Ultrakurzzeitphysik II

Prof. Reinhard Kienberger
PD. Hristo Iglev
[email protected]
[email protected]
Lehrstuhl für Laser und Röntgenphysik E11
Ultrakurzzeitphysik II
SS 2014
Mittwoch, 10 Uhr c.t.
PH II 127, Seminarraum E11
Die Intensitäts Autokorrelation
nichtkollineare SHG
durch Veränderung des zeitlichen Abstands beider
Impulse ergibt sich das Intensitäts Autokorrelationssignal, A(2)(ττ).
elektrisches Feld: E(t) E(t-τ)
Intensitätssignal: I(t) I(t-τ)
unbekannter
Puls
Strahlteiler
variable
Verzögerung, τ
Intensitäts
Autokorrelation:
E(t–τ)
∞
(2)
A
(τ ) ≡ ∫ I (t )I ( t −τ ) dt
−∞
SHG
Kristall
Detektor
Esig(t,τ)
E(t)
A(2) (τ ) = A(2) (−τ )
das resultierende Signal ist immer symmetrisch
keinen Schluß auf die Richtung der Zeitachse
2
Interferometrische Autokorrelation
kollineare Geometrie + zusätzlicher Filter
Michelson
Interferometer
Linse
SHG
kristall
Entwickelt
von J-C Diels
Filter
Detector
E(t)
Spiegel
Strahlteiler
E(t–τ)
[ E (t ) − E (t − τ )] 2
E (t ) − E (t − τ )
Verzögerung
(2)
IA (τ ) ≡
Spiegel
∫
Diels und Rudolph,
Ultrashort Laser
Pulse Phenomena,
Academic Press,
1996.
∞
[ E (t ) − E (t − τ )] 2
2
dt
−∞
neue
Terme
Normaler
Autokoterm
(2)
IA (τ ) ≡
∫
∞
E 2 (t ) + E 2 (t − τ ) − 2 E (t ) E (t − τ )
2
dt
−∞
Auch genannt “Fringe-Resolved Autocorrelation”
Das gemessene Signal in Abhängigkeit von der Verzögerung:
IA(2) (τ ) ≡
∫
∞
 E 2 (t ) + E 2 (t − τ ) − 2 E (t ) E (t − τ )   E *2 (t ) + E *2 (t − τ ) − 2 E * (t ) E * (t − τ )  dt
−∞
3
Interferometrische AC: Beispiele
7-fs sech2 800-nm Puls
Puls mit kubischer
spektralen Phase
Doppel-Puls
4
Vermessung ultrakurzer Pulse: FROG
Spektrogramm:
∫
Σ E (ω ,τ ) ≡
g(t-τ) - Gate-Funktion;
2
∞
E (t ) g (t − τ ) exp(−iω t ) dt
τ - Verzögerungszeit.
−∞
Das Spektrogramm gibt Auskunft über Frequenz und Intensität von E(t) zum Zeitpunkt τ.
Beispiele:
Frequenz
ß<0
ß=0
Verzögerung
Das Spektrogramm bestimmt eindeutig den Intensitätsverlauf I(t), und den Phaseverlauf φ(t).
Das Gate soll nicht viel
kürzer sein als E(t)
∫
2
∞
E ( t ) δ ( t − τ ) ex p ( − iω t ) d t
E (τ ) ex p ( − iω τ )
=
2
−∞
Intensität (keine Phasen-Information!)
=
E (τ )
2
Das Spektrogramm löst das Dilemma! Es benötigt kein kürzeres Ereignis! Es löst die
langsamen Komponenten zeitlich und die schnellen Komponenten spektral auf.
5
Beispiele für FROG-Spuren
SHG FROG sind symmetrisch und
uneindeutig in Bezug auf die Zeitrichtung,
man kann es aber Lösen
FROG-Spuren für kompliziertere Pulse
SHG FROG Mesung eines 4.5-fs Pulses!
Baltuska, Pshenichnikov, und Weirsma,J. Quant. Electron., 35, 459 (1999).
6
Erzeugung Messung und Anwendung
von Attosekunden-Pulsen
+ Exkursion MPQ
?
•
electronics, quantum information technology:
how can electronic current be ever faster controlled & how do quantum
states dephase in ever smaller nanostructures & molecular systems
⇒ coherent quantum devices? ultimate limits of electronics?
•
physical chemistry:
how does electronic excitation – either localized (inner-shell) or
delocalized (valence) – affect chemical/biochemical reaction pathways
⇒ ultimate reaction control by steering electrons on molecular orbitals?
•
structural biology, medicine:
how can x-rays be trained to control electronic excitation for minimizing
radiation damage to biological systems or maximizing its selectivity
⇒
optimized bioimaging and radiation therapies?
attosecond physics:
science of electrons in motion on atomic scales
ee-
0.0
0.1
0.2
0.3
0.4
[nanometers]
real-time observation
direct control
&
of electronic motion in atoms, molecules and nanostructures
the time & length scales of microscopic motion
are connected by the laws of quantum mechanics
∆t ~
h
∆W
W1
∆W
W0
 1
∆W ~ f  
∆x 
∆x
structure and dynamics in the microcosm
space (m)
atoms in
electrons in
molecules & solids
nanostructures
10-9
molecules
∆Welectron/hole ~ sub-eV
atoms
∆Wvibr ~ milli-eV
∆Wvalence» 1eV
nuclear distance
10-12
∆Wcor» 10 eV
nuclear
structure &
dynamics
time (s)
10-18
10-15
10-12
10-15
attosecond physics
femtosecond chemistry
1878: E. Muybridge, Stanford
Tracing motion of animals
by spark photography
E. Muybridge, Animals in Motion, ed. by L. S. Brown (Dover Publ. Co., New York 1957)
sharp
blurred
Limit: Exposure time
Mikrosekunden-Photographie
Projektil in Glasblock
chronoscopy in the microworld:
tracing the motion of atoms
Ahmed Zewail, 1987
Nobel Prize in Chemistry 1999
evolution of ultrafast metrology
10-6
nanosecond
time resolution (seconds)
10-9
electronics
ultrafast optics:
physical quantity with
controlled temporal gradient
provided by the
amplitude of laser pulses
picosecond
10-12
transistor
optics
laser
femtosecond
T0 ≈ 2.5 fs @ λ0 ≈ 750 nm
10-15
femtochemistry
light wave cycle
attoattophysics? second
10-18
1940
1950
1960
1970
year
1980
1990
2000
Attosecond pulses are short-wavelength
pulses.
The shortest possible pulse of a given wavelength is one cycle long.
If you compress a single-cycle pulse of one wavelength, you
change its wavelength!
A single-cycle
red pulse:
A compressed
single-cycle pulse,
which is now violet:
A single-cycle 800-nm
pulse has a period of
2.7 fs. To achieve a
period of 1 fs requires
a wave-length of 300
nm.
The VUV, XUV, and soft x-ray regions
Vacuum-ultraviolet (VUV)
180 nm > λ > 50 nm
•Soft x-rays
•5 nm > λ > 0.5 nm
Absorbed by <<1 mm of air
Ionizing to many materials
•Strongly interacts with core
electrons in materials
Extreme-ultraviolet (XUV)
50 nm > λ > 5 nm
Ionizing radiation to all materials
X-ray wavelengths between 2.2 and 4.5 nm
have major biological applications.
1
Carbon
0.5
Water
10 9
8
7
6
5
4
3
Transmission
Water
window
2
Wavelength (nm)
Carbon absorbs these wavelengths, but water doesn’t.
This is the “water window.”
Quellen für Attosekundenpulse
• Freie Elektronenlaser (X!FEL)
• Erzeugung Hoher Harmonischer
(Frequenzkonversion) von hochintensiven
phasenstabilisierten fewfew-cycle Pulsen
hochintensive phasenstabilisierte
few-cycle Pulse
The Laser System
SPM
Hollow Fiber/
Chirped Mirror
Pulse Compressor
Experiment
<3.5 fs pulse duration
400 µJ energy
CPA
CPA Amplifier
20 fs pulse duration
1.3 mJ energy
3 kHz repetition rate
Kerr-Linsen Modenkopplung
Ti:Sapphire Oscillator
sub-10 fs pulse duration
4.6 nJ energy
82 MHz repetition rate
key tools of attosecond technology:
synthesized few-cycle wave & synchronized sub-fs xuv pulse
hollow fiber
neon gas
intensity
104
spectrum
102
100
400
700
1000
λ [nm]
normalized intensity
8
pulse energy
> 0.4 mJ
pulse duration
< 3.5 fs
7
6
< 1.5 cycles
5
> 0.1 TW
4
3
2
1
A. L. Cavalieri et al, New J. Phys. 9, 242 (2007);
E. Goulielmakis et al, Science 317, 769 (2007)
0
-20
-15
-10
-5
0
delay [fs]
5
10
15
20
Die Carrier-Envelope-Phase
der Pulse
und die Messung der CE-Phase
FewLaser
Pulses
Few-Cycle
Control
of the
Waveform
E(t) = Ea(t)cos(ωLt + φ)
Cosine waveform
φ=0
Sine waveform
φ = π/2
TT0 0/4=≈λ625
as (@ λ ≈ 0.75 µm)
0/c ≈ 2.5 fs 0
Requires measurement & control of φ
Frequenz-Bereichs Regelung von ∆ϕ
frequency
doubling
T. W. Hänsch et al., 1997
f
c e o
m
k 2m
Beating of the fundamental
and SH
for k=2m:
→UV
CE phase-stabilization (f-to-0)
SPM
T. Fuji et al., Opt. Lett. 30 (2005)
phase-stabilization scheme
Q-switched
Pump Laser
Multipass
Ti:Sapphire Amplifier
BS
Hollow-FiberChirped-Mirror
Pulse
Compressor
phaselocked
pulses
pump laser synchronization
CW Pump
Laser
AOM
PhasePhaselocking
Electronics
SPM
DFG
/26000
f-to-2f
fr Dividers
interferoSPM meter
/4
f-to-0
interferoECDC meter
Ti:Sapphire
Oscillator
fCEO
Phase
detector
fast-jitter feedback
A. Baltuška et al., Nature 421 (2003)
J. Rauschenberger et al., Laser Phys. Lett. 3 (2006)
0.4mJ
3kHz
Measurement and
control of CE phase
SHG
CCD
slow-drift feedback
Detektion der absoluten Phase
Trigger:PD
Left-right ATI spectra
slit
Laser beam
Phase change by glass
wedges
Previous results:
average of 10000
shots
Paulus et al. Nature, 414 182 (2001)
CEP of consecutive phasephase-stabilized pulses
consecutive time-of-flight ATI spectra of
rescattered electrons (laser rep. rate = 3kHz)
phase distribution of CEP-stabilized shots
(4500 shots; 3kHz)
Stdsingle shot = 278mrad
shot-to-shot evolution of the CEP
Parametric (Lissajous(Lissajous-like) representation
single shot left-right TOF spectra
CEP=π
asymm 2
CEP=0
Non-phase-stabilized single shotsrandom distribution
π
5π/6
7π/6
4π/3
Left-Right
Left+Right
phase scan- limited by fluctuations
2π/3
3π/2
asymm 1
asymm. 2
5π/3
mean
std
11π/6
asymm. 1
π/2
2π
High
precision
No phase
ambiguity
π/6
π/3
Wittmann et al. Nature Physics 4 (2009)
NonNon-phasephase-stabilized laser shots as they’re
they’re arriving…
non-stabilized shots has
random phase distribution
first principle calibration:
phase difference between shots
is immediately given
real CEP retrieved by
TDSE
Wittmann et al. Nature Physics 4 (2009)
PhasePhase-scan with a stabilized laser
Wittmann et al. Nature Physics 4 (2009)
Pulsdauermessung mit StereoStereo-ATI
Kurzer Puls……..
……..stärkere Asymmetrien
Wittmann et al. Nature Physics 4 (2009)
key tools of attosecond technology:
synthesized few-cycle wave & synchronized sub-fs xuv pulse
energy [eV]
90
85
80
75
70
65
60
55
energy [eV]
90
85
80
75
70
65
60
M. Schultze et al (MPQ), J. Kim
55
& D. Kim (POSTECH, Pohang),
6
4
2
0
delay [fs]
-2
-4
-6
New J. Phys. 9, 243 (2007)
Die Erzeugung
Hoher Harmonischer
(High-Order Harmonic Gerneration HHG)
Step 1
Step 3
Optical field ionization
EL(t)
XUV emission on recollision
EL(t)
-
e
e-
Step 2
Spectral Intensity
High-order Harmonic Generation
-
e Acceleration
EL(t)
-
e
P.B. Corkum, PRL 71 (1993)
steering bound electrons with controlled light fields:
the birth of an attosecond pulse
xuv-filter
intensity [a.u.]
1000
EL(t)
EL(t)
EL(t)
EL(t)
EL(t)
0
50
60
70
80
90
100
photon energy [eV]
110
EL(t)
ħωx
electron trajectories
cosine wave
A. Baltuska et al, Nature 421, 611 (2003)
Recombination Emission from StronglyStrongly-Driven Atoms
MultiMulti-cycle driver pulse : τp » To
HighHigh-order odd harmonics of the driver laser
Spectral intensity
25 nm
7.5 nm
12.5 nm
1
0.1
21
51
81
111
Harmonic order
L’Huillier, Balcou, 1993, PRL 70,, 774
Macklin et al, 1993, PRL 70, 766
CutCut-off harmonics: train of attosecond bursts
Paul et al, Science 292, 1689 (2001)
Tsakiris, Charalambidis et al, 2003
HHG: Electron trajectories
Correlation between recollision
time and energy
- Linear chirp in the plateau range
(has to be compensated)
- No/little chirp near the cut-off
Krausz & Ivanov, Rev.Mod.Phys. 81 (2009) 163.
Mairesse et al., PRL 93 (2004) 163901.
Dispersion control of XUV pulses
Dispersion control
with filter
Spatial selection
with iris ---DIVERGENCE!!!
López-Martens et al.,
PRL 94, (2005)
High Harmonic Generation in a gas
X-ray spectrometer
800 nm
detector
< 1ps
1015W/cm2
grating
Laser dump
HHG in neon
Photons/pulse
7
10
Harmonic
31
15
6
10
65
5
10
4
10
50
40
30
Wavelength (nm)
20
Symmetry issues
prevent HHG from
occurring at even
harmonics. But it
yields odd harmonics
and lots of them!
Close to
0-transition
17° from max
Up = e2 E/4m ω2
The cut-off wavelength depends on the
medium.
1000
o
Cut-off harmonic order
∆
experimental results
calculated results (ADK model)
Ip = 24,4 eV
Up ∝ I λ2
∆
o
quiver energy of e-
He
Ip = 21,6 eV
100
Ip = 15,8 eV
∆o
Xe
10
10
∆
o
Kr
∆
o
Ne
h υcutoff = Ip + 3.2U p
o∆
Ar
ionization
potential
of atom
Ip = 13,7 eV
Ip = 11,7 eV
20
Ionization potential (eV)
30
HHG works best with the shortest pulses.
25 fs pulse (4x)
Number of Photons
Argon
50 fs pulse (2x)
PRL 76,752 (1996)
PRL 77,1743 (1996)
PRL 78,1251 (1997)
100 fs pulse
23
27
31
35
39
43 47 51 55 59
Harmonic Order
• Shorter pulses generate higher harmonics and do so
more efficiently.
what does the future bring?
J. Seres et al., Nature 436, 234 (2005)
100
30
90
70
20
60
50
15
40
10
30
20
5
10
0
10
0
0.5
1
2
1.5
3
2.5
photon energy (keV)
Up = e2 E/4m ω2
3.5
0
filter transmission (%)
80
kiloelectronvolt
high harmonic
emission from
fewfew-cyclecycle-driven
helium atoms
⇒
HH internsity (a.u.)
25
time-resolved
spectroscopy with
atomic (~ 24 as)
resolution
4
Up = (9,33 x 10-14 eV) I (W/cm2) λ2 (µm2),
bei λ = 1 µm und 1013 W/cm2 : Up = 1 eV
IR-Quellen als Treiber für HHG
Extending the cutoff
Up = (9,33 x 10-14 eV) I (W/cm2) λ2 (µm2)
using an IR driving field
Comparison VIS / IR driver
V. Tosa and V. Yakovlev
2.1 μm fewfew-cycle OPCPA system
pump laser
Disc regen
3 kHz / 1.5
12 ps
mJ/ 27 mJ
>0.9
2mJ…
.??fs
mJ, 15
New pump for OPCPA: disc regen
T. Metzger et al., OL (2009)
IR – driven HHG
CutCut-off ~1.6 keV
Quasi-Phasenanpassung für HHG
HHG in a hollow fiber yields a longer
interaction length and “phase-matching.”
•By propagating the laser light in a
hollow fiber, its phase velocity can
be “phase-matched” to that of the
generated x-rays, increasing the
conversion efficiency.
•The wave-guide refractive index
depends on the pressure (as usual),
but also the size of the wave-guide
and the cladding material.
femtosecond light pulse
coherent EUV light
hollow fiber filled with noble gas
Science 280, 1412 (1998)
Modulated fiber for even better phase matching
drawback?
Relative energy of 29th harmonic
Pressure-tuned phase-matching of
soft x-rays
H
Xe Kr
2
29th harmonic
at 27nm
1
Created in a
hollow fiber
0
0
•
•
•
•
Ar
20
40
60
Pressure (Torr)
80
100
Phase-matched length in fiber: 1-3 cm
Output enhanced by 102-103
Can phase-match harmonic orders 19 - 60 (or 28 - 90 eV)
Harmonic photon energy is limited by the presence of plasma
Quasi-Phase-Matching (QPM) für HHG
Gasdichte

Download Report