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Non-linear Raman
Spectroscopy
2013.11.22
Carl-Zeiss Lecture 4
IPHT Jena
Hiro-o HAMAGUCHI
Department of Applied Chemistry and Institute of Molecular
Science, College of Science, National Chiao Tung University,
Taiwan
Vibrational Motions of Ensembles
of Acetone Molecules
What Does Raman look at?
p = aE
Raman Looks at a Normal Mode of Vibration.
What Does CARS/SRS Look at?
CARS/SRS Looks at a Vibrational Coherence
p = cE12E2
2w1-w2, 2k1-k2
w2, k2
w1, k1
c3
2w2-w1, 2k2-k1
w1, k1
w2, k2
Coherent Raman Spectroscopy with Excitation
Angular Frequency w1-w2
CARS Coherent Anti-Stokes Raman Scattering: 2w1-w2, 2k1-k2
SRL Stimulated Raman Loss (Inverse Raman): w1, k1 SRG Stimulated Raman Gain: w2, k2
CSRS Coherent Stokes Raman Scattering: 2w2-w1, 2k2-k1
CARS
SRL
SRG
CSRS
c3
Sample Medium with Third-order Optical Susceptibility
w1-w2
Generation of Coherent Vibrational Excitation with Beat
Angular Frequency w1-w2= W (Raman resonance)
SRG
CARS
w1-w2
Interaction of Coherent Vibrational Excitation
w1-w2 with w1
w1-w2
CSRS
SRL
Interaction of Coherent Vibrational Excitation
w1-w2 with w2
Coherent Raman Spectroscopy
CARS Coherent Anti-Stokes Raman Scattering: 2w1-w2, 2k1-k2
SRL Stimulated Raman Loss (Inverse Raman): w1, k1 SRG Stimulated Raman Gain: w2, k2
CSRS Coherent Stokes Raman Scattering: 2w2-w1, 2k2-k1
CSRS
SRG
SRL
CARS
c3
Raman Spectroscopy
High-resolution Raman (1970-72, Tokyo), UV-VIS resonance Raman (1972-77, Tokyo),
Compact gas Raman (1977-79, Cambridge/Aberystwyth), Matrix isolated Raman (1979-
81, Tokyo), Nanosecond time-resolved Raman (1981-1989, Tokyo; 1990-1995, KAST),
Multichannel cw Raman (1986-90, Tokyo; 1990-95, KAST; 1997-2012, Tokyo),
Picosecond time-resolved Raman (1990-1995, KAST; 2004-2012, Tokyo), NIRRaman
(1984-86, Tokyo; 1992-97, KAST; 1997-2012, Tokyo), Low-frequency Raman (2004-
2012, Tokyo, 2012-,Hsinchu), Raman microspectroscop (2004-2012, Tokyo; 2012-,
Hsinchu)
Non-linear Raman Spectroscopy
Inverse Raman (1983-88, Tokyo), Partially CARS (1990-95, KAST) , Picosecond time-
frequency 2-D CARS (1992-87, KAST; 1997-2012, Tokyo), Polarization-resolved CARS
(1997-2001, Tokyo), Picosecond OKE gated CARS (2002-03, Tokyo), Femtosecond
OKE (2002-, Tokyo), Broadband multiplex CARS microspectroscopy (2002-,2012 Tokyo),
CARS spatial distribution (2004-, 2012, Tokyo), Hyper-Raman microspectroscopy (2005-
12, Tokyo; 2013-, Hsinchu), CARS ROA (2011-2012, Tokyo)
Infrared (IR) spectroscopy
Microsecond Time-resolved IR (1986-90, Tokyo), Nanosecond Time-resolved IR (1990-
97, KAST; 1997-2012, Tokyo; 2007-, Hsinchu), Millisecond multiplex FT-IR (1991-95,
KAST), Infrared electroabsorption (1995-2007, Tokyo; 2007-, Hsinchu), Sub-picosecond
time-resolved IR (2003-212)
Non-linear Raman Spectroscopy at Tokyo and KAST
Inverse Raman (1983-88, Tokyo)
Partially CARS (1990-95, KAST)
Picosecond time-frequency 2-D CARS (1992-87, KAST;
1997-2012, Tokyo)
Polarization-resolved CARS (1997-2001)
Picosecond OKE gated CARS (2002-03, Tokyo)
Femtosecond OKE (2002-, Tokyo)
Broadband multiplex CARS microspectroscopy (2002-2012,
Tokyo)
CARS spatial distribution (2004-, Tokyo)
Hyper-Raman microspectroscopy (2005-2012, Tokyo; 2012-,
Hsinchu)
CARS ROA (2011-2012, Tokyo)
Sample
k1
k2
kCARS
CARS
Energy conservation:
wCARS =2w1-w2=w1+W Momentum conservation:
k = 2k1-k2
w1 w2 w1 wCARS
W
Multiplex CARS Spectroscopy
n=0
n=1
w2 w1 wCARS w1
probed
Multiplex CARS to obtain the whole Raman spectrum
simultaneously
B. N. Toleutaev, T. Tahara and H. Hamaguchi, Appl. Phys. B., 59, 369-375 (1994).
Optical Heterogeneity and CARS Phase Matching
(i) Optically homogeneous system (3) (3)
1 2 1 1 2 1( , , , ; , ) ( , , , )x zc w w w w c w w w w- - = - -
/ 2(3) (3) 2
1 2 1/ 2 0
(3) 2 2
1 2 1
( , , , ) exp sin exp 2 sin ( / 2)
( , , , ) exp sin ( / 2) sinc sin 2 sinc sin ( / 2)
R L
Rdx i x dz i z
RL i L R L
c w w w w
c w w w w
- - -
= - -
E k k
k k k
(ii) Optically heterogeneous system (local structure formation)
(3) 2 2 2 2 2sinc sin 2 sinc sin ( / 2)R LI R L k k
Local structure
(3) (3)
1 2 1domain
exp( ) ( , , , ; )exp( )jj
j
i d i c w w w w - - E r r k r
j
Siganal waves coherently added only within local structure
Phase matching condition is relaxed by extra phase
factor exp(ij)
js 2 2
2
(3) sinc sin 2 sinc exp( ) sin ( / 2)j j jj
j
s s siI k k
・・Ordinary CARS
Polarization rule: tanfR=rtan r; Raman depolarization ratio)
Sample
k1
k2
kCARS
Polarization-resolved CARS Spectroscopy
w1 0o
w2 =60o
wCARS fR Analyzer fa
Energy conservation:
wCARS =2w1-w2=w1+W Momentum conservation:
k = 2k1-k2
w1 w2 w1 wCARS
W
p: r<0.75
Totally symmetric mode
dp: r=0.75
Non-totally symmetric mode
Polarization-resolved CARS Spectroscopic System
=60o
Variable fa
Polarization-resolved CARS Spectra of Liquid Cyclohexane 2
R21
R
G)ww(w
G
---=
R R
RNR
i
HACARSI
CH2 twisting (eg) 1267 cm-1 0.749±0.002
CH2 scissors (eg) 1445 cm-1 0.750±0.002
Depolarization Ratios of Two eg Bands of Cyclohexane
Polarization-resolved CARS Spectra of 1,2-Dichloroethane
T. Shimanouchi, Tables of Molecular Vibrational Frequencies, NSRDS-NBS 39, p.
97.
Depolarized Totally-symmetric Raman Band?
dp → p
Raman optical activity (ROA)
Chiral sensitive vibrational spectroscopy for
absolute configuration determination
Coherent anti-Stokes Raman scattering (CARS)
CARS-ROA
Polarization-resolved heterodyne-detected CARS
Polarization-resolved heterodyne-detected CARS System
28
Polarization-resolved CARS Spectra of (−)-b-pinene
29 Ultimate Spectroscopy and Imaging
Laboratory
CARS-ROA spectrum of (−)-b-pinene
Contrast ratio (chiral signal/ achiral background)
1/10
1/1000
First observation of ROA with CARS using pulsed lasers!
K. Hiramatsu, M. Okuno, H. Kano, P. Leproux, V. Couderc, and H. Hamaguchi, Phys. Rev. Lett. 109, 083901
(2012).
Partially Coherent Anti-Stokes Raman
Scattering (PCARS)
w1
w2
Enhanced anti-Stokes Raman
scattering = PCARS
Sample
T. Ishibashi and H. Hamaguchi, CPL 175, 543 (1990); JCP 106, 11 (1997).
The concentration dependence
of PCARS intensity suggests
microscopic optical inhomogeneity
in the solutions.
CARS
Sample
k1
k2
k = 2k1-k2
k
(Phase matching)
A New Non-linear Raman Probe of Liquid Structure:
Spatial Distribution of CARS Intensity
Spatial Distribution of CARS Signal and
Local Structures in Liquids and Solutions (i) Optically homogeneous system
(3) (3)
1 2 1 1 2 1( , , , ; , ) ( , , , )x zc w w w w c w w w w- - = - -
/ 2(3) (3) 2
1 2 1/ 2 0
(3) 2 2
1 2 1
( , , , ) exp sin exp 2 sin ( / 2)
( , , , ) exp sin ( / 2) sinc sin 2 sinc sin ( / 2)
R L
Rdx i x dz i z
RL i L R L
c w w w w
c w w w w
- - -
= - -
E k k
k k k
(ii) Optically heterogeneous system (local structure formation)
(3) 2 2 2 2 2sinc sin 2 sinc sin ( / 2)R LI R L k k
Local structure
(3) (3)
1 2 1domain
exp( ) ( , , , ; )exp( )jj
j
i d i c w w w w - - E r r k r
j
Siganal waves coherently added only within local structure
Phase matching condition is relaxed by extra phase
factor exp(ij)
js 2 2
2
(3) sinc sin 2 sinc exp( ) sin ( / 2)j j jj
j
s s siI k k
・・Ordinary CARS
0.35 mm
0.10 mm
Polystyrene Beads Dispersed in Water
Polystyrene Beads Dispersed in Water: Nuemrical
Simulation
Relative phase Radius of a sphere
Normalized at = 0° Not normalized
40% Aqueous Solution of Ethanol
Neat ethanol
Ethanol/H2O (soon after mixing)
Ethanol/H2O (after two weeks)
Raman Spectra of 40% Aqueous Solution of Ethanol
40% Aqueous Solution of Ethanol
Neat ethanol
Ethanol/H2O (soon after mixing)
Ethanol/H2O (after two weeks)
Cnmim[PF6] (n=4,6,8)
n = 4 n = 8
Larger local structures due to stronger
Interactions with longer chains?
cf. viscosity @ 20℃
C4mim[PF6]: 371 cP,
C6mim[PF6]: 680 cP,
C8mim[PF6]: 866 cP
* J. G. Huddleston, A. E. Visser, W. M. Reichert, H. D. Willauer, G. A. Broker, and R. D. Rogers, Green Chem. 3, 156 (2001).
Change of distribution pattern
with chain length
Existence of local structures in Cnmim[PF6]
2011.11.29
ASC2011
Xiamen, China
Super Vibrational Spectroscopy with
Hyper-Raman Scattering
Hiro-o Hamaguchi
Nano vibrational spectroscopy with the molecular near-field effect
Super-resolution Raman/Hyper Raman Microscopy
Intermolecular Fano Resonance
Are there still new possibilities of
vibrational spectroscopy?
超 SUPER, ULTRA, HYPER
超 SUPER, ULTRA, HYPER
Superman
超 SUPER, ULTRA, HYPER
Superman Ultraman
超
SUPER, ULTRA, HYPER
Superman Ultraman Hyperman
?
SUPER, ULTRA, HYPER
Superman Ultraman Hyper-
Raman
超
Raman Scattering and Hyper-Raman Scattering
Raman Hyper-Raman
w0- w
2w0- w
w0 w0
w0
Selection Rules in Vibratioal Spectroscopies
– IR and Raman inactive modes can be HR active.
– The ‘Mutual exclusion rule’ holds for centrosymmetric spiecies.
– IR active modes are always HR active.
IR
Raman
HR
x,y,z
xx,xy,xz,...,zz
xxx,xxy,xyz,...,zzz
ΓHR = ΓIR ⊗ ΓRaman
12
8
4
0
Inte
nsity / a
.u.
3000 2500 2000 1500 1000 500 0
Wavenumber / cm-1
3.0
2.0
1.0Ab
so
rptio
n
16
12
8
4
0
Inte
nsity / a
.u.
Complete Vibrational Spectra of Benzene
IR
HR
Raman
Experimental Setup
Sample
Camera lens
Short pass
filter
Telescope (1.5x)
laser
Ti:sapphire
oscillator
Wavelength: 800 nm
Pulse width: 3–4 ps
Rep. rate: 82 MHz
Power: 300-500 mW
R. Shimada
Resonance HR Spectrum of b-carotene in
Cyclohexane
Concentration: 1mM
Excitation: 450 mW @ 800 nm Exposure: 1 min.
Resonance Hyper-Raman, Infrared and Resonance Raman Spectra of Crystalline All-trans-b-carotene
Mechanism of Resonance Hyper-Raman
Scattering and Molecular Symmetry
(B term)
Qcar
0
m
e
s
HR process
1Bu
2Ag or 3Ag
Centrosymmetric
Y. C. Chung, L. D. Ziegler, J. Chem. Phys. 88, 7287 (1988) .
M. Mizuno, H. Hamaguchi, T. Tahara, J. Phys. Chem. A 106, 3599 (2002) .
Qcar
0
m
e
HR process
Ground
state
Non-
centrosymmetric
(A term)
s
1564 cm-1 1944 cm-1
5 mm
Wavenumber /cm-1
Microscopic image
Spectrum
Hyper-Raman images
Hyper-Raman Imaging with an Infrared-active Mode
Inte
nsity
“Infrared” imaging with much
higher spatial resolution
2012.08.29
EUCMOS2012
Cluj, Romania
New Possibilities of Vibrational Spectroscopy
with Hyper-Raman Scattering
Hiro-o Hamaguchi
National Chiao Tung University, Taiwan/University of Tokyo, Japan
Nano vibrational spectroscopy with the molecular near-field effect
Super-resolution Raman/Hyper-Raman Microscopy
Intermolecular Fano Resonance
1.5x103
1.0
0.5
Inte
nsity
3000 2500 2000 1500 1000 500
Wavenumber / cm-1
2.0x103
1.5
1.0
0.5
Inte
nsity
3x103
2
1Inte
nsity
1.5x103
1.0
0.5Inte
nsity
2.5x103
2.0
1.51.0
0.5
Inte
nsity
Hyper-Raman Spectra of All-trans b-carotene in
Solutions
Benzene
CS2
Crystal
Cyclohexane
CCl4
15
64
1370
1
32
2
Cyclohexane Solution
b-carotene/
cyclohexane
HR
IR
Cyclohexane
HR
CCl4 Solution
b-carotene/CCl4
CCl4
HR
IR HR
CS2 and Benzene Solutions
HR
IR
HR
IR
b-carotene/
CS2
CS2 Benzene
b-carotene/
benzene
Theory of Hyper-Raman Intensities
Mλ,μ,ν : elements of dipole moment operator
εn : energy of state n
ω0 : frequency of the incident light
D. A. Long, and L. Stanton, Proc. R. Soc. London, Ser. A 318, 441 (1970).
Y. C. Chung, and L. D. Ziegler, J. Chem. Phys. 88, 7287 (1988).
Under a two-photon resonant condition,
| ] : electronic state
| ) : vibrational state
Gni : damping constant
Under a Born-Oppenheimer approximation,
Theory of Hyper-Raman Intensities
Using the Herzberg-Teller expansion to electronic states,
The molecular Hamiltonian is divided into three parts;
Electronic Vibrational Vibronic interaction
PERTURBATION
Theory of Hyper-Raman Intensities
Intramolecular
Intermolecular
Theory of Hyper-Raman Intensities
Theory of Hyper-Raman Intensities
A~ B1~ B2~
One photon transition
Two photon transition
Vibronic coupling
Theory of Hyper-Raman Intensities
Intramolecular
Intermolecular
Theory of Hyper-Raman Intensities
How Solvent Vibrations Take Part in Resonance
Hyper-Raman Scattering of Solute
Qcar
0
m
e
s
Solute
1Bu
1Ag
2Ag or 3Ag
Qsolvent
0
Solvent
e
s
Solute molecule
Solvent molecule
B1 term B1’ term
HR intensity enhancement by intermolecular vibronic coupling
The Molecular Near-field Effect
R. Shimada, H. Kano, H. Hamaguchi, J. Raman Spectrosc. 37, 469 (2006).
R. Shimada, H. Kano, H. Hamaguchi, J. Chem. Phys., 129, 024505 (2008).
Detection of Ensembles of Single Molecules!
Detection of Ensembles of Single Molecules!
Detection of Ensembles of Single Molecules!
Detection of Ensembles of Single Molecules!
Resonance HR Spectra of ß-carotene in
Benzene
Benzene
All-trans-ß-carotene in
Benzene-d6
Benzene
Benzene-d6
Resonance HR Spectra of ß-carotene in
Cyclohexane
Cyclohexane
All-trans-ß-carotene in
Cyclohexane-d12
Cyclohexan
e
Cyclohexane-
d12
Cyclohexane
solution
Observed Selection Rule
a2u
e1u e1u
e1u
a2u
e2g
e2g e2g
e2g e1g e2g
a1g
e1g
e2u
e2g
eu
a2u
eu
eu eu
eu eu eu
eu a2u
eg
eg eg
eg
a1g eg
eg eg
a1g
Benzene
solution
a1g
?
Benzene
Benzene-d6
Cyclohexan
e
Cyclohexane-d12
R. Shimada
Observed Selection Rule
Enhanced:
IR active modes
Raman active (non-totally symmetric) modes
Not enhanced:
Raman active (totally symmetric?) modes
IR inactive but HR active modes
Theory of Hyper-Raman Intensities
B
(Solvent)
R
A
(Solute)
R. Shimada, H. Hamaguchi, J. Chem. Phys. 134,
034516 (2011).
Dipole–Dipole
Dipole-Quadrupole
Selection rule
Theory of Hyper-Raman Intensities
Dipole–quadrupole interaction
Dipole–dipole interaction
R. Shimada, H. Hamaguchi, J. Chem. Phys. 134,
034516 (2011).
IR active modes!!
Raman active
modes!!
≈
Quadrupole: TRACELESS No or weak enhancements
for totally symmetric modes
Theory of Hyper-Raman Intensities
Dipole–quadrupole interaction
Dipole–dipole interaction Quantum chemical calculation
Geometric factors
-2 +1 0 +3 -3/2
Dipole–quadrupole
Dipole–dipole
R
x
y
z x
y
z
Calculation of Hyper-Raman Intensities
Calculated Orientation Dependent Spectra
x
y
z
x
y
z
x y
z
x y
z
x y
z
Δ Inte
nsity
Inte
nsity
In
tensity
In
tensity
In
tensity
In
tensity
|Dipole derivative|2
|Quadrupole derivative|2
Difference Spectrum (obs.)
Difference Spectrum: Benzene-h6/-d6
|Dipole derivative|2
|Quadrupole derivative|2
Observed
Calculated
(Random orientation)
band width:20 cm-1 Distance: 8 Å
Difference Spectrum: Cyclohexane-h12/-d12
|Dipole derivative|2
|Quadrupole derivative|2
Observed
Calculated
(Random orientation)
band width:20 cm-1 Distance: 8 Å
Solute molecule
Solvent molecule
Dipole-dipole, Dipole-quadrupole interaction
Geometric information (orientation, distance) of
proximate molecules can be obtained
The Hyper-Raman Molecular Near-field Effect
Structure determination in solutions!
Structure determination in biological
systems!
Simultaneous Observation of Raman and Hyper-
Raman Scattering
Theoretical Bckground of Super-resolution
Raman/HR Apparatus
Constructed at Tokyo
K. Matsuzaki
Raman imageRaman imageRaman imageRaman imageRaman image
Raman : < 635 nm
Hype r-Raman : < 419 nm
Supe r-resolution : < 176 nm !
Simultaneous Mapping of TiO2 Nanostructure with
Raman and Hyper-Raman Scattering Raman Hyper-Raman
Raman/Hyper-
Raman SEM
Laser field
Raman imageRaman imageRaman imageRaman imageRaman image
Raman : < 635 nm
Hype r-Raman : < 419 nm
Supe r-resolution : < 176 nm !
Raman: 620 nm
HR: 390 nm
R/HR: 160 nm
Simultaneous Mapping of TiO2 Nanostructure with
Raman and Hyper-Raman Scattering
Raman imageRaman imageRaman imageRaman imageRaman image
Raman : < 635 nm
Hype r-Raman : < 419 nm
Supe r-resolution : < 176 nm !
Super-resolution Achieved !
Raman: 620 nm
HR: 390 nm
R/HR: 160 nm
Fano Resonance: Quantum-mechanical Interference of a
Discrete Level with a Continuum
q: Fano parameter
Raman and Hyper-Raman Spectra of TiO2
Nanoparticles (Anatase, 100-300 nm)
IR spectra:
B. C. Trasferetti, C. U. Davanzo, and R. A. Zoppi, Electrochem. Commun., 4, 301-304 (2002).
E. Hendry, F. Wang, J. Shan, T. F. Heinz, and M. Bonn, Phys. Rev. B, 69 (8), 081101 (2004).
D. Wang , X. Zhang, K. Wu, and S. Xu, Chem. Lett., 35 (8), 884-885 (2006).
LO phonon combination
band coupled to electronic
state
Intermolecular Fano Resonance: Hyper-Raman Spectrum of TiO2 Nanoparticle (100~300 nm) Dispersed in Benzene
Intermolecular Fano Resonance: Benzene and
Deuteriated Benzene on TiO2 Nanoparticle
C6H6
C6D6
Organic Molecules on TiO2 Nanoparticle
1000 800 600
Hyper-Raman Shift / cm-1
benzene
Dichloro-
methane
chlorofom
carbon
tetrachloride
Coherent interaction of adsorbed molecules with TiO2
Selective detection of adsorbed molecules on TiO2