four wave mixing – a mirror in time yehiam prior weizmann institute of science, rehovot, israel...
TRANSCRIPT
Four Wave Mixing – a Mirror in Time
Yehiam Prior
Weizmann Institute of Science, Rehovot, Israel
Suzdal NLO-50(+) September 2011
And in 1960 the LASER was invented:
Soon to be described as a “solution looking for a problem”
It took a long time….
1960 - 7th grade1970 - student in Jerusalem, deciding to
continue my studies in the US1971 - Berkeley, looking for a Thesis advisor
Options: Shen, Townes, Hahn1977 - post doc position: Nico Bloembergen1979 – Weizmann Institute (ever since)
Where was I ?
How does a laser work ?
Monochromatic, Directional, Intense, Coherent
IncoherentCoherent
So, what can we do with these Coherent sources?
Spontaneous Raman spectrum of CHCl3
Direct spontaneous Raman spectrum (from the catalogue)
221
212
2
2
1
2)3(
)(
)(sin
kl
klIIICARS
Dk
k1 k1
k2 kCARS
Energy conservation Conservation of Momentum(phase matching )
WRaman
w1 w1
w2 wAS
2w1- w2- wAS = 0 Dk = 2k1-k2-kAS= 0
Four Wave Mixing (FWM) and Coherent Anti Stokes Raman Scattering (CARS)
FWM Applications included:
• Molecular spectroscopy• Rotational and vibrational dynamics• Solid state fast relaxation phenomena• Photon echoes• Combustion diagnostics• Surface diagnostics• Biological applications• Microscopy• Remote sensing• …….
• Spectroscopy can be performed either in the frequency domain or in the time domain.
• In the frequency domain, we scan the frequency of excitation (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 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
However, practically ALL CARS and Four Wave
Mixing experiments were/are performed in the
frequency domain.
i.e. one is not directly measuring the molecular
polarization (wavefunction) which is oscillating at
optical frequencies.
Combined Time Frequency Detection of Four Wave Mixing
With: Dr. Yuri Paskover (currently in Princeton)Andrey Shalit
• Time Frequency Detection (TFD) : the best of both worlds
• Single Shot Degenerate Four Wave Mixing • Tunable Single Shot Degenerate Four Wave
Mixing• Multiplex Single Shot Degenerate Four Wave
Mixing• TFD simplified analysis• Conclusions
Outline
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
Also A. Eckbreth, Folded BOXCARS configuration
~ 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
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
3k1k
2k
sk
1 2 3sk k k k
Three pulses - Box-CARS geometry
Time delays Spatial coordinates
+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
Geometrical Effects : Phase mismatching
xy
z
3k
1k
2k
sk
s s
ck
n
1 2 3sk k k k
Shalit et al. Opt. Comm. 283, 1917 (2010)
Calculated Measured
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
Phase matching tuned spectra
TFD Single Shot – Sum
100 300 500 700
-600
-300
0
300
6001
10
100
1000
10000
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
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
Single Shot multiplexing: Focused Beam
2k k sk k
L
+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
Time [fs]
[
cm-1
]
500 1000 1500
400
200
0
-200
-400
Time Frequency Detection: Single Shot Image
Focusing angle : δ = 3 mrad (CH2Br2)
Time Frequency Detection by Single Shot: Fourier Transformed
(CH2Br2)
R
[cm-1]
[c
m-1
]
100 200 300 400 500
-400
-200
0
200
400
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]
[c
m-1
]
100 200 300 400 500
-400
-200
0
200
400
R
[cm-1]
[c
m-1
]
100 200 300 400 500
800
600
400
200
0
-200
-400
-600
-800
Taken by single shot
Scanning method (10 min)
Signal to noise comparison 150 pulses 1500 pulses
15,000 pulses 150,000 pulses
Time [fs]
[
cm-1
]
500 1000 1500
400
200
0
-200
-400
Time Frequency Detection: Single Shot Image
Focusing angle : δ = 3 mrad (CH2Br2)
TFD Single Shot – polarization dependence
• 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
AcknowledgementsDr. Alexander Milner, Dr. Riccardo Castagna, Dr. Einat Tirosh, Sharly
Fleischer, Andrey Shalit, Atalia Birman, Omer Korech, Dr. Mark Vilensky, Dr. Iddo Pinkas
Thank you