2. Highorder harmonic generation in gases

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1. Introduction to nonlinear optics
2. High-order harmonic generation in
gases Attosecond pulse generation
2
Introduction to nonlinear optics
Polarization induced by a laser field
linear response
nonlinear response
Second harmonic generation
3
First demonstration of second-harmonic generation

• P.A. Franken (1961)

The second-harmonic beam was very weak because
the process was not phase-matched.
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First demonstration of second-harmonic generation
The actual published results
5
Introduction to nonlinear optics
Generate field solution of a wave equation
Fundamental
Harmonic generation
Different phase velocity
2nd harmonic
6
Out of phase
z
Coherence length
7
Phase-matching second-harmonic generation
Refractive index
Frequency
Using birefringence
8
Depletion
Efficiency (h)
L
9
Dependence of SHG intensity on length
Large Dk
Small Dk
The SHG intensity is sharply maximized if Dk 0.
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Wave vectors
11
The lengths of the problem
Efficiency (h)
L
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Fgen(z)- Fpol(z)
Phase
Dipole phase
40
Dispersion
z
1 cm
-1 cm
Dispersion free electrons
Focusing
-40
Intensity, pressure, focusing, many parameters!
Asymmetry before/after the focus
13
Fgen(z)- Fpol(z)
40
p
-1 cm
1 cm
Localized in space and in time!
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Wave vectors
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Generation of short light pulses
2.7 fs
1 eV
30 eV
2 cycles
XUV!
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Generation of short light pulses
Fourier Transform
0.1 eV
Time
Frequency
10 eV
Broad bandwidth!
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Strong-Field Atomic Physics
I
The electron can tunnel through the distorted
Coulomb barrier
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Interaction with the core
III
III
The electron wave packet interacts with the
remaining core
The electron is accelerated by the field, and may
return to the atomic core
II
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High-Order Harmonic Generation in Gases
Multiphoton
Plateau
. .
Cut-off
Ferray et al., J. Phys. B 21, L31 (1988)
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Semi-classical three-step model
High-Order Harmonic Generation in Gases
The electron tunnels through the distorted
Coulomb barrier
I
The free electron is accelerated by the field,
and may return to the atomic core
II
III
The electron recombines with the atom, emitting
its energy as an XUV photon
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High-Order Harmonic Generation in Gases
Electron dynamics
Field
Electrons
Atom
Several bursts per half laser cycle
Long
Short
Group delay dispersion
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High-Order Harmonic Generation in Gases
Plateau
Cut-off
. .
The electron recombines with the atom, emitting
its energy as an XUV photon
III
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High-Order Harmonic Generation in Gases
Atomic Medium
Laser
Gas cell with rare gas
Titanium-Sapphire, 800 nm 1 kHz, 2 mJ, 35 fs
pulses
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Tunneling Acceleration in the continuum Recombinat
ion Attosecond pulse train
Time
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Attosecond pulse train
Harmonic spectrum
Energy
Time
Is this always true?
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Generation of short light pulses