Single Shot Combined Time Frequency Four Wave Mixing Andrey Shalit, Yuri Paskover and Yehiam Prior...
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Transcript of Single Shot Combined Time Frequency Four Wave Mixing Andrey Shalit, Yuri Paskover and Yehiam Prior...
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
• 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.
• 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
• 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
Spontaneous Raman spectrum of CHCl3
Direct spontaneous Raman spectrum (from the catalogue)
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)
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
~ 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
Time Resolved Four Wave Mixing
F.T.
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
Experimental System (modified)
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:
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:
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
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
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
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
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
• 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
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
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
+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
Single Pulse CARS Image
CH2Cl2
Time Resolved Signal and its Power Spectrum
CHBr3
Several modes in the range
Time Resolved Signal and its Power Spectrum
• 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
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
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
Measured and calculated tuning curve
max 0
41 cot
3
Measured
Calculated
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
Phase matching tuned spectra
TFD Single Shot – Sum
100 300 500 700
-600
-300
0
300
6001
10
100
1000
10000
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
• 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
CC
DC
CD
k1 k1k3
k3
k2
k2 ks
x
z
y
2
Single Shot Geometry: Parallel beams
Single Shot Geometry: Focused Beam
k1
k2
k3
CC
D
L
z
x
y
+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
+y-yk1 first k3 first
z
Intersection Region: y-z slice
+y-y
z
Δ
Intersection Region: y-z slice
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)
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)
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
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
TFD Single Shot – polarization dependence
• 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
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
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
Spectral Distribution of the Signal Produced by Intensity Beat
Detuning from a carrier (Δ)
2 11
2
0
1 2( )
2
1 2( )
2
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
TFD analysis: CCL4
Lines at 99, 147, 246 cm-1
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
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
• 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
• 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
The End
Thank you