Atoms in intense ultrashort laser pulses and the absolute phase

166 Pages·2004·9.06 MB·English

by  Lindner, Fabrizio

Atoms in intense ultrashort laser pulses
and the absolute phase
Dissertation der Fakult¨at fu¨r Physik
der Ludwig-Maximilians-Universit¨at Mu¨nchen
vorgelegt von
Fabrizio Lindner
aus Mailand (Italien)
Mu¨nchen, April 2004
Erster Gutachter: Prof. Dr. H. Walther
Zweiter Gutachter: Prof. Dr. D. Habs
Tag der mu¨ndlichen Pru¨fung: 30.06.2004
Abstract
The subject of this work is the experimental investigation of atomic processes under
the influence of intense, ultrashort laser pulses. Emphasis is given to the twin effects
of high-order harmonic generation (HHG) and above-threshold ionization (ATI). In
particular, the latter is explored in detail here for the case of few-cycle laser pulses.
While the generation of light pulses of duration below 5fs is today routine, a complete
control of the constituting electric-field waveform was so far not possible. This is
here achieved with the first unambiguous measurement of the absolute phase of the
laser pulses. The precision and reliability of the measurement permitted to establish
a new approach for active phase stabilization, which will presumably play a major
role in future research. The experiments described here address also general optical
properties such as the Gouy phase anomaly showing up in a focused wave, being
precisely measured for the first time. Finally, it is shown how ATI with few-cycle laser
pulses can be regarded not only as a powerful tool for phase diagnostics, but also as
a novel method for studying the interaction of atoms with light with unprecedented
sub-fs time resolution.
i
Zusammenfassung
Diese Arbeit besch¨aftigt sich mit der experimentellen Analyse atomarer Prozesse in
intensiven ultrakurzen Laserpulsen. Der Schwerpunkt liegt hierbei bei den Zwillings-
effektenderErzeugunghoherHarmonischer(“high-orderharmonicgeneration”, HHG)
und der Ionisation u¨ber Zust¨ande im Kontinuum (“above-threshold ionization”, ATI).
Besonders letzterer Effekt wird detailliert in Verbindung mit der Wechselwirkung mit
Laserpulsen von nur wenigen Zyklen L¨ange untersucht. W¨ahrend es heutzutage Rou-
tine ist solche Pulse von weniger als 5fs zu erzeugen, war die vollst¨andige Kontrolle
u¨ber das zugrundeliegende elektrische Feld bisher noch nicht m¨oglich. Dies wurde in
dieser Arbeit durch die erste eindeutige Messung der den Laserpuls charakterisieren-
den “absoluten Phase” erreicht. Die Genauigkeit und Zuverl¨assigkeit dieser Messung
erweist sich als hinreichend, um eine neue Methode der aktiven Phasenstabilisierung
einzufu¨hren, welche voraussichtlich eine tragende Rolle in zuku¨nftigen phasenstabil-
isierten Lasersystemen spielen wird. Die beschriebenen Experimente widmen sich zu-
dem auch allgemeinen optischen Effekten, wie beispielsweise der Gouy’schen Phase-
nanomalie in einem fokussierten Strahl, welche hier erstmals im optischen Bereich und
u¨ber den gesamten Fokusbereich gemessen wurde. Schließlich wird gezeigt, wie ATI
in Verbindung mit Wenig-Zyklen-Laserpulsen nicht nur als leistungsf¨ahiges Werkzeug
zur Phasendiagnostik genutzt werden kann, sondern auch einen neuen Zugang zur
Untersuchung der Wechselwirkung von Atomen und Licht mit bis dato unerreichter
Zeitau߬osung bietet.
ii
That which is static and repetitive is boring. That which is
dynamic and random is confusing. In between lies art.
John A. Locke (1632-1704)
iii
iv
Contents
Introduction 1
1 Atoms in strong laser fields 5
1.1 Strong-field approximation (SFA) and the two-step model . . . . . . . . 6
1.2 First step: ionization . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
1.2.1 Tunneling and multiphoton limits . . . . . . . . . . . . . . . . . 8
1.2.2 Ionization yields and saturation . . . . . . . . . . . . . . . . . . 11
1.3 Second step: free electron evolution . . . . . . . . . . . . . . . . . . . . 12
1.4 High-order harmonic generation (HHG) . . . . . . . . . . . . . . . . . . 13
1.4.1 Single-atom response . . . . . . . . . . . . . . . . . . . . . . . . 14
1.4.2 Macroscopic response: phase-matching . . . . . . . . . . . . . . 17
1.5 Above-threshold ionization (ATI) . . . . . . . . . . . . . . . . . . . . . 20
1.5.1 Single-atom response . . . . . . . . . . . . . . . . . . . . . . . . 21
1.5.2 Macroscopic response: volume effects . . . . . . . . . . . . . . . 22
1.6 Non-sequential double ionization (NSDI) . . . . . . . . . . . . . . . . . 24
2 High-order harmonic generation at a repetition rate of 100 kHz 25
2.1 The laser system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
2.2 The XUV spectrometer . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
2.3 Experimental results . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
2.3.1 Longitudinal dependence . . . . . . . . . . . . . . . . . . . . . . 30
2.3.2 Quantum path separation . . . . . . . . . . . . . . . . . . . . . 32
2.3.3 Active spectral reshaping . . . . . . . . . . . . . . . . . . . . . . 35
3 Determination of the absolute phase of few-cycle laser pulses 39
3.1 The absolute phase . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
3.1.1 Absolute phase stabilization . . . . . . . . . . . . . . . . . . . . 41
3.1.2 Absolute phase and nonlinear phenomena . . . . . . . . . . . . 43
3.2 The laser system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
3.3 The stereo-ATI spectrometer . . . . . . . . . . . . . . . . . . . . . . . . 45
3.3.1 Sensitivity of the spectrometer . . . . . . . . . . . . . . . . . . . 47
3.4 Experimental results . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
3.5 Theoretical analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
3.5.1 Semiclassical model . . . . . . . . . . . . . . . . . . . . . . . . . 53
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Contents
3.5.2 Strong-field approximation . . . . . . . . . . . . . . . . . . . . . 55
3.5.3 Numerical integration of the Schr¨odinger equation . . . . . . . . 58
4 A new stabilization scheme for the absolute phase 59
4.1 The stereo-ATI as a phase meter . . . . . . . . . . . . . . . . . . . . . 59
4.2 Phase stabilization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
4.2.1 Basic idea . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
4.2.2 Experimental results . . . . . . . . . . . . . . . . . . . . . . . . 64
4.2.3 A first application: ATI and NSDI in parallel . . . . . . . . . . 67
4.3 Future developments . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
5 Full spatiotemporal characterization of the absolute phase 71
5.1 Spatial dependence: the Gouy effect . . . . . . . . . . . . . . . . . . . . 72
5.1.1 Physical picture . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
5.1.2 Gouy phase measurement . . . . . . . . . . . . . . . . . . . . . 74
5.2 Intensity dependence . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
5.2.1 Ionization yield . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
5.2.2 ATI spectra . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
5.3 Pulse duration dependence . . . . . . . . . . . . . . . . . . . . . . . . . 86
5.3.1 Ionization yield . . . . . . . . . . . . . . . . . . . . . . . . . . . 86
5.3.2 ATI spectra . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
6 Quantum mechanics in ATI with few-cycle pulses 91
6.1 Electron interference in ATI . . . . . . . . . . . . . . . . . . . . . . . . 92
6.2 The double-slit experiment . . . . . . . . . . . . . . . . . . . . . . . . . 94
6.2.1 Experimental evidence . . . . . . . . . . . . . . . . . . . . . . . 94
6.2.2 Semiclassical description . . . . . . . . . . . . . . . . . . . . . . 98
6.3 Beyond the classical model: classically forbidden trajectories . . . . . . 101
6.4 Heisenberg’s uncertainty principle . . . . . . . . . . . . . . . . . . . . . 106
Conclusion 109
List of publications 111
Bibliography 147
vi
Introduction
This work deals with elementary processes occurring when exposing atoms to very
intense laser fields. Since the early developments, lasers have been used for studying
the behavior of matter under strong electromagnetic radiation. Progress in laser tech-
nology has been enormous: today, table-top laser systems delivering intensities up to
∼1015W/cm2 at high repetition rates (1kHz and more) are commercially available.
Such intensities are by no means the highest obtainable with lasers. Indeed, peak
intensities exceeding 1020W/cm2 can be produced (at repetition rates < 1Hz) in vari-
ous large-scale laser facilities. At these regimes, relativistic effects are highly dominant
in laser-matter interaction; in addition, any material at these intensities is fully ion-
ized, and any experiment must cope with collective behavior of the ionized medium
(plasma physics).
The experiments presented here consisted in ionizing dilute gas media by focusing
laserpulsesinthenon-relativisticrange(intensitiesbelow∼1015W/cm2). Underthese
conditions the physics of laser-matter interaction can be studied in a clean and elegant
way at unprecedented high intensities while remaining in the field of atomic physics.
In other words, all elementary processes studied and described in the following can
be understood and explained in the simple frame of one atom exposed to a strong
oscillating electric field (magnetic field effects play a significant role only at higher
intensities). Collective behavior can only occur through interference of the elementary
processes, not through mutual interactions. All physical processes in this context are
also referred to as multiphoton processes, since the typical energy of a single photon
(∼1,5eV) is not sufficient to ionize an atom through the well-known photoeffect.
The most known of these processes is probably high-order harmonic generation
(HHG), first presented in 1987 [McPherson87, Ferray88]. It consists of efficient co-
herent radiation emission at frequencies that are odd multiples of the laser frequency,
occurring when exposing atoms to intense laser fields. For this effect, it was discovered
that the initial decrease of harmonic yield was followed by a flat annex, i.e. the har-
monic intensity was roughly independent of its order. This plateau-like feature ends
with a sharp cutoff (Fig. 1). The complete disagreement with standard perturbation
theory suggests the presence of different underlying mechanisms.
Less knowncurrentlybutin factolderthanHHG,above-thresholdionization(ATI)
was discovered in 1979 by Agostini et al. [Agostini79]. Its discovery marked the begin-
1
Introduction
Figure 1: Discovery of high-order harmonic generation (HHG). After the initial exponential
decrease of yield with increasing harmonic order, a flat annex (plateau) not explainable
within perturbation theory was found. From [McPherson87] (left) and [Ferray88] (right).
Figure 2: (left) Discovery of above-threshold ionization (ATI). The photoelectron spectrum
shows two maxima separated by the laser photon energy, indicating the absorption of one
photon more than necessary to overcome the ionization potential barrier. From [Agostini79].
(right) Discovery of the plateauin ATI. These results suggested that the physical mechanism
at the basis of ATI and HHG is the same. From [Paulus94b].
2