2. High-order harmonic generation in gases Attosecond pulse generation
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2. High-order harmonic generation in gases Attosecond pulse generation 1. Introduction to nonlinear optics
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1. Introduction to nonlinear optics. 2. High-order harmonic generation in gases Attosecond pulse generation. Introduction to nonlinear optics. Polarization induced by a laser field. linear response. nonlinear response. Second harmonic generation. P.A. Franken (1961). - PowerPoint PPT Presentation
Transcript of 2. High-order harmonic generation in gases Attosecond pulse generation
2. High-order harmonic generation in gasesAttosecond pulse generation
1. Introduction to nonlinear optics
Polarization induced by a laser
field
)( 3)3(2)2()1(0 EEEP
linear response
nonlinear response
Introduction to nonlinear optics
202 dEPNL
Second harmonic generation
First demonstration of second-harmonic generation
P.A. Franken (1961)
The second-harmonic beam was very weak because the process was not phase-matched.
The actual published results…
First demonstration of second-harmonic generation
ccetzPtzP ziktiNL
2222
12 ),(),(Harmonic
generation
ccetzEtzE zikti
2222
12 ),(),(
Different phase velocity
Introduction to nonlinear optics
ccetzEtzE zikti ),(),( 12
1Fundamental
2nd harmonic
2
2
22
2
22 11
t
P
ct
E
cE
NL
Generate field = solution of a wave
equation
c
nk
kLcoh
z
ziktie 22
ziktie 22
nLcoh
4
Out of phase
Coherence length
Phase-matching second-harmonic generation
(2 ) ( )n n
2Frequency
Ref
ract
ive
inde
x
2Frequency
Ref
ract
ive
inde
x
ne
on(2 ) ( )o en n
Using birefringence
L
Eff
icie
ncy
()
cohL
2L
)/(sin 2cohLL
Depletion
Dependence of SHG intensity on length
Large k Small k
The SHG intensity is sharply maximized if k = 0.
321 kkk
12 321
3
1k3k
2k
Wave vectors
L
Eff
icie
ncy
()
cohL
2L
)/(sin 2cohLL
absLLeL /2 absL
The lengths of the problem
ampL
)(2 LFL q
Phase
Dispersion kz
z
gen(z)- pol(z)
Dipole phase
)(zIi
Dispersion free electronsFocusing
)/2(tan 1 bzq
-1 cm 1 cm
40
-40
Intensity, pressure, focusing, many parameters! Asymmetry before/after the focus
gen(z)- pol(z)
Localized in space and in time!
-1 cm 1 cm
40
z
zzzL polgen
coh
)]()([
/)(
),()( tzLzL cohcoh
321 kkk
12 321
3
1k3k
2k
Wave vectors
2.7 fs
2 cycles
Generation of short light pulses
cT
2 XUV!
1 eV
30 eV
Generation of short light pulses
Frequency Time
4.0
Broad bandwidth!
0.1 eV
10 eV
Fourier Transform
The electron can tunnel through the distorted Coulomb barrier
Strong-Field Atomic Physics
I
III
Interaction with the core
The electron wave packet interacts with the remaining core
IIThe electron is accelerated by the field, and may return to the atomic core
III
Ferray et al., J. Phys. B 21, L31 (1988)
Multiphoton
Plateau
Cut-off
High-Order Harmonic Generation in Gases
3
7
5
)12( q
.
.
Semi-classical three-step model
IIThe free electron is acceleratedby the field, and may return to theatomic core
III The electron recombines with the atom, emitting its energy as an XUV photon
The electron tunnels through thedistorted Coulomb barrierI
High-Order Harmonic Generation in Gases
High-Order Harmonic Generation in Gases
Electron dynamics
Group delay dispersion
Several bursts per half laser cycle
Atom
FieldElectrons
Short
Long
Plateau Cut-off
High-Order Harmonic Generation in Gases
3
7
5
)12( q
.
.
50 60 70 80
H53
H49
H43H37
H31
Photo
ns
Energy (eV)
IIIThe electron recombines with the atom, emitting its energy as an XUV photon
High-Order Harmonic Generation in Gases
AtomicMedium
Laser
Titanium-Sapphire, 800 nm 1 kHz, 2 mJ, 35 fs pulses
Gas cell with rare gas
Time
Time
Tunneling
Acceleration in the continuum
Recombination
Attosecond pulse train
Broad spectrum Single attosecond pulse
2200
Energy Time
as
Harmonic spectrum Attosecond pulse trainEnergy Time
L22L Time domainFrequency domain
=20eV
Attosecond pulse train
Time
0
Harmonic spectrum
Energy
02
Is this always true?
Generation of short light pulses
