Armin Scrinzi

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Basic Mechanisms of High Harmonic Generation in
Gases
Armin Scrinzi
2
Early measurements of high harmonics
Development parallel with intense, short laser
pulses High harmonics from gases late
1980ties Pulse durations ps 248 nm,
1015W/cm2 McPherson et al. 1987 Ferray et al.
1987 The discovery of the 3.17 UP cutoff
from LHuillier, Balcou, 1993
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Looking through the water window
Intense, few-cycle laser pulses Pulse rises to
high intensities before the atom
disintegrates I5x1014 3x1015 W/cm2 , 7fs FWHM,
800 nm
What determines the limits ?
Schnürer et al., 1999
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Control the cutoff modulation
High harmonic spectra
Phase stabilized pulses The modulation of the
Harmonic spectrum depends on the Carrier-envelop
e phase
A. Baltuska et al., 2003, Nature 421, 611
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Even harmonics ?
With short pulses High harmonics do NOT only
appear at odd multiples of the fundamental
What breaks the symmetry ?
Yakovlev, PhD thesis
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Attosecond pulses
Phase locking between plateau harmonics
Time-structure of Cutoff harmonics
Single pulses
Pulse trains
Hentschel et al., 2001 Spectrum from
Kienberger et al., 2004
Paul et al., 2001
What is the origin of time structures in HHG ?
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Stimulated raman
Vibrational excitation of D2 Near-resonantly
driven by a two-color field Molecular excitations
and side-band phases become locked - High
conversion efficiencies - Spectrum into the UV -
Trains of pulses, - Peaks 1 fs duration
Sokolov et al. 2000
Kaplan, PRL 73, 1243 (1994) Harris and Sokolov
PRA 55, R4019 (1997)
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The magic cutoff 3.17 Up
Harmonic dipole response of a Hydrogen atom to a
5 fs laser pulse (800 nm, peak intensity 4 x 1014
W/cm2)

wcut
Harmonic yield
(simulation)
Plateau of harmonics Cutoff frequency wcut
Ip 3.17 Up Ip ... ionization potential, Up
ponderomotive potential
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High harmonics are generated by recollision
Classical motion of a free electron in the laser
field
Field E(t)cos(2pt/T) Maximum energy
at trelease - 0.45 T trecollision 0.2 T
Note Harmonics when recollisions are repeated
with the laser period
P. Corkum 1993 K. Kulander 1993
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Numerical solution of the time-dependent
Schrödinger equation
Ansatz Pl Legendre, Lnl
Laguerre polynomials System of
equations Solved numerically, absorption of
outgoing flux by complex scaling
Highly accurate results
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When is the radiation generated ?

• Full confirmation
• of classical recollision picture
• Highest frequencies appear during
• very brief (attosecond) times
• Times are locked to laser period

V. Yakovlev and A. Scrinzi, PRL 91, 135901,
(2003)
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Short and long trajectories
Velocity in the field v(t)
Several solutions for given final energy
Recollision condition
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Quantum model The strong field approximation
(SFA)
Ansatz initial bound state plus free motion in
the field Volkov
states Solution
Approximations no atomic potential for the
scattering states, no ground state depletion,
no continuum-continuum transitions
Confirms classical model
I.e. integrate by saddle point method (near
classical trajectories)
Keldysh Sov. Phys. JETP, M. Lewenstein et al.,
Phys. Rev. A
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NOT Bremsstrahlung, NOT capture !
- Spectral characteristics differ from
Bremsstrahlung - Intensities differ from capture
Interference of residual atomic population with
rescattering wave
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Accuracy of the SFA
Dipole d(t) sum over all birth times tb

• with a few corrections beyond SFA
• Use exact (not SFA) ionization rates
• Correct for initial state depletion
• Photon energy derivative of the action

Yakovlev, PhD thesis
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3-d propagation of high harmonics

• What can go wrong ?
• Distortion of the fundamental laser pulse
• Loss of laser peak intensity
• Fundamental pulse intensity profil
• gt Spatial variation of harmonic yield
• blurring of harmonic time structure
• Spatial variation of harmonic phase
• harmonic pulse does not propagate
• Phase slip between fundamental and harmonics
• gt limitation of intensity

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Simplified 3-d propagation equations -)
Laser pulse propagation with strong ionization
Free electron generation and energy loss due to
ionization
Harmonic pulse linear propagtion with source
Absorption and atomic dipole source term
Solved numerically on a grid !
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Calculated and measured harmonic spectra
Brabec and Krausz, Rev. Mod. Phys.
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Importance of carrier-envelope phase
Time-frequency plot Cosine pulse (phase j
00)
Harmonic spectrum
Unmodulated cutoff single XUV pulse
A. Baltuska et al., Nature 2003, Nature 421, 611
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Frequency-time analysis of the harmonic power
spectrum after propagation
We can (partially) see the generating pulse in
the harmonic spectrum
V. Yakovlev and A. Scrinzi, PRL 91, 135901,
(2003)
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Spatiotemporal profile of the cutoff-harmonics A
ttosecond pulse after propagation
Ar, 1.75x1019 cm-3 N 27-30 I0 2x1014 W/cm2 l0
800 nm w0 150 mm
t 750 as w0 1.5 mm I0 5x1013 W/cm2 (?)
XUV pulses are smooth in space and time
N. Milosevic, M. Kitzler, A. Scrinzi and T.
Brabec, 2002, PRL 88, 093905
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Measuring the time structure of harmonics

• Autocorrelation need efficient non-linear XUV
  processe
• Two-photon ionization of He Tzallas et al.,
  Nature 426, 267 (2003)
• Cross-correlation need short time scale for
  comparison
• Laser envelope gt 5 fs
• Laser field optical
  period 2.6 fs _at_ 800 nm
• Non-linear mechanism photo- plus
  field-ionization !
• Modulations of total xuv photo-ionization yield
  in a laser field
• A. Scrinzi, M. Geissler, T. Brabec, 2001, PRL
  86, 412.

• Reconstruction of the relative harmonic phases
  from ATI spectra
• P. Paul et al. 2001, Science 292, 1689.

• Shifts of the photo-electron spectrum
  attosecond streak camera
• E. Constant, V. D. Taranukhin, A. Stolow, and
  P. Corkum, 1997, Phys. Rev. A 56, 3870.

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RABITT frequency domain ReconstructionofAttoseco
ndBeatingbyInterferenceofTwophotonTransitions
Photoelectron spectra from harmonics fundamental
Side-bands between harmonic orders
Vary time delay t Phase difference between Beats
of side-band amplitudes (jq jq2 ) (jq-2 jq
)
Phase chirp d2j/d2q 2jq - jq-2 - jq2
Interference cos(2twlaser jq - jq2) t
delay between laser and harmonics
Veniard et al., PRA54, 721 (1996)
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The attosecond pulse train
Pulse trains the frequency domain
Paul et al, Science 292, 1698 (2001)
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The attosecond streak camera time domain
Xuv ionization in a laser field Initial electron
momentum
Acceleration in the field
Shift and broadening of the final electron
spectrum
Laser streaking maps time into momentum
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Measured streaking image
Harmonics from 5fs (two-cycle) pulse Streaking
images for different laser phases Delay for
maximal streaking
Kienberger et al., Nature 427, 817 (2004)
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Measure the attosecond pulse chirp
Sensitivity of streaking to (linear) XUV chirp
Kienberger et al., Nature, 2003, to appear
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Full characterization of harmonic pulses
The offspring of FROG and SPIDER RABITT,
TIGERS, and CRAB put a fence around the zoo
Cross-correlation electron spectra (general form)

• FROG with a phase gate measure a 2-d plot,
  reconstruct 1-d complex function
• High redundancy, good accuracy of
  reconstruction

Quere and Mairesse, UFO, 2003
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Emission times of individual harmonics
CRAB reconstruction of emission times
Mairesse et al., Science 302, 1540 (2003)
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Towards higher harmonics and shorter pulses
Competion between ionization and harmonic
generation
Maximal harmonic yield from Helium at 98
ionization
Harmoic order
?
Pulse duration (fs)
10 fs pulse !
Scrinzi et al., PRL 83, 706 (1999)
Seres et al., PRL 92, 163002 (2004)
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Relativistic limitation ?
For electron velocities c Lorentz force pushes
electron away from the nuclues
Harmonic spectrum 5 fs FWHM, 3x1016 W/cm2, 800 nm
Walser et al., PRL 85, 5082 (2000)
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Ellipticity switching

• Recollisions only with linear polarization
• Construct a laser pulse with
• Brief period of linear polariztion
• Single harmonic pulses
• from long laser pulse
• Advantage no pulse compression needed

Kovacev et al., Eur. Phys. J. D 26, 79 (2003)
P.B. Corkum et al., Opt. Lett. 19, 1870, (1994)
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Chirp compensation pulse trains

• Chirp of the laser
• Chirp of the harmonics
• Lopez-Martens, App. Phys. B 78, 835 (2004)

Chirp can be compensated e.g. 3 x 20 mm Al Pulse
trains with 170 as Varju et al., presented at
the ATTO network meeting
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Single 50 as pulses by ionization quenching
Suppress periodic structure of radiation by
ionization after a single recollison Compensate
chirp by 700 nm of Sn
Low intensity