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
Mark Boyle Wednesday, February 27, 2002 3
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???
Mark Boyle Wednesday, February 27, 2002 4
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
Mark Boyle Wednesday, February 27, 2002 5
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
Mark Boyle Wednesday, February 27, 2002 6
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.
Mark Boyle Wednesday, February 27, 2002 7
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
Mark Boyle Wednesday, February 27, 2002 8
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)
Mark Boyle Wednesday, February 27, 2002 9
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
Mark Boyle Wednesday, February 27, 2002 10
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
Mark Boyle Wednesday, February 27, 2002 11
Scattering of a “probe” pulse
( ) ( )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
~
Mark Boyle Wednesday, February 27, 2002 12
Scattering of a “probe” pulse
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
Mark Boyle Wednesday, February 27, 2002 13
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)
Mark Boyle Wednesday, February 27, 2002 14
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.
Mark Boyle Wednesday, February 27, 2002 15
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
Mark Boyle Wednesday, February 27, 2002 16
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).
Mark Boyle Wednesday, February 27, 2002 17
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
Mark Boyle Wednesday, February 27, 2002 18
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)
Mark Boyle Wednesday, February 27, 2002 19
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
Mark Boyle Wednesday, February 27, 2002 20
MBI Experiments : SF6
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
Mark Boyle Wednesday, February 27, 2002 21
MBI Experiments : SF6
Spectral Results for a short probe pulse
Spectral broadening and down shift of probe pulse
Experiment Theory
Mark Boyle Wednesday, February 27, 2002 23
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
Mark Boyle Wednesday, February 27, 2002 24
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.
Mark Boyle Wednesday, February 27, 2002 25
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)
Mark Boyle Wednesday, February 27, 2002 26
MBI: C60?
Idea: To excite C60 using trains of pulses with frequency equal to the vibrational frequencies. (ISRS)
Mark Boyle Wednesday, February 27, 2002 27
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:
Mark Boyle Wednesday, February 27, 2002 28
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?
Mark Boyle Wednesday, February 27, 2002 29
Conclusions
•Introduced basic theory behind Impulsive Stimulated Raman Scattering
•Initial experimental results shown in gas phase
•introduced questions about future experiment with C60
Mark Boyle Wednesday, February 27, 2002 30
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