Experimental examination of ionization processes of noble gases in strong laser fields [Elektronische Ressource] / vorgelegt von Rolf Wiehle
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Experimental examination of ionization processes of noble gases in strong laser fields [Elektronische Ressource] / vorgelegt von Rolf Wiehle

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Experimental Examinationof Ionization Processesof Noble Gasesin Strong Laser FieldsInaugural-DissertationZur Erlangung des Doktorgrades derFakult at fur? Mathematik und PhysikAlbert Ludwigs Universit at, Freiburgvorgelegt vonRolf WiehleMarch 7, 2005Dekan: Prof. Dr. J. HonerkampErstgutachter: Prof. Dr. H. HelmZweitgutachter: Prof. Dr. M. Weidemuller?Datum der mundlic? hen Prufung:? 24.02.2005AbstractThis thesis discusses experimental results on the interaction of intense light withisolated atoms. Inside the focus of modern pulsed lasers, electric fields are pro-duced, which are comparable with the atomic field strength. The correspondinghigh number of photons available, allows the ionization of noble gas atoms byabsorption of a great number of IR-photons, whose individual energy is muchsmaller than the atom’s ionization potential. Alternatively, the interaction maybe described in terms of fields: The laser modifies the binding potential, sup-pressing the Coulomb barrier, such that an electron may tunnel out.Theoreticalcalculationsforsingleionizationwereabletoreproduceexperimentalresults, but strong deviations were observed for double ionization. The rescatter-ing model was invented which accounts for many of the previously unexplainedfeaturesfoundinexperiments. Withinthismodelthefirstelectronisfreedbythelaser and subsequently accelerated in its oscillating electric field. Upon return toitsparention,theelectroninteractswithitandfreesasecondelectron.

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Published 01 January 2005
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Experimental Examination
of Ionization Processes
of Noble Gases
in Strong Laser Fields
Inaugural-Dissertation
Zur Erlangung des Doktorgrades der
Fakult at fur? Mathematik und Physik
Albert Ludwigs Universit at, Freiburg
vorgelegt von
Rolf Wiehle
March 7, 2005Dekan: Prof. Dr. J. Honerkamp
Erstgutachter: Prof. Dr. H. Helm
Zweitgutachter: Prof. Dr. M. Weidemuller?
Datum der mundlic? hen Prufung:? 24.02.2005Abstract
This thesis discusses experimental results on the interaction of intense light with
isolated atoms. Inside the focus of modern pulsed lasers, electric fields are pro-
duced, which are comparable with the atomic field strength. The corresponding
high number of photons available, allows the ionization of noble gas atoms by
absorption of a great number of IR-photons, whose individual energy is much
smaller than the atom’s ionization potential. Alternatively, the interaction may
be described in terms of fields: The laser modifies the binding potential, sup-
pressing the Coulomb barrier, such that an electron may tunnel out.
Theoreticalcalculationsforsingleionizationwereabletoreproduceexperimental
results, but strong deviations were observed for double ionization. The rescatter-
ing model was invented which accounts for many of the previously unexplained
featuresfoundinexperiments. Withinthismodelthefirstelectronisfreedbythe
laser and subsequently accelerated in its oscillating electric field. Upon return to
itsparention,theelectroninteractswithitandfreesasecondelectron. Theopen
question is, why double ionization is observed, even if the rescattered electron is
much too slow to ionize the ion.
This thesis examines the processes underlying the ionization of rare gases. The
focus is on double ionization, especially at intensities, which produce rescattered
electronstooslowforionization. Ourexperimentalapproachistorecordtheions’
time of flight and simultaneously the doubly differential momentum distribution
of the photoelectrons. The latter reveals a rich structure indicate of different
ionization processes.
In chapter 1 some theoretical background to the topic of ionization of atoms in
strong laser fields is given. Chapter 2 describes the experimental techniques used
to obtainthe data presentedsubsequently. Single ionization of argon is discussed
in detail in chapter 3, where our experimental data are compared with numerical
calculations. In Chapter 4 measurements on the intensity dependence of the ion
yield and simultaneously recorded electron momentum distributions for argon,
krypton and xenon are presented and discussed. An experiment on the optimiza-
tion of ionization processes, by iteratively changing the shape of the driving laser
pulse is presented in chapter 5. Photoelectron spectra resulting from electrons
producedindoubleionizationprocessesarepresentedinchapter 6, together with
the experimental technique used to selectively record these electrons.Results from this thesis have been published in the following articles:
R.Wiehle and B.Witzel, Correlation between Double and Nonresonant
Single Ionization, Physical Review Letters, 89, 223002, (2002)
R. Wiehle, B. Witzel, H. Helm and E. Cormier, Dynamics of strong-field
above-threshold ionization of argon: Comparison between experiment
and theory, Physical Review A, 67, 063405 (2003)
R. Wiehle, B. Witzel, V. Schyja, H. Helm and E. Cormier, Strong-field pho-
toionization of argon: a comparison between experiment and the SAE
approximation, Journal of Modern Optics, 50, 451 (2003)
E.Cormier,P.-A.Hervieux,R.Wiehle,B.WitzelandH.Helm,ATIofcomplex
systems: Ar and C , European Physical Journal D, 26, 83 (2003)60
R. Wiehle, P. Kaminski, W. Kamke, B. Witzel and H. Helm Charge state re-
solved electron momentum spectra for strong field double ionization
of Xe, in preparation
The following article has published with contributions from the author:
P.Kaminski,R.Wiehle,V.Renard,A.Kazmierczak,B.Lavorel,O.Faucher,and
B.Witzel, Wavelength dependence of multiphoton ionization of xenon,
Physical Review A, 70, 053413 (2004)Contents
1 Ionization of Atoms in Strong Laser Fields 5
1.1 Single Ionization . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
1.1.1 Multi Photon Ionization (MPI) . . . . . . . . . . . . . . . 5
1.1.2 Above Threshold (ATI) . . . . . . . . . . . . . . 6
1.1.3 Tunnelling Ionization / Over the Barrier Ionization . . . . 7
1.1.4 Single Active Electron Approximation (SAE). . . . . . . . 7
1.2 Double Ionization . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
1.2.1 Coincidence Measurements . . . . . . . . . . . . . . . . . . 9
1.2.2 One Dimensional Calculations . . . . . . . . . . . . . . . . 12
1.2.3 Semiclassical . . . . . . . . . . . . . . . . . . 13
1.2.4 S-Matrix Calculations . . . . . . . . . . . . . . . . . . . . 14
1.2.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
2 Experimental Details 17
2.1 The fs Laser System . . . . . . . . . . . . . . . . . . . . . . . . . 17
2.2 Photoelectron Imaging and Ion Detection . . . . . . . . . . . . . . 18
2.2.1 The Spectrometer . . . . . . . . . . . . . . . . . . 18
2.2.2 Ion Detection . . . . . . . . . . . . . . . . . . . . . . . . . 20
2.2.3 Image Processing . . . . . . . . . . . . . . . . . . . . . . . 21
2.2.4 Calibration of the Spectra . . . . . . . . . . . . . . . . . . 24
2.2.5 Setup for the Coincidence Experiment . . . . . . . . . . . 25
2.2.6 Calibration of the Powermeter . . . . . . . . . . . . . . . . 29
2.3 Quantum Control of Ionization in Strong Laser Fields . . . . . . . 29
2.3.1 Pulse Shaping . . . . . . . . . . . . . . . . . . . . . . . . . 30
2.3.2 The Spatial Light Modulator (SLM) . . . . . . . . . . . . 30
2.3.3 Characterization of the SLM . . . . . . . . . . . . . . . . . 32
2.3.4 The Control Algorithm . . . . . . . . . . . . . . . . . . . . 34
2.3.5 Experimental Setup . . . . . . . . . . . . . . . . . . . . . . 35
2.3.6 Characterization of Laser Pulses . . . . . . . . . . . . . . . 36
3 Strong-field photoionization of argon: a comparison between ex-
periment and the SAE approximation 39
3.1 Experiment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
12 CONTENTS
3.1.1 Experimental Setup . . . . . . . . . . . . . . . . . . . . . . 39
3.1.2 Intensity Calibration . . . . . . . . . . . . . . . . . . . . . 40
3.2 Theoretical Approach . . . . . . . . . . . . . . . . . . . . . . . . . 41
3.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
3.3.1 Channel Switching . . . . . . . . . . . . . . . . . . . . . . 45
3.3.2 Resonant Ionization. . . . . . . . . . . . . . . . . . . . . . 45
3.3.3 AC Stark Splitting . . . . . . . . . . . . . . . . . . . . . . 49
3.3.4 Nonresonant Ionization . . . . . . . . . . . . . . . . . . . . 50
3.3.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . 51
4 Combined electron ion spectroscopy (CEIS) of rare gases 53
4.1 Experimental Technique . . . . . . . . . . . . . . . . . . . . . . . 53
4.2 Xenon . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
4.2.1 Intensity Calibration . . . . . . . . . . . . . . . . . . . . . 54
4.2.2 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
4.3 Argon . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
4.3.1 Intensity Calibration . . . . . . . . . . . . . . . . . . . . . 60
4.3.2 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
4.4 Krypton . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
4.4.1 Intensity Calibration . . . . . . . . . . . . . . . . . . . . . 66
4.4.2 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
4.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
4.5.1 Consistency of the Intensity Calibrations . . . . . . . . . . 71
4.5.2 Interpretation of the Data . . . . . . . . . . . . . . . . . . 71
5 Optimization of Ionization Processes by Pulse Shaping Tech-
niques 73
5.1 Experimental Setup . . . . . . . . . . . . . . . . . . . . . . . . . . 73
5.2 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
5.3 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
6 Momentum resolved spectra of electrons resulting from double
ionization of xenon 79
6.1 Experimental Setup . . . . . . . . . . . . . . . . . . . . . . . . . . 79
6.2 Detection Efficiencies . . . . . . . . . . . . . . . . . . . . . . . . . 80
6.3 Data Processing . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82
6.4 Abel versus Vrakking Inversion . . . . . . . . . . . . . . . . . . . 83
6.5 Proof of Principle . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
6.6 Stability of Experimental Parameters . . . . . . . . . . . . . . . . 88
6.7 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88
6.8 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
7 Conclusions 97CONTENTS 3
A Calibration of the Powermeter 99
B Statistics of the Experiment 101
C Rescattering Energy 107
D Momentum Resolved Photoelectron Spectra 111
D.1 Photoelectron Spectra of Xenon . . . . . . . . . . . . . . . . . . . 112
D.2 Spectra of Krypton . . . . . . . . . . . . . . . . . . 121
D.3 Photoelectron Spectra of Argon . . . . . . . . . . . . . . . . . . . 126
bibliography 1314 CONTENTSChapter 1
Ionization of Atoms in Strong
Laser Fields
Thesubjectunderconsiderationhereisnotasgeneralasthetitlemightindicate.
Forallprocessestobediscussedinthisthesistheionizationpotentialoftheatom
is much larger than the photon energy, the range of laser-intensities is limited to
13 15 2about10 to10 W=cm andthepolarizationisusuallylinear. Mostofthetime
”atoms”referstonoblegasatomsand”laser”meanstitanium-sapphirelaserwith
pulse durations of roughly 5 to 150 fs and wavelengths of 780 to 800 nm.
1.1 Single Ionization
The ionization of atoms in strong laser fields may be divided into two different
intensity regions in which ionization is governed by different processes: Multi
photon ionization (MPI) and tunnelling ionization. An indicator whichp
picture is applicable, is the adiabatic or Keldysh parameter ? = I =2U .p p
Here I denotes the ionization potential of the atom under consideration andp
2e IU = is the ponderomotive potential, equal to the average quiverp 22m † c!e 0
energy of a free electron subjected to the electric field of the laser. ? ? 1
indicates MPI, whereas tunnelling is dominant for ? ¿1 [Kel64], [DK99].
1.1.1 Multi Photon Ionization (MPI)
Inthemultiphotonpictureaninitiallyboundelectronabsorbsanintegernumber
n of photons and thereby gains sufficient energy to reach the continuum. The
electron gains kinetic energy defined by the difference between the photons’ en-
ergy and the ionization potential E =n¢h!¯ ¡I .kin p
Usually the initial electronic state is the ground state of the atom. If the photon
energyissuitabletheelectronmaybepromotedtoanexcitedstatebyabsorption
ofm<nphotons. Subsequently, theelectronmayionizebyabsorbingadditional
56 CHAPTER 1. IONIZATION OF ATOMS IN STRONG LASER FIELDS
n¡m photons. This process is more likely than direct n-photon ionization, be-
cause the higher the number of photons necessary, the lower the probability,
nwhich generally scales with I . This process is called resonance enhanced
multi photon ionization (REMPI). Although it is limited by the energetic
constraints it plays an important role.
The strong oscillating electric field of the laser induces an intensity dependent
shift of the atomic energy levels (AC Stark shift). For small photons h!¯ ¿ Ip
it is a good approximation to assume that the ionization potential I as well asp
high excited states shift linearly with the laser intensity. Their energies increase
by the ponderomotive potential U . The ground state energy on the other handp
remains (almost) constant. This implies that as the laser intensity is varied, dif-
ferent excited states shift into and out of m-photon resonance with the ground
state. Within the focus of a pulsed laser there is a smooth spacial and temporal
distribution of intensities. For high enough peak intensities there is always a
space-time-region within the focus, where the ground state is m-photon coupled
with some excited state.
MPI and REMPI leave different traces in (experimental) momentum-resolved
photoelectron spectra. MPI electrons have a continuous energy distribution, be-
cause electrons produced at different intensities contribute to the spectra. Each
intensity yields electrons witht kinetic energy, due to different AC Stark
shifts oftheI . REMPI electrons havewelldefined discrete kinetic energies. Thep
energetic difference between excited states and the continuum is unaffected by
the laser intensity, since they shift equally.
1.1.2 Above Threshold Ionization (ATI)
Electronsmayabsorbmorephotonsthanrequiredforionization. Inthiscaseone
speaks of above threshold ionization (ATI) [AFMP79]. The corresponding
electronenergyspectraexhibitastructurewithevenlyspacedpeaksseparatedby
the photon energy, the envelope decreasing exponentially with energy. A plateau
+appearsat2U thatextendsupto10U [PNX 94],whichwasattributedtoelasticp p
backscattering of the electron on the parent ion.
Figure 1.1: Experimental ATI Spec-
+trameasuredbyPaulusetal[PNX 94]
with a 40 fs, linearly polarized laser
at 630 nm. The intensity was 3 ¢
14 2 14 210 W=cm for He and 2¢ 10 W=cm
for the other rare gases.