Impulsive Stimulated Raman Scattering -...

Impulsive Stimulated Raman Scattering

Wednesday, March 13, 2002

Mark Boyle

Mark Boyle Wednesday, February 27, 2002 2

Motivation

• Control of vibrational motion of molecules time resolved spectroscopy

• Ultrashort pulse generation


Outline

• Introduction to Stimulated Raman Scattering (Szymanski, Raman Spectroscopy, 1967)

• Theory of Impulsive Stimulated Raman Scattering (JCP 83, 5391 (1985), PRA 58, R61(1998))

• Experiments MBI (PRL 83, 2560 (1999); Appl. Phys. B 70, S261 (2000); PRL 84, 5508,

2000; Optics Letters 26, 298, (2001)) JILA and Univ. of Michigan (Murnane, Kapteyn, Bucksbaum) CPL 344, 333

(2001))

• Prospects for C60???


Raman Scattering

Raman scattering describes the inelastic scattering of a photon by a molecule

Stokes Rayleigh Anti-Stokes

For a molecule to be Raman active, the polarizability must change with the vibrational motion.

ωω

I

ωωοο


Polarizability

In a molecule, polarizability is dependent on the nuclear coordinate positions. A vibration can be Taylor expanded (Plazcek Model, 1934):

K+−∂∂+−

∂∂+= 2

02

2

00 )(2

1)()()( QQ

QQQ

QQQ

αααα

Q is the normal vibrational coordinate

CO O CO O CO O

ex. CO2


Raman Scattering

A Raman active transition occurs when the normal mode involved belongs to the same symmetry group as any one or more of the Cartesian components of the polarizability tensor of the molecule.

0≠ge ψαψ

( ) L+−

∂∂+= ∫∫ dQQQQ

dQ gegenm ψα

ψψαψα 0*

0*

≠≠0 when e=g

diagonal terms

≠≠0 when e=g±1

off-diagonal terms

For Ideal H.O.


Impulsive Stimulated Raman Scattering (ISRS)

StimulatedRaman Scattering

Impulsive StimulatedRaman Scattering

νν

πτ

Ω≡< 2

TL

Ων

∆ν

∆ν

L

ωωL ωωs

∆ν∆νL

∆ν∆νs

ωωL ωωs

Ων


ISRS Equations of Motion

( )L

L

QEtQ

Nct

Ecn

zE

EQM

QtQ

tQ

2

2

022

2

2

2

2

2

22

2

2

4

2

12

δδ

δδαπ

δδ

δδ

δδα

δδ

γδδ

ν

⋅

=−

=Ω++

Q is the normal coordinateγγ is the damping constantΩΩνν is the vibrational frequency

N0 is the number density of oscillatorsαα is the optical polarizability tensorn is the refractive index tensorM is the reduced mass of the oscillator

The incident light creates a vibrational motion, which can be expressed as:

MolecularVibrational motion

ScatteredElectric Field

The resulting scattered electric field from a second probe pulse will be:

Yan et al. JCP 83, 5391 (1985);Nazarkin and Korn, PRA 58, R61 (1998) SRS: Shen and Bloembergen, PRA 137, 1787 (1965)


Molecular Vibrational Motion

( ) 22 //22

2

2

2

12 LcznteA

QMQ

tQ

tQ τ

ν δδα

δδ

γδδ −−

=Ω++

The solution for γγ small (γγ <<ΩΩνν),

( ) ( ) ( )[ ]cznteQtzQ cznt /sin0,0 /0 −Ω=>> −−

νγ

4/0

222 Le

QMcW

Q τ

ν

ν

δδαπ Ω−

Ω

=vibrational amplitude

W is the integrated intensity of the pulse (pulse shape unimportant)*

Q0

tt=0


Scattering of a “probe” pulse

Consider now a second, “probe” pulse, which follows at a time delay, tD,

The impulsive force exerted by the “probe” pulse either enhances or dampens the vibrational motion.

( )teQQ t ′Ω= ′−ν

γ sin1 t´=tD-zn/c

t=0 t=-tD

probe pulse excitation pulse

Phase velocity ofoscillation =speed of light in meduim



( ) ( )φνγ +′Ω=>′ ′−

Σ teQtQ t sin0

Resultant vibrational motion from excitation and probe pulses:

From equation for amplitude:

1.) when the probe pulse is in phase with vibrational motion(i.e. tD=0, Tνν, 2Tνν,…), then the amplitude is increased

2.) when the probe pulse is out of phase (i.e. = Tνν /2/2, 3 Tνν /2/2, …)then the amplitude is decreased

where ( )DtQQQQQ νΩ++=Σ cos~

2~

102

120

2 DteQQ γ−= 00

~



Furthermore when the probe pulse is of equal intensity

and in phase, then the amplitude is doubled

and out of phase, then the vibration is stopped

( )DtQQQQQ νΩ++=Σ cos~

2~

102

120

2

A succession of in phase and short pulses will drive the vibrational mode withincreasing effectiveness, thus increasing mode selectivity.

e.g. control of molecular vibrations


Spectral effects of Raman scattering

[ ])()(42

2

2

02

2

2

2

tEtQtQ

Nctz

Ecn

zE

L ′′′

=

′−

δδ

δδαπ

δδδ

δδ

Using slowly varying amplitude approximation:

Yan, et al.

( ) ip

ii

i

i EQvztQc

QQN

it

EzE 1

0

00

/

21 −−

−=+44 344 21

β

δδαπω

δδ

νδδ

Nazarkin, et al.

νi is the injection pulse group velocityE(z,t)


Spectral effects of coherent scattering(low interaction regime)

The of the outgoing pulse is found by a Fourier Transformation.spectral content

( ) ( ) ( )[ ]00/ 00),( ωωωωωω ωωω −−++= −−

Lti

Lti

Lczin EeEeBEewzE DD

Stokes shiftanti-Stokes shiftunshifted field

For a short probe pulse, the spectral width exceeds the spectral separation.Thus there is an interference of the three fields which is dependent time delay.

In-phase probe pulse - experiences a red shiftOut-of-phase probe pulse - experiences a blue shift

For a long probe pulse, three well defined frequencies will result.


Spectral effects of coherent scattering(general result)

Solution: ( ) ( ) ( ) ( )

∆−Ω×

∆∆−= KzKKz

iEzE iii τβττ υsinsin

exp,0,

2/])()[( 11 −− −Ω=∆ piK ννν

( ) ( ) ( )ξωω ν2

22

nn

ii JnfF ∑∞

−∞=Ω−∆=∆

Spectrally, this results in:

( )KKz

i ∆∆= sin

βξwithn=0n=-1 n=1n=-2 n=2

ΩΩνν

ωω0 ωω0+ΩΩννωω0-ΩΩνν

Characterizes group velocity difference


Ultrashort pulse generation

ISRS provides a linear scattering regime (for the probe pulse) which is generated in the periodically varying index of refraction created by the excitation pulse.

The nature of ISRS provides a coherence control, plus the independenceof the excitation field time structure provides a “stability” against amplitude or phase distortion.

Thus, using a short probe pulse, spectral broadening occurswhich can be compressed (current record 3.8 fs).


Impulsive Stimulated Raman Scattering...

•general aspect of ultrafast laser-matter interactionwhich occurs with one sufficiently short laser pulse

•Vibrational and spectral results are dependent on the separation time of a pump and probe pulse

•controlling of vibrational modes

•ultrashort pulse generation


MBI Experiments: SF6

Hollow waveguides filled with SF6

t

800nm, 30fspump

400nm, 200fsprobe

Important parameters for SF6:

1.) vibrational period, ττv =43 fs2.) coherence time, ττc> ττv

3.) high IP and dissociation level (>10eV)


MBI Experiments : SF6

Pressure Dependence of ISRS

0 mbar

346 mbar

395 mbar

410 mbar

470 mbar

++,,88--

Solid lines are from computer modeling

( ) ( ) ( )

∆∆

Ω−∆=∆ ∑∞

−∞= KKz

JnfF inn

ii

sin22

2 βωω ν

( ),...1,0 ±=Ω+= nnin νωω



Temporal structure of output spectra

100 fs2

0 fs2

-100 fs2

The field frequency is periodically modulatedfrom leading to trailing edge: ωi(τ)=ωi+∆ωi(τ)

where ∆ωi(τ)=-GiΩz cos(Ωτ)

In a dispersive medium, the frequency modulationbecomes an amplitude modulation, with peaks occurring where the frequency sweeping has anextremum.

( ) ( )Ω+=− m

m

ππτ

22/

m=0,1,2...

[found for condition cos(Ωτ)=0]

( )0<

∂∆∂

ττω i

( )0>

∂∆∂

ττω i

( ) ( )Ω+=+ m

m

ππτ

22/3



Spectral Results for a short probe pulse

Spectral broadening and down shift of probe pulse

Experiment Theory



with pump

without pump


JILA + Univ. of Michigan Experiments

Pulse shaper: deformable mirror to control the shape of the pump pulse

Goal: Control of the vibrational motion of SF6 and CO2 at room temperature

CPL 344 (2001) 333

Hollow Waveguide

SF6 or CO2


JILA + Univ. of Michigan Experiments: SF6

No unique solution was found for either case

The power spectrum for optimization show a local maximum at 23.25THz

The power spectrum for suppression show a local minimum at 23.25Thz.


JILA + Univ. of Michigan Experiments: CO2

Optimization of νν1=38.6THz(symmetric stretch mode)

Optimization of 2νν2=41.6THz(2 times the OCO bending mode)


MBI: C60?

Idea: To excite C60 using trains of pulses with frequency equal to the vibrational frequencies. (ISRS)


MBI:C60?

10 Raman Active Modes of C60

Ag(1) 496 cm-1 67 fsAg(2) 1470 cm-1 22 fsHg(1) 271 cm-1 123 fsHg(2) 433 cm-1 77 fsHg(3) 710 cm-1 47 fsHg(4) 774 cm-1 43 fsHg(5) 1099 cm-1 30 fsHg(6) 1250 cm-1 27 fsHg(7) 1426 cm-1 24 fsHg(8) 1575 cm-1 21 fs

⇒⇒Suitable for experimentat available laser systems

Ag(1), Hg(1), Hg(2)Hg(3), Hg(4)

For impulsive excitation to occur:

2 )( duration pulse υτ

T<∆Rule of thumb:


MBI:C60?

Experimental Questions:

1.) Coupling to other vibrational modes? (De-phasing) Fragmentation and ionization?

2.) Measurement?

Similar measurements to what is listed seems improbable-high number density needed to see a large effect

Looking at fragmentation pattern could be ambiguous

Current measurements on C60 done at 500 CelsiusCold source?


Conclusions

•Introduced basic theory behind Impulsive Stimulated Raman Scattering

•Initial experimental results shown in gas phase

•introduced questions about future experiment with C60


Classical and Quantum Mechanical Correspondence

νν

ν=0ν=0

Vibrational levels of a harmonic oscillator

Initially : <νν>=0 (Q0=0)

Consider:

δδ-kick

Result: Poissonian distribution:

νν

ν ν

ν −= ep!

pνν

<νν>

<νν> ~ Q02

Q0 is the classical amplitude

<(∆ν∆ν)2> = <νν>

∆ν∆ν

For a Harmonic Oscillator


Definitions

100

00

cos~

sin~

tanQtQ

tQ

D

D

+=

ωω

φ

Definition of φφ

Definition of Gi

( ) cNrG iSRS

ii /)(8 01212 ρωπω=

Impulsive Stimulated Raman Scattering -...

Documents

Transcript of Impulsive Stimulated Raman Scattering -...