which electron has been emitted first.
With this in mind, two different cases have to be
considered. Equation (12) reflects the fact that a limited
range of electron energies can be obtained in such
processes, and different situations will occur depending
whether in the intermediate state, real ionic states can
be reached with emission of an electron in this energy
range, as schematised on figure 2.
If not (case A of Fig. 2), the intermediate states of
expression (20) can only be virtual ionic state, and no
particular problem arises in expression (20). But such
states are very short lived (a few optical cycles) and
double ionization can be considered as a direct process.
If a real atomic state (ground or excited) can be reached
(case B of Fig. 2), the situation is quite different : one
of the denominators of equation (20) will vanish, in a
way similar to what happens in resonant multiphoton
ionization (while the first case considered above was
typically a non resonant process). Also, real ionic states
have much longer lifetimes than virtual states so that
it is reasonable to think of double ionization as a two
step process. We should however remember that this
approach has failed giving a satisfying description of
resonant multiphoton ionization. Therefore, though
the terms of « direct » and « stepwise » will still be
used throughout this paper it should be remembered
that these two processes are not fundamentally different : stepwise double ionization is only a double
ionization process presenting a resonance in electron
energy which should however be distinguished from
resonances in photon energy which may occur in
higher order processes. The use of o stepwise » should
not conceal the fact that the
ionization process takes
place in a time much shorter that the radiative lifetime
of the real states involved in these resonances. Such
resonances will of course produce peaks in the electron
energy distribution but cannot be detected in experiments based on ion detection only.
So far we have limited ourselves to the case of lowest
order processes. Considering processes of higher order
increases the energy range in which electrons can be
ejected, and thus the number or resonances which can
be reached, as shown on figure 2, case C. Though of a
higher order, such processes, because they are resonant, may not be negligible if no resonance occurs in the
lowest order process. This is thoroughly discussed in
the case of helium in reference [30], and the conclusion
in this case is that the non resonant process is negligible when compared to resonant processes of the
same order, which was expected, and cannot be
neglected when compared to resonant processes of a
higher order. However generalization to high order
multiphoton processes is not trivial and only a precise
calculation in the experimental situation, when possible, will give an unambiguous answer to this question.
Concerning now the question of ATI and double
ionization, the same remarks can be made than for
production of excited ion states : ATI does produce
excited electrons whose energy would, in the case of
two photon double ionization discussed above, lio
above the second ionization limit, but it does not
produce core excitation and thus cannot yield multiple
ionization, and therefore states reached by ATI are not
privileged intermediate states of the multiple ionization
process.
Experimental set up.
Our experimental set up
3.
is schematized in figure 3.
Most of its elements have been described in previous
publications so that we will limit ourselves to a brief
description of its main characteristics.
Two different lasers have been
3.1 LASER SYSTEM.
used in this experiment. The first one is a commercial
-
Difl’erent double ionization processes : (A) lowest
resonant (direct) process; (B) lowest order
resonant (stepwise) process; (C) higher order resonant
(stepwise) process.I g &#x3E; : neutral atom ground state;
I g1 &#x3E; : singly charged ion ground state; !I e1 &#x3E; : singly
charged ion excited state ;g2 &#x3E; : doubly charged ion
Fig.
2.
order
-
non
ground state.
Fig.
3.
-
Schematic of the
experimental set-up.
801
Nd : Yag laser system (Quantel) delivering 20 ps Fourier limited pulses at a 10 Hertz repetition rate. After
frequency doubling, this system can deliver at 0.53 gm
up to 20 mJ per pulse. The Nd : Yag oscillator is both
passively and actively mode locked, keeping the pulseto-pulse energy fluctuations at a low level (± 5 %).
This system can be used directly in the experiment,
or it can alternatively be used to synchronously pump
a dye oscillator-amplifier system as described in [31].
This system can deliver up to 2 mJ in a single 20 ps
Fourier limited pulse whose wavelength can be tuned
throughout the rhodamine 6G emission band (557 to
575 nm).
Because of the long duration of such a wavelength
scan (up to 15 h when one electron spectrum is taken
every angstrom) it is necessary to lock the energy per
pulse mean value. This is achieved through a servo
controlled Fresnel rhomb-Glan prism attenuator
placed in front of the experiment chamber with this
system, the long term intensity drifts can be compensated for, and the mean laser intensity kept stable
within ± 5 % throughout one wavelength scan.
Different focusing lenses have been used in this
experiment. At low intensity a 140 mm focal length
plano-convex lens is used. When high intensities are
necessary, a 70 mm focal length sphero-parabolic
lens can be used. It allows to reach intensities of a few
Tw . cm - 2 in the interaction region without having to
face overwhelming space charge problems.
3.2 ELECTRON SPECTROMETER. - The laser beam is
focused in a vacuum chamber (residual pressure of
10- 8 torr), crossed at a right angle with an effusive Sr
beam similar to the one used in [7], with Sr densities
of a few 109 cm- 3. The electron spe’ctrometer is also
identical to the one described in [7]. It is an electrostatic time of flight spectrometer with a 23 cm length. As
shown in figure 3, a grid system allows to apply an
acceleration field in the interaction region while
keeping the analysis energy at any desired value. This
system is very useful in the case of very low energy
electrons which are very sensitive to both space charge
and stray magnetic fields.
At the exit of the flight tube, the electrons are
detected by a separated dynodes electron multiplier
and fed into a multichannel analyser : counts are
temporarily stored into shifts registers, before being
accumulated into the analyser memory.
Up to 1024 channels of 10 ns to 1 gs time width are
available. After accumulation, the content of the
analyser memory can be transferred to a LSI 11 microcomputer system which is in charge of data processing
and storage. This computer is also used to tune the dye
laser and if necessary control the laser intensity and
the spectrometer settings.
The spectrometer can also be used in ion detection.
In this case, an analog signal is obtained which is
processed by a boxcar averager after being, if necessary,
amplified.
Because
throughout this
paper,
peaks
of different
electron energy will be compared, the question of the
spectrometer transmission has to be considered.
Figure 4 shows an experimental measurement of this
transmission in the energy range of interest here, which
was obtained as follows : a well known and well
isolated peak of our electron spectrum (three photon
ionization of Sr, leaving the ion in its ground state and
an electron of energy 0.89 eV, obtained at low laser
intensities) was shifted by scanning the flight tube
voltage between - 0.2 and 2 eV, resulting in the variation of the peak amplitude shown in figure 4. This
variation has two different origins :
of the collection angle due to the
the
electrons between the interaction
of
acceleration
volume and the flight tube;
(ii) variations of the flight tube transmission due
probably to stray magnetic fields whose action on low
energy electrons is strong and energy dependent.
The first of these two effects can easily be computed
and subtracted from the measurement of figure 4,
allowing a measurement of the second effect only
(broken line in Fig. 4).
It shows that for electron energies less than 1.5 eV,
losses in the flight tube cannot be neglected. However,
contrary to the variations of the collection angle due to
acceleration, they do not depend on the electron
initial energy but on the electron energy inside the flight
tube only, and can be taken into account using the
curve of figure 4.
Two typical voltage settings have been used in this
experiment. Some spectra were taken with all electrodes grounded but this does not allow detection of
low energy electrons both because of space charge,
contact potentials and losses in the flight tube. Therefore, when such electrons were studied, a small
d.c. electric field (between 5 and 10 V/cm) was applied
in the interaction volume to help charge separation
(i) variations
Fig. 4. Variations of the spectrometer transmission with
the electron energy : 0-0 : variations of the electron
peak amplitude with the accelerating voltage; . ::
variation of the t.o.f. tube transmission with the analysis
energy.
-
802
and the flight tube potential was set to a positive value
(1 V generally), to prevent important losses in the flight
tube.
4.
Experimental results.
Multiphoton ionization of Sr was studied at 532 nm
(Nd : Yag second harmonic) and between 558 nm and
575 nm (tuning range of our rhodamine 6G dye laser).
Both the ions and the electrons were studied, but the
results on ions obtained with the dye laser have already
been published [20] and will not be discussed here.
Some preliminary results on the electrons have also
been reported in [32] and will be presented in more
details here.
Before presenting the experimental results, a brief
summary of the Sr spectroscopy relevant to our experiment is necessary, particulary to precise a few ionization channels which play an important role in this
experiment, and which are outlined on figure 5.
The
Fig. 5. Different ionization
and double ionization.
-
paths involved
in Sr
simple
simplest ionization process for Sr is the three photon ionization of the ground state neutral
Absorption of a fourth photon can leave the Sr II ion in either the ground state, or two excited states :
«
Stepwise » (resonant)
double ionization
using the above transitions
Note that the non resonant ionization process (# 8)
is of order 8. Resonant processes can be of order 8
or 9 depending on the laser wavelength. The electron
energies also depend on the laser wavelength. Within
the tuning range of the dye laser two thresholds are
crossed in channels # 4 and # 5. Channel # 6
is of order 4 with the frequency doubled Nd : Yag laser
and of order 5 with the dye laser.
4 .1 IONIZATION oF Sr AT 532 nm.
Single ionization
of Sr was detected for intensities of the order of
1012 W . cm- 2 and above, using a 75 mm focal length
lens. Double ionization was detected for intensities
of the order of 5 x 1012 W.cm-2 and above. Variations of the ion signal with the laser intensity are
shown in figure 6 using the usual log-log representation. They show that doubly ionized Sr is detected
for intensities just above the onset of saturation for
single ionization. This behaviour has usually been
considered as the signature of a stepwise double
-
as a
first step
can
also
occur :
Slopes measured in the linear
respectively 3.3 for single ionization and
ionization process.
region
are
5.4 for double ionization, in agreement with the
number of photons necessary to ionize the neutral
(3 photons) or the ground state singly charged
ion (5 photons).
In many respects these results are analogous to
those obtained in Ca [19] at the same wavelength,
except that the intensity gap between single and second
ionization is larger in the case of Ca.
Figure 7 shows different electron spectra obtained
at this wavelength in different conditions.
The spectrum of figure 7a was obtained for a laser
intensity of 2.8 x 1012 W . cm- 2 and without electron
acceleration. The energies of the three peaks displayed
on this spectrum are found to be 1.2, 1.8 and 3.1 eV.
Two processes can be responsible for the peak at
1.2 eV, which are the three photon ionization of
neutral Sr (# 1 or Fig. 5) which yield an electron
of 1.29 eV, and four photon ionization of the 5p
atom
803
to 0.6 eV electrons. This peak is clearly
in figure 7c, taken at an intensity of 1.2 x
respond
visible
1012 W.CM-2 . Electrons with such an energy can
be created in both processes # 4 ( four photon
ionization in the 5p ion state) and # 5 (five photon
ionization of the ground state ion). A third peak
is clearly visible on figure 7c, corresponding to
electrons with an energy of 0.1 eV, such as the ones
created in process # 6 (four photon ionization of
the 4d ions). The electrons created in process # 7
would appear at the same energy as those of process # 1 (1.3 eV). The intensity behaviour of these
different peaks, shown in figure 8 indicates that the
electrons of the 0.6 eV peak are mostly created in the
double ionization process, as those of the 0.1 eV
peak, since they do not saturate as the 1.3 eV peak
does. Even the 1.3 eV peak does not saturate as
strongly as the singly charged ion signal does (Fig. 6),
Fig. 6. Variation of the number of singly (o---o)
doubly (.-.) charged Sr ions with the laser energy.
-
and
(# 7) which yield an electron of 1.23
1.32 eV (depending of the J value of the 5p state).
These energies are too close to be separated in our
spectrometer, but comparing the ion signals at this
intensity shows that this peak is certainly mainly due
to single ionization of channel # 1. The peak at
1.8 eV can unambiguously be assigned to the process
of channel # 3 (single ionization leaving the ion
in one of the 4d states). The last peak at 3.1 eV is
certainly due to ATI, but here the resolution of our
spectrometer is too low to ascertain whether it is due
to ATI following single ionization of channel # 2
(yielding 3.5 eV electrons) or ATI following double
ionization of channel # 5 (yielding 2.9 eV electrons)
which, as we will see, is already important at such
state of Sr II
or
an
intensity.
The two following spectra (Figs. 7b and c) have
been obtained using a 6.7 V/cm separation field
and a 1 V acceleration voltage on the flight tube.
The increase of the collection efficiency allows to
work at both a lower neutral density and laser intensity. The spectrum of figure 7b is taken at an intensity
of 0.3 x 1012 W. Crn - 2.
It shows only one peak at 2.2 eV, which is the
remnant of the 1.2 eV peak of figure 7a. The 1.8 eV
peak either has disappeared or is not separated from
the main peak. On the trailing edge of the main peak,
there is a weak feature whose position would cor-
804
Fig.
A
=
7. - Different electron energy spectra taken at
532 nm and for different experimental conditions
(see text).
Fig. 8. Variations of selected peaks amplitude (from
Fig. 7) with the laser energy. Labels correspond to different
processes of figure 5.
-
and this may be due to the contribution of electrons
of channel # 7, which may not be negligible at high
intensities.
The main conclusion arising from these data is
that double ionization of Sr at 530 nm is essentially
a « stepwise » (resonant) process involving principally
the ground state and the first two excited states of the
Sr ion. It can also be deduced from the comparison
of the two higher energy peaks of figure 7a that
excited ion state production is more probable than
ATI of the same order. This suggests than multiphoton ionization of alkaline earths goes along with
a noticeable degree of core excitation.
4.2 IONIZATION OF Sr FROM 558 nm TO 574 nm.
This experiment was repeated using our dye laser,
in the wavelength range between 558 and 574 nm.
Spectra corresponding to those of figure 7 were
obtained and are presented in figure 9. The spectrum
of figure 9a was taken without collection field and
at an intensity of 3 x 1012 W.em-2. The spectrum
of figure 9b was obtained with a few V. cm-1 collection field and a 1 V net acceleration between the focal
volume and the flight tube. The intensity in this case
was about 1011 W . cm - 2. On these spectra, peaks
corresponding to all the processes discussed in the
previous chapter can be observed. Processes # 2, 5
and 6 do not appear on the spectrum of figure 9b
because it is taken at a much lower intensity, and they
disappear of the spectrum of figure 9a when the
intensity is decreased.
Some aspects of these results have already been
presented in [32] and will be further discussed here.
We first note that the differences in the peak positions
-
between figures 7 and 9 are due to the change in the
laser wavelength and are all consistent with the interpretations given here for each peak.
The peak labelled 5 in figure 9a corresponds to
six photon ionization of the ground state ion. Depending whether the wavelength is shorter or longer than
520 nm (five photon ionization threshold for the
ground state ion) this is either a normal MPI peak
or a first order ATI peak. As reported in [32], no
rapid variation of this peak amplitude is observed
when the laser wavelength is scanned through the
threshold wavelength. This was interpreted on the
ground of the continuity between the wavefunctions
of the discrete spectrum when n - oo and of the
continuum when E - 0. However it is impossible
to identify a five photon ionization peak which should
appear at short wavelength, because it is superimposed to the peak # 4, and the dye laser intensity is
too small to allow an identification through the
intensity dependence. As shown in the previous
paragraph, this is possible at 532 nm and gives us
full confidence in the above interpretation.
The peak labelled 4 (in Fig. 9b) is essentially due
(totally at low intensities) to 4 photon ionization of
Sr, leaving the ion in the 5p excited states. The one
labelled (1) + (3) by following peaks (1) and (3)
of figure 9 a when increasing the accellerating field.
Peak (4) is identified, as discussed below, by its wavelength dependence. The slight energy mismatch visible
in figure 9b is probably due to the use of a separation
805
0.1 eV - typically
when they are emitted preferentially along the laser polarization direction). This
detection scheme was usefull in identifying peak # 4
but causes strong variations of the collection efficiency
with the energy.
Figure 10 represents the variations of the peak # 4
amplitude, for a laser intensity of 1011 W.cm-’, and
for laser wavelengths between 565 nm and 574 nm.
The laser polarization is along the detection direction
so that this peak amplitude is a good representation
of the excitation probability for the 5p ion states. The
-
are still clearly visible, the ionization
probability presenting in both cases a maximum about
two thresholds
Fig.
9.
-
Two different electron energy spectra taken with
the
Dye laser for different conditions (see text). Labels
on the peaks correspond to different ionization
processes
of figure 5.
field which makes the electron
energies (inside the
flight tube) critically dependent on the position of
the laser focus.
Here again, the two thresholds corresponding to
excitations of the 5P3/2 and 5P 1/2 states of Sr+ are
crossed within the dye laser wavelength range, for
567,8 nm and 574,4 nm respectively. In [32], in order to
emphasize the threshold effect, the variations of the
peak # 4 with the laser wavelength in the threshold
region were recorded with the laser polarization at a
right angle from the collection axis. (In this configuration, our electron spectrometer works as a « threshold
spectrometer » because the weak accelerating field is
too low to collect electrons with energies above
45 cm-1 above the ionization threshold. In addition,
for wavelengths between 590 nm and 572 nm, a broad
maximum can be seen, which was completely cut-off
by the transmission drop in [32]. It corresponds to
two photon intermediate resonances on the 5p2 3p 0
and 5s 5d 3Di states of Sr which were observed on the
ion signal in [20, 28]. As will be shown in a forthcoming
paper at the intensity used in this experiment, these
resonances are strongly shifted and broadened and
thus are not clearly resolved on the spectrum of figure
10. We finally note that in this wavelength range, the
peak labelled 3 on figure 8a, corresponding to four
photon ionization in the 4d states is negligible.
Many two and three photon resonances in the ion
signal were also observed in the wavelength range
between 558 nm and 564 nm [20, 28]. These resonances
can also be seen on the electron signals, as shown in
figures 11 and 12. These two figures show the wavelength dependences of different peaks. Figures 11 and
12 correspond respectively to a laser linearly polarized
along the direction of detection and circularly polarized. Figures 11 (12) a, b and c correspond respectively
to three photon ionization into the Sr+ ground state
(channel # 1), four photon ionization into the 4d
(channel # 3) and 5p (channel # 4) states. Figure 11c,
was taken at a laser intensity of 1011 W . cm- 2, figures
11a and b at an intensity of 1.6 x 1011 W .cm-2, and
figures 12a, b, c at 2 x 1011 W .em-2. As usual with
tightly focused picosecond pulses, absolute intensities
are not determined to a better precision than a factor 2.
However comparison between the different figures
quoted above is exact within 20 %. Intensity changes
between the different spectra of figures 11 and 12
were made necessary by experimental constraints
owing to the limited range of satisfying operating
conditions for the spectrometer and of course to
the accumulation time. The wavelengths plotted in
abscissa are in the vacuum and are taken directly from
the computer scanning program, so that the small
differences between the positions of the peaks in
different spectra only reflect the limited precision of
our wavelength scanning/measurement system, which
is about 1 angstrom.
Some general remarks can be made concerning
these spectra. All the resonances of figures 11 and 12
have already been seen with ion detection [20, 28].
806
Figure 10. Wavelength dependence of peak 4, of figure 9b (Sr (5s2) + 4 hv
threshold region. Vertical bars indicate the position of the thresholds.
-
-+
Sr+ (5p)
+
e-) in the 5P 1/2,3/2 ionization
labelled (I) to (V) in figure l la which can be seen, to a
different degree, on all the spectra of figures 11 and 12.
Resonance (I) at 559.4 nm, with a small satellite at
559.6 nm (which in some cases appears merely as a
shoulder) appears, as in [20, 28] at the wavelength
corresponding to a three photon resonance on the
5p 6s 1P’ state as deduced from the results of reference
[33]. The fact that this resonance is clearly seen with a
circularly polarized laser is a first indication that
Fig. 11. - Wavelength dependence of selected peaks of
figure 9 in the 558-nm-564 nm region, for a linear polarization of the laser, along the detection direction.
Changing the laser polarization from linear to
circular lead to a decrease of the ionization probability which made necessary and increase of the laser
intensity by a factor of 1.5 to 2 to restore the signal
level. It also results in a sharpening of the resonances,
Fig.
laser.
12. - Same
as
figure 11,
with
a
circularly polarized
807
configuration mixing has to be considered to interpret
data.
Resonance
our
(II) is
at 560.6 nm where two different
explanations can be considered : a two photon resonance on the
state or/and a three photon
resonance on the 4d
state of [33].
4f(3/2
5p2 3P2
(2D5/2)
1)01
Both are allowed with circular polarization. Note that
for linear polarization, this resonance appears only as a
broad weak feature in process # 3, while for circular
polarization it is, on the contrary, the tallest and
thinest resonance on spectrum b. On the two other
spectra, though keeping the same shape, its importance
decreases for circular polarization, compared to linear.
No known state can be found in the literature to
explain resonance (III) at 561.6 nm. It can only be said
that it should correspond to a state with J
3 because
it is certainly a three photon resonance and it is
maintained in circular polarization.
In [28], resonance (IV), at 563 nm was tentatively
assigned to a three photon resonance on the
4f(3/2)’ state [33]. In [20], it was noted that a better
wavelength fit was obtained for this state with resonance (V) at 563.5 nm. The new results do not support
this hypothesis for two reasons : first resonance (V) is
suppressed in circular polarization, which should not
be the case for such a state; secondly because on the
different spectra of figure 10, it appears to be much
stronger in ionization towards the 5p state (c) than
towards the 4d (b) or 5s (a) state. It follows from the
analysis of 2 .1 that, if a definite core can be assigned to
the state responsible for resonance (V), it should be a
5p core rather than a 4d despite the wavelength
difference our results tend to confirm the interpretation
given in [28] for resonance (IV), which leaves (V)
unidentified.
=
4d(2D3!2)
Figures 11 and 12 bring up an other problem : the
analysis of 2.1 led to the hope that strong differences
between the different resonance spectra would help
assigning a core to the different states responsible for
the observed resonances. This is obviously not the case,
except may be for resonance (V). Two explanations
be considered for this behaviour. It could first be
argued that the ionization mechanism involved in the
production of ion excited states is not the one considered in section 2. The fourth photon could hit the wing
of a broad (because relatively low lying) 6s nl autoionizing resonance, which then ionizes into all the
available channels.
In this case, the spectra of figures 11,12b and c would
only differ by a branching ratio which would not be
wavelength dependent, and the spectra should be
strictly identical, which is not observed. It seems more
reasonable to think that a strong configuration mixing
has to be considered for the states involved in these
resonances. Note that this configuration mixing must
be also invoked to explain the three photon excitation
of 4d nf states from a 5S2 ground state.
One might also ask which are the possible candidates
for the unidentified resonances. Two remarks can be
can
made : in
[33]
three 4d 4f states
identified : both
4f(3/2)0, states, but
are
4d(2DsI2)’ 4f(3/2)0 an&#x26;4d(2 D 3/ )
only the 4d(2DS/4) 4f(1/2)1, state. Simply using the
energy of this state and the 4d(2DsI2,3/2) fine structure
a
splitting deduced from the other pair of states gives
wavelength of 560.9 nm, close to resonance (II) which
already has two candidates. However, this calculation
is probably a little crude in such a complicated
situation.
Another possible candidate is a 5p 5d state. This
state does not appear in [33]. It has been searched for
unsuccessfully by absorption techniques using U.V.
light [34] where it is concluded that, in Sr, transition
from 5s2 to 5p 5d is anomalously weak. A possible
explanation for this is that such a one photon transition can only originate from an admixture of 5p2 in the
5s2 ground state. This is not true anymore when three
photon transitions are considered. It should also be
said that some results on the a.c. stark shift of the 5p2
and 5d 5s states seems to point at the presence of such
a state in this energy region.
Note that a 5p 5d 1P01 state would be a reasonable
candidate for resonance (V), but our data are too
limited to consistently back up such an assignment.
Last, one should consider the question of the
branching ratios. Data of figures 10 and 11 are raw
electron counts per laser shot. Corrections from the
transmission effects have not been introduced. Spectra
a and b are taken together without acceleration field
so that the only correction to be made is that of the
flight tube transmission between 0.9 eV and 1.3 eV.
From the results of figure 4 it can be deduced that
compared to a, spectrum b is overestimated by a
factor 1.5, as noted in the top left comer. In the case of
spectra c, a 1 V acceleration is used which is rather
efficient on 0.1 eV electrons so that spectra c are
overestimated by a factor of about 11. If, in figure 11, we
take 0.04 as an average value of the signal for spectrum
a, 0.015 for spectrum b and 0.5 for spectrum c, it can be
concluded that on the average, at intensities of the
order of 1011 W . cm2 and in this wavelength range,
about 10 % of the ionization occurs in state 4d and
almost 50 % in state 5p which is certainly an important
effect. Of course this ratio is wavelength dependent :
almost no 4d state is reached for wavelengths above
564 nm, and close to the 5P3/2 ionization threshold,
this channel is the dominant one.
5. Conclusion.
Single and double multiphoton ionization of Sr has
been studied using electron spectroscopy techniques.
Single ionization has been shown to occur for a
significant part in excited states of the ion even though
these processes require the absorption of one more
photon than ionization in the ground state. A multiphoton process of the same order, that is first order ATI
leaving the ion in the ground state, is shown in this
case, to be less probable. This leads to the conclusion
that the question of multiphoton ionization of alkaline
808
earth cannot be tackled without considering that of
core excitation (or equivalently the question of two
electron excited states). It is also clear that configuration mixing plays a major role in the problem of resonant multiphoton ionization of Sr, be the resonance on
an intermediate state or on an auto-ionizing final state.
All this makes the problem of MPI of alkaline earths
considerably more complicated than that of one
electron atoms.
Concerning double ionization, it has been shown to
be essentially a stepwise (or resonant) process. Low
lying two-electron excited states or ion excited states
play a major role in these resonant transitions but it
merely results in the excitation of a few low lying ion
states. Of course this may be a particular property of
alkaline earths because they have low lying ion states,
and the situation may be different for rare gases whose
first excited ion state is lying at about one half of the
ion ionization threshold.
Although the assignement of resonances was sometimes uncertain, no clear evidence of resonances on
two electron states could be found. No
evidence was found either of non resonant double
ionization. We conclude that these processes have a
low probability at the wavelengths investigated here.
Given the reasonable number of photons involved and
the fact that one can even point at some specific MPI
channels, the perturbative approach, even if it does not
lead to easy calculations, still seems reasonably
qualified to treat the problem of double multiphoton
ionization of alkaline earths.
high lying
6.
Acknowledgments.
The authors would like to thank A. L’Huillier, Pr W.
Cooke and P. Lambropoulos for many interesting
discussions, and Dr Manus for his critical reading of
the manuscript. They also would like to acknowledge
the help of C. Boudigues and M. Bougeard in building
up the equipment and that of A. Sanchez in designing
and maintaining the intricated electronical equipment
which was used in this experiment.
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