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Single Shot Combined Time Frequency Four Wave Mixing
Andrey Shalit, Yuri Paskover and Yehiam Prior
Department of Chemical PhysicsWeizmann Institute of Science,
Rehovot, Israel
LPHYS 09 Barcelona July 17, 2009
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• Molecular spectroscopy can be performed either in the frequency domain or in the time domain.
• In the frequency domain, we scan the frequency of excitation (IR absorption), or the frequency of observation (Spontaneous Raman spectroscopy), etc.
• Alternatively, we can capture the time response to impulse excitation, and then Fourier Transform this signal to obtain a frequency domain spectrum.
• We are always taught that the choice of one or the other is a matter of convenience, instrumentation, efficiency, signal to noise, etc. but that the derived physical information is the same, and therefore the measurements are equivalent.
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• Time Frequency Detection (TFD) : the best of both worlds
• Single Shot Four Wave Mixing
• Tunable Single Shot Four Wave Mixing
• Multiplex Single Shot Four Wave Mixing
• TFD simplified analysis
• Conclusions
Outline
![Page 4: Single Shot Combined Time Frequency Four Wave Mixing Andrey Shalit, Yuri Paskover and Yehiam Prior Department of Chemical Physics Weizmann Institute of](https://reader038.vdocuments.us/reader038/viewer/2022110207/56649d395503460f94a12a36/html5/thumbnails/4.jpg)
• Time Frequency Detection (TFD) : the best of both worlds
• Single Shot Four Wave Mixing
• Tunable Single Shot Four Wave Mixing
• Multiplex Single Shot Four Wave Mixing
• TFD simplified analysis
• Conclusions
Outline
![Page 5: Single Shot Combined Time Frequency Four Wave Mixing Andrey Shalit, Yuri Paskover and Yehiam Prior Department of Chemical Physics Weizmann Institute of](https://reader038.vdocuments.us/reader038/viewer/2022110207/56649d395503460f94a12a36/html5/thumbnails/5.jpg)
Spontaneous Raman spectrum of CHCl3
Direct spontaneous Raman spectrum (from the catalogue)
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221
212
2
2
1
2)3(
)(
)(sin
kl
klIIICARS
k
k1 k1
k2 kCARS
Energy conservation Conservation of Momentum(phase matching )
Raman
1 1
2 AS
1- 2- AS = 0 k = 2k1-k2-kAS= 0
Coherent Anti Stokes Raman Scattering (CARS)
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Time Resolved Four Wave Mixing
31 s2• A pair of pulses (Pump and
Stokes) excites coherent vibrations in the ground state
• A third (delayed) pulse probes the state of the system to produce signal
• The delay is scanned and dynamics is retrieved
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~ 50-100 femtosecond pulses ~ 0.1 mJ per pulse
EaEb Ec
Time delay
( )s a b ck k k k Phase matching
Time Resolved Four Wave Mixing
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Time Resolved Four Wave Mixing
F.T.
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Time Domain vs. Frequency Domain
2
(3)( ) ( , )S P t dt
In this TR-FWM the signal is proportional to a (polarization)2
and therefore beats are possible
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Experimental System (modified)
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Time frequency Detection (CHCl3)
500 1000 1500 2000 2500
1
Time [fs]
Arb
. Un
itsSummation over all
frequencies (Δ)
Time [fs]
[
cm-1
]
500 1000 1500 2000 2500
-800
-600
-400
-200
0
200
400
600
800
Open band:
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500 1000 1500 2000 2500
1
Time [fs]
Arb
. Un
its
0 100 200 300 400 500 600 7000
1
R
[cm-1]
Arb
. Un
itsF.TOpen band:
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Limited Band Detection
Time [fs]
[
cm-1
]
500 1000 1500 2000 2500
-800
-600
-400
-200
0
200
400
600
800
500 1000 1500 2000 25000
1
Time[fs]
Arb
.Un
its
Summation over 500cm-1 window
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Open vs. Limited Detection
500 1000 1500 2000 2500
1
Time [fs]
Arb
. Un
its
0 100 200 300 400 500 600 7000
1
R
[cm-1]
Arb
. Un
its
500 1000 1500 2000 25000
1
Time[fs]
Arb
.Un
its
100 200 300 400 500 600 7000
1
R
[cm-1]
Arb
. Un
its
Open band:
Limited band:
F.T
F.T
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Time [fs]
[
cm-1
]
500 1000 1500 2000 2500
-800
-600
-400
-200
0
200
400
600
800
Time Frequency Detection CHCl3
R
[cm-1]
[
cm-1
]
100 200 300 400 500 600 700
-800
-600
-400
-200
0
200
400
600
800
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Spectral Distribution of the Observed Features
104 cm-1 365 cm-1
Observed frequency: 104 cm-1
Observed detuning : 310 cm-1
Observed frequency: 365 cm-1
Observed detuning : 180 cm-1
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However, this is a long measurement, it takes approximately 10 minutes, or >> 100 seconds.
In what follows I will show you how this same task can be performed much faster.
1015 times faster, or in < 100 femtoseconds !
Time [fs]
[
cm-1
]
500 1000 1500 2000 2500
-800
-600
-400
-200
0
200
400
600
800
R [cm-1]
[
cm-1
]
100 200 300 400 500 600 700
-800
-600
-400
-200
0
200
400
600
800
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• Introduction, or “TFD: the best of both worlds”
• Single Shot Four Wave Mixing
• Tunable Single Shot Four Wave Mixing
• Multiplex Single Shot Four Wave Mixing
• TFD simplified analysis
• Conclusions
Outline
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Spatial Crossing of two short pulses:Interaction regions
k3 k1
5mmBeam diameter – 5 mm
100 fsec = 30 microns
Different regions in the interaction zone correspond to different times delays
k1 arrives first
k3 arrives first
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Three pulses - Box-CARS geometry
1
cos
sin
0
k
2
cos
0
sin
k
3
cos
sin
0
k
3,1
2 12,1
2,3
sin2 ,
sin,
sin.
r yc
r z y T Tc
r z yc
,
i
i
j
i jjr r T
k k
cT
Time delays Spatial coordinates
CC
DC
CD
k1 k1k3
k3
k2
k2 ks
x
z
y
2
1 2 3sk k k k
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+y-yk1 first k3 first
z
k1k2k3
Pump-probe delay
k1k2 k3
Pump-probe delay
2,1 0
z y
2,3 0
z y
Intersection Region: y-z slice
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Single Pulse CARS Image
CH2Cl2
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Time Resolved Signal and its Power Spectrum
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CHBr3
Several modes in the range
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Time Resolved Signal and its Power Spectrum
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• Introduction, or “TFD: the best of both worlds”
• Single Shot Four Wave Mixing
• Tunable Single Shot Four Wave Mixing
• Multiplex Single Shot Four Wave Mixing
• TFD simplified analysis
• Conclusions
Outline
![Page 28: Single Shot Combined Time Frequency Four Wave Mixing Andrey Shalit, Yuri Paskover and Yehiam Prior Department of Chemical Physics Weizmann Institute of](https://reader038.vdocuments.us/reader038/viewer/2022110207/56649d395503460f94a12a36/html5/thumbnails/28.jpg)
Geometrical Effects
CC
DC
CD
k1 k1k3k3k2
k2 ks
x
z
y
2
s s
ck
n
xy
z
3k
1k
2k
sk
1 2 3sk k k k
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740760
780800
820840
-3
-2
-1
0
1
2
[cm-1]
[mrad]
Spectrum of the central frequency (coherence peak) as a function of the Stokes beam deviation
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Measured and calculated tuning curve
max 0
41 cot
3
Measured
Calculated
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For each time delay, a spectrally resolved spectrum was measured.
Time [fs]
[
cm-1
]
500 1000 1500 2000 2500
-800
-600
-400
-200
0
200
400
600
800
R [cm-1]
[
cm-1
]
100 200 300 400 500 600 700
-800
-600
-400
-200
0
200
400
600
800
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Phase matching tuned spectra
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TFD Single Shot – Sum
100 300 500 700
-600
-300
0
300
6001
10
100
1000
10000
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Compare with scanned Results
100 300 500 700
-600
-300
0
300
6001
10
100
1000
10000
R
[cm-1]
[
cm-1
]
100 200 300 400 500 600 700
-800
-600
-400
-200
0
200
400
600
800
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• Introduction, or “TFD: the best of both worlds”
• Single Shot Four Wave Mixing
• Tunable Single Shot Four Wave Mixing
• Multiplex Single Shot Four Wave Mixing
• TFD simplified analysis
• Conclusions
Outline
![Page 36: Single Shot Combined Time Frequency Four Wave Mixing Andrey Shalit, Yuri Paskover and Yehiam Prior Department of Chemical Physics Weizmann Institute of](https://reader038.vdocuments.us/reader038/viewer/2022110207/56649d395503460f94a12a36/html5/thumbnails/36.jpg)
CC
DC
CD
k1 k1k3
k3
k2
k2 ks
x
z
y
2
Single Shot Geometry: Parallel beams
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Single Shot Geometry: Focused Beam
k1
k2
k3
CC
D
L
z
x
y
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+y-yk1 first k3 first
z
k1k2k3
Pump-probe delay
k1k2 k3
Pump-probe delay
2,1 0
z y
2,3 0
z y
Intersection Region: y-z slice
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+y-yk1 first k3 first
z
Intersection Region: y-z slice
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+y-y
z
Δ
Intersection Region: y-z slice
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Y pixels
Z p
ixel
100 200 300 400 500 600
100
200
300
400
500
600
Time Frequency Detection:Multiplex single Shot Image
τ [fs]Δ
Focusing angle : δ = 3 mrad (CH2Br2)
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TFD Single Shot – Fourier Transformed
R
[cm-1]
[
cm-1
]
150 200 250 300 350 400 450 500
400
300
200
100
0
-100
-200
-300
-400
-500
(CH2Br2)
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TFD Scanned (CH2Br2)
Time [fs]
[c
m-1
]
500 1000 1500 2000 2500
-800
-600
-400
-200
0
200
400
600
800
R
[cm-1]
[
cm-1
]
150 200 250 300 350 400 450 500
-800
-600
-400
-200
0
200
400
600
800
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R
[cm-1]
[
cm-1
]
150 200 250 300 350 400 450 500
400
300
200
100
0
-100
-200
-300
-400
-500
R [cm-1]
[
cm-1
]150 200 250 300 350 400 450 500
-800
-600
-400
-200
0
200
400
600
800Compare with scanned Results
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TFD Single Shot – polarization dependence
![Page 46: Single Shot Combined Time Frequency Four Wave Mixing Andrey Shalit, Yuri Paskover and Yehiam Prior Department of Chemical Physics Weizmann Institute of](https://reader038.vdocuments.us/reader038/viewer/2022110207/56649d395503460f94a12a36/html5/thumbnails/46.jpg)
• Introduction, or “TFD: the best of both worlds”
• Single Shot Four Wave Mixing
• Tunable Single Shot Four Wave Mixing
• Multiplex Single Shot egenerate Four Wave Mixing
• TFD simplified analysis
• Conclusions
Outline
![Page 47: Single Shot Combined Time Frequency Four Wave Mixing Andrey Shalit, Yuri Paskover and Yehiam Prior Department of Chemical Physics Weizmann Institute of](https://reader038.vdocuments.us/reader038/viewer/2022110207/56649d395503460f94a12a36/html5/thumbnails/47.jpg)
1k 2k 3k sk
sg
e
2k 1k 3k sk
sg
e
0 3ˆΨ t μ Ψ t 2 1ˆΨ t μ Ψ t 3totP t +
R 0 R
Detuning from a probe (k3) carrier frequency
g
e
'g
'e
g
g
g
g
k1
-k2
k3
g
g
g
'e
g
e
'g
'g
k1
-k2
k3
Time Frequency Detection2
(3)( ) ( , )S P t dt
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Detuning from a probe carrier frequency (Δ)
11
0
1
2
1
2
Spectral Distribution of the Signal Produced by a Fundamental Mode
In TR-DFWM, we have shown that because of the quadratic dependence on the polarization, fundamental modes may be seen only after linearization of the signal, i.e. by heterodyne detection
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Spectral Distribution of the Signal Produced by Intensity Beat
Detuning from a carrier (Δ)
2 11
2
0
1 2( )
2
1 2( )
2
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Identification of signals:
Fundamental modes of frequency Ω1 are
spectrally peaked at Ω1/2
Intensity beats at frequency )Ω1 ± Ω2(
spectrally peaked at [ )Ω1-Ω2(/2 ]
Based on this result, it is now possible to directly and unambiguously identify the character of each peak
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TFD analysis: CCL4
Lines at 99, 147, 246 cm-1
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Homodyne beat : (Ω1-Ω2)=99cm-1
Detuning : (Ω1+Ω2) /2=260 cm-1
Ω1 = 210 cm-1 ; Ω2 = 309
Homodyne beat : (Ω3-Ω4) = 246cm-1
Detuning : (Ω3+Ω4)/2 =337 cm-1
Ω4 = 214 cm-1 ; Ω3 = 460
TFD analysis: CCL4
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Homodyne beat : (Ω5-Ω6) = 147cm-1
Detuning : (Ω5+Ω6) /2 = 385 cm-1
Ω5 = 317 cm-1 ; Ω6= 464 cm-1
210 309
317 464
214 460
DERIVED fundamental frequencies
214 313 460
KNOWN CCl4 Modes
TFD analysis: CCL4
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• Time Frequency Detection (TFD) : the best of both worlds
• Single Shot Four Wave Mixing
• Tunable Single Shot Four Wave Mixing
• Multiplex Single Shot Degenerate Four Wave Mixing
• TFD simplified analysis
• Conclusions
Outline
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• Time Frequency combined measurements offer advantages over either domain separately
• Specific advantages in spectroscopy of unknown species, by the ability to identify the character of observed lines (fundamental or beat modes)
• Advantages in cleaning up undesirable pulse distortions
• Single mode FWM measurements
• Tunable single mode FWM measurements
• Multiplex single mode FWM measurements
• Significant theoretical foundation (not discussed here)
• More work needed to improve resolution, bandwidth, accuracy, reproducibility, etc
Conclusions
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The End
Thank you