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