Ultrafast temporal pulse shaping
R. STOIAN
Max-Born-Institut
outline
• Light manipulation (pulse shaping)
• Working group at MBI; topic-pulse shaping
• Available techniques
• Micromachining with shaped pulses
• Pulse-shaping; a global activity
• Self-learning
• Optimal control
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Max-Born-Institut
introduction
• Light manipulation (pulse shaping)
➪
spectral phase
➪
spectral amplitude
➪
polarization
➪
spatial profile
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Max-Born-Institut
INTENSITY
-0,2
0,0
0,2
750
775
800
825
W AVELENGTH [nm ]
850
775
800
825
W AVELENGTH [nm ]
850
INTENSITY
-0,2
0,0
TIM E [ps]
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0,2
750
PHASE
INTENSITY
TIM E [ps]
0
PHASE
INTENSITY
Temporal pulse shaping
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Max-Born-Institut
Temporal pulse shaping-Theory
∞ ~
~
Ε(Ω ) = ∫ Ε(t )⋅ eiΩt dt
~
Ε(t ) = E (t )⋅ e iϕ (t ) ⋅ e iωt
TIME DOMAIN
~
Ε in (t )
~
Ε in (Ω )
FREQUENCY DOMAIN
Dispersive unit
−∞
~
h (t )
~
~
~
Ε out (t ) = Ε in (t ) ⊗ h (t )
Black
Box
~
~
Ε out (Ω ) = H (Ω )⋅ Ε in (Ω )
~
H (Ω )
~
 ∂x 
Ω
H (Ω ) → M 
 ∂Ω 
A. Weiner CLEO 2001 Tutorial
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Max-Born-Institut
modulation in the frequency space
70 fs
INTENSITY
THz repetition rates
-1,0
-0,5
0,0
TIM E [ps]
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0,5
1,0
70 fs pulses
INTENSITY
70 fs
-1,0
-0,5
0,0
0,5
1,0
TIM E [ps]
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Max-Born-Institut
Temporal pulse shaping-Theory
dt
df
T
dB
Shortest temporal feature related to bandwidth:
B ⋅ δt ≅ 0.44
Temporal window related to spectral resolution:
T ⋅ δf ≅ 0.44
Complexity:
B T
η=
=
δf δt
Problems related to diffraction on sharp edges/ abrupt phase changes
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Max-Born-Institut
methods of pulse shaping
AOM
SLM
Individually addressed pixels
-vary phase
-vary amplitude
-scattering/pixelation
-slow refresh
Modulated RF field
-time dependent phase and
amplitude grating
-continuous phase modulation
-fast refresh
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Actuators based
-spectral phase only
-slow refresh
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-high attenuation
Max-Born-Institut
Pulse-shaping at MBI
• large palette of interests
• Activity in progress
• Perspectives
➪
MIR transients
➪
Impulsive Raman excitation / C60
➪
micromachining
➪
Improvements in spatial profiles for
high-power lasers
➪
X-ray optimization
➪
Coherent control
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Max-Born-Institut
cheap pulse shaper
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Max-Born-Institut
Temporal pulse shaping
-1,5
-0,8
0,0
0,8
1,5 -1,5
-0,8
TIME [ps]
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0,0
0,8
1,5
-1,5 -1,0 -0,5 0,0 0,5 1,0 1,5
TIM E [ps]
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Max-Born-Institut
material response
Material response
Electronic
response
coupling
Lattice
response
Non-Thermal
Thermal
ABLATION
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Max-Born-Institut
free electron build-up
pulse duration 0.1 ps
rate equation:
∂n
n
= P(I ) + αIn −
∂t
τ
Te ⇒ Ti
LOSSES
Heat exchange
10 24
LASER PULSE
M ULTIPHOTON
12
+ AVALANCHE
10
10 22
8
10 20
M ULTIPHOTON
10 18
+ AVALANCHE
10 16
+TRAPPING
10 14
4
2
10 12
10 10
-0,2
6
0,0
0,2
0
0,4
INTENSITY [TW /cm 2 ]
MPI avalanche
ELECTRON DENS. [cm -3 ]
damage ⇔ ncr~1021 at 800 nm
Electrons:
TIM E [ps]
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Max-Born-Institut
ODT-TP/ODT-SP
2,0
SAPPHIRE
FUSED SILICA
1,6
1,2
1,0
SIZE/FOCUS
SIZE/FOCUS
ODT-DP/ODT-SP
optical damage thresholds
0,8
0,6
0,2
0,4
0,6
0,8
1,0
2,8
SAPPHIRE
2,4
FUSED SILICA
2,0
Spatial laser profile
1,6
-electron decay on the wings
1,0
0,8
0,6
0,4
0,2
0,4
0,6
0,8
1,0
PULSE SEPARATION [ps]
PULSE SEPARATION [ps]
DOUBLE SEQUENCE
TRIPLE SEQUENCE
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Max-Born-Institut
modulated depth profile in SiO2
TRIPLE PULSE, 0.3 ps separation
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TRIPLE PULSE, 1 ps separation
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Max-Born-Institut
depth profile in Al2O3
TRIPLE PULSE, 0.3 ps separation
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TRIPLE PULSE, 1 ps separation
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Max-Born-Institut
profile improvement in SiO2
SINGLE PULSE
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TRIPLE PULSE 0.3 ps separation
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Max-Born-Institut
pulse-width dependence
20 µm
Al2O3
200 fs
20 µm
20 µm
2.0 ps
200 fs
4.5 ps
SiO2
τ
20 µm
20 µm
CaF2
200 fs
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1.8 ps
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Max-Born-Institut
structures with single and shaped pulses
-triple pulse sequences
CaF2 SAMPLES
N=5, F=7 J/cm2
Single pulse
10 µm
N=5, F=12 J/cm2
Reduced
exfoliation
Triple pulses
-1,4 -0,7 0,0 0,7 1,4
TIME [ps]
Stoian et al. Appl. Phys. Lett. 80,
353 (2002)
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Max-Born-Institut
surface softening (with THz rep. rates)
Timescale for:
carrier self-trapping
lattice induced deformations
atomic displacements (transient defect states)
surface softening
stress dissipation
∆τ~0.5-1 ps
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Max-Born-Institut
structures with single and shaped pulses
-triple pulse sequences
FUSED SILICA SAMPLES
cracking
less cracking
cracking
80 µm
70 fs
300 fs
INTENSITY
INTENSITY
INTENSITY
1000 fs
-1,4 -0,7 0,0
0,7
TIM E [ps]
1,4
-1,4 -0,7
0,0
0,7
TIME [ps]
1,4
-1,4 -0,7 0,0
0,7
1,4
TIME [ps]
τ
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Max-Born-Institut
material characteristic response
•Electronic response
modulated excitation
•Lattice response
optimum energy transfer
Material reaction
Candidates:
•materials with fast electron trapping
(strong electron-phonon coupling)
•brittle materials
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Max-Born-Institut
summary:
Material response characteristic times
Temporally tailored pulses
The potential for quality microstructuring
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Max-Born-Institut
pulse shaping; a global activity
• short pulse optimization/ automated pulse
compression
• attosecond and high-harmonics generation
• laser-plasma interactions / X-ray production
• THz radiation
• femtochemistry and coherent control
– multiphoton transitions
– wavepackets
– selective excitation
– selective dissociation
• telecommunications / encoding of information
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Max-Born-Institut
HHG optimization
JILA Colorado
Bartels et al. Nature 406, 164 (2000)
Bartels et al. Chem. Phys. 267, 277 (2001)
HHG in Argon
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Max-Born-Institut
Chemical reactions
Uni-Würzburg
Assion et al. Science 282, 919 (1998)
Brixner et al. Chem. Phys. 267, 241 (2001)
Controlling
fragmentation yields
CpFeCOCl+
CpFe(CO)2Cl
MAX
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FTL
FeCl+
MIN
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Max-Born-Institut
8S1/2
ω2
∆ω
ω0/2
ω0/2
7P
ωFl
ω1
6S1/2
Two photon fluorescence
Coherent control on MPI
Weizmann Institute
S2 =
2
= ∫ E (ω 0 / 2 + Ω )E (ω 0 / 2 + Ω )dΩ
=
∫ A(ω
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0
Meshulach et al. Nature 396, 239 (1998)
Dark pulse
-1 0 1 2 3 4 5 5 6 7 8 9 10
phase m odulation
/ 2 + Ω )A(ω 0 / 2 − Ω )exp{i[Φ ( 0 / 2 + Ω ) − Φ ( 0 / 2 + Ω )]}dΩ
2
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Max-Born-Institut
Wakefield optimization
University of Texas, Austin
Compact electron accelerators
laser produced plasmas
http://www.ph.utexas.edu/~femtosec/index.html
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Max-Born-Institut
Polarization pulse shaping
3D-Electric field distribution
Time dependent polarization
Brixner et al. Opt. Lett. 26, 557 (2001)
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Max-Born-Institut
Spatio-temporal shaping
time
Spatio-temporal shaping and imaging
Koehl et al. Chem. Phys. 267, 151 (2001)
Propagating lattice waves
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Max-Born-Institut
Photonics
University of Tokushima, Japan
Tremendous potential for
3D field distribution/modifications
Kondo et al. Appl. Phys. Lett.
79, 725 (2001)
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Max-Born-Institut
Photonics
Purdue University
Advances in pulse shaping techniques
Encoding /decoding information
Accept/Reject
Zheng et al. Chem. Phys. 267, 161 (2001)
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Max-Born-Institut
Tendencies
•Frequency conversions with NLO
•Spectral holography and time-to-space transformation
•Multi-dimensional pulse shaping
•Multiple-wavelength selection and add/drop switches
•Active phase-control for broadband fs continuum
to reach the sub-fs region
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Max-Born-Institut
Self-learning
• Genetic/evolutionary algorithms
• Simulated annealing
• Simplex downhill
• Iterative Fourier transformations
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Max-Born-Institut
Genetic algorithms
pixels
• Each pixel 2n values of phase/amplitude
• initial bit streams; “parents”, initial solution population
• parents produce children through genetic propagators
ASEXUAL
• rank the parents according to
the achievement
• mutate each parent
individually by bit switching
• mutate best parents more
often than the worst
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SEXUAL
• pair up the parents
• exchange genetic information
• use occasional mutations
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Max-Born-Institut
Genetic algorithms
•“Random” search
•Parameterization of the solution space
E.g. Taylor series etc.
parents
•Mutation
•Crossover
Optimal
solution
offsprings
•Evolution
•Selection
•Fitness
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Better to survive in the
environment
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Max-Born-Institut
Simulated annealing
Implementation of cost functions (H) associated with the system states (T)
Implementation of a way to change the system state
Input and asses
initial solution
•Propose changes (solution generator)
Initial state
(Temperature)
Generate new
solution
•“Random” search
•Parameterization of the solution space
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Asses new
solution
Reject/Accept
(also bad
solutions with
low probability)
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Max-Born-Institut
Downhill simplex
•Simplex = geometrical figure of N+1 points in N-dim space
Pi = P0 + λ ⋅ ei
Evaluation:
Highest point
Lowest point
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Highest point
Reflection
Expansion/Contraction
Asses
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Max-Born-Institut
Fourier algorithms
Initial pulse
target pulse
~
Ein (ω ) = A(ω )⋅ e iΦ (ω )
A(ω )⋅ e
iΦ (ω )
M. Hacker et al. Opt. Exp. 9, 191 (2001)
I Tar (t ) = z (t )
FT-1
b(t )⋅ e
2
iΘ (t )
Frequency domain constraint
Time domain constraint
B (ω ) :⇒ A(ω )
b(t ) :⇒ z (t )
B(ω )⋅ e
iΨ (ω )
FT
z (t )⋅ e iΘ (t )
Phase to shaper
Ψ (ω ) − Φ (ω )
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Max-Born-Institut
examples
Iterative
Fourier
Transform
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Max-Born-Institut
examples
IFT
N~10
GA
N~2000
random
SASD
N~200
Taylor
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Max-Born-Institut
optimal control
Economics; Engineering and Robotics; Web; Life sciences and Ecology
•Optimization of systems governed by differential equations and
at least one control function
•Influencing systems with little external effort
•nature is optimal
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Max-Born-Institut
optimal control
~
E (t ) = ???
LASER FIELD
Ψi (t = T )
Ψi (t = 0 ) = Φ i
Φ f t =T
Ψ
Φ
Ψi (T ) Φ f
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Destination
e.g. population
2
MAXIMUM !!!
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Max-Born-Institut
optimal control-functional
[
]
Zhu et al. J. Chem. Phys. 108, 1953 (1998)
K.Sundermann et al. J. Chem. Phys. 110, 1896 (1999)
~
J Ψi (t ), Ψ f (t ), E (t ) =
Overlapping integral
= Ψi (T ) Φ f
2
Energy optimization
−∫
T
0
~ 2
α ⋅ E (t ) dt −


2
T
i
∂
~


Ψi (t ) dt 
− 2 Re Ψi (T ) Φ f × ∫ Ψ f (t ) H − µE (t ) +
0
h 442444
∂t4443 
4244
3 1
4
4
4
4
14
T1
T2


[
]
Fulfillment of the Schrödinger equation
δJ = 0
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α = α (T )
For realistic situation
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Max-Born-Institut
optimal control-IR excitation of OH
Morse potential
[
]
2
Energy
V (r ) = D0 e − β (( r −r0 ) )
v=1
v=0
1
2
3
4
O-H distance
Φ f (T )
Ψi (T )
2
2
Sundermann et al. J. Chem. Phys. 110, 1896 (1999)
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Max-Born-Institut
optimal control-stimulated emission
pumping in K2
∆t=75 fs
∆ω
∆T1-5
CLASSICAL SCHEME
Pump-dump cycle
Sundermann et al. J. Chem
Phys. 110, 1896 (1999)
v=0 to 5
via A1Σu
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Max-Born-Institut
optimal control-realistic pulses
Spectrally unconstraint
OCT calculations
Hornung et al. J. Chem. Phys.
115, 3105 (2001)
Spectral pressure added
Population transfer
X1Σg v’’=0 to v’’=2 via A1Σu
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Max-Born-Institut
alignment and orientation
Hoki et al. Chem. Phys. 267, 187 (2001)
OCT can derive functionals for:
CO molecule: Takes into account:
•alignment / orientation
•rovibrational levels
•polarizability/ dipole moments
time [ps]
time [ps]
θ[rad]
θ[rad]
E(t)
E(t)
1
3
850 cm-1
2
4
Time [ps]
= 0, MStoian
= 0 → v = 1, J = 1, M = 0
v = 0, JRazvan
v = 1, J = 1, M = 0 → v = 2, J = 2, M = 0
5
6
48
Time [ps]
-1]
ω [cmMax-Born-Institut
Inversion problem
Zhu et al. J.. Phys. Chem. A 103,
10187 (2001)
Optimization results
Experimental electric fields
Inversion algorithms
Potential energy curves
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Max-Born-Institut
conclusions
• Powerful technique
• Large applicability
• Together with OCT; possibility of control and
understanding
• There is a tendency to see pulse shaping and selflearning as a “philosophical stone”
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Max-Born-Institut