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Darin J. Ulness, Concordia College
Noisy Light Spectroscopy
U Toronto, February 18, 2011
Noisy Light
Spectroscopy:
Putting noise to good use
Darin J. Ulness
Department of Chemistry
Concordia College
Moorhead, MN
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Darin J. Ulness, Concordia College
Noisy Light Spectroscopy
U Toronto, February 18, 2011
Outline
I. Introduction
II.Theory
III. Experiment
• Coherent Raman Scattering
IV. Connections
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Darin J. Ulness, Concordia College
Noisy Light Spectroscopy
U Toronto, February 18, 2011
Spectroscopy
Using light to gain information
about matter
Information
•Lineshape function
•Transition frequencies
•Cross-sections
•Susceptibilities
Uses of information
•In Chemistry
•In Biology
•In Engineering
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Darin J. Ulness, Concordia College
Noisy Light Spectroscopy
U Toronto, February 18, 2011
Modern Spectroscopy
Frequency Domain Time Domain
•Measure Spectra
•Examples
•IR, UV-VIS, Raman
•Material response
•Spectrally narrow
•Temporally slow
•Response to light pulse
•Examples
•PE, transient abs.
•Material response
•Spectrally broad
•Temporally fast
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Darin J. Ulness, Concordia College
Noisy Light Spectroscopy
U Toronto, February 18, 2011
Modern Spectroscopy
Frequency Domain Time Domain
•Measure Spectra
•Examples
•IR, UV-VIS, Raman
•Material response
•Spectrally narrow
•Temporally slow
•Response to light pulse
•Examples
•PE, transient abs.
•Material response
•Spectrally broad
•Temporally fast
4
Darin J. Ulness, Concordia College
Noisy Light Spectroscopy
U Toronto, February 18, 2011
Modern Spectroscopy
Frequency Domain Time Domain
•Measure Spectra
•Examples
•IR, UV-VIS, Raman
•Material response
•Spectrally narrow
•Temporally slow
•Response to light pulse
•Examples
•PE, transient abs.
•Material response
•Spectrally broad
•Temporally fast
Is there another useful technique?
Noisy light? YES!
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Darin J. Ulness, Concordia College
Noisy Light Spectroscopy
U Toronto, February 18, 2011
Light
Electromagnetic radiation
•Focus on electric field part
Spectrum
One frequency (or color)
frequency
time
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Darin J. Ulness, Concordia College
Noisy Light Spectroscopy
U Toronto, February 18, 2011
Noisy Light: Definition
Time resolution on
the order of the
correlation time, tc
E letric F ield S trength
Noisy Light Spectrum
•Broadband
•Phase incoherent
•Quasi continuous wave
Frequency
T im e
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Darin J. Ulness, Concordia College
Noisy Light Spectroscopy
U Toronto, February 18, 2011
Noisy Light: Alternative
•Its cw nature allows precise measurement
of transition frequencies.
•Its ultrashort noise correlation time offers
femtosecond scale time resolution.
•It offers a different way to study the
lineshaping function.
•It is particularly useful for coherent
Raman scattering.
•Other spectroscopies: photon echo, OKE,
FROG, polarization beats…
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Darin J. Ulness, Concordia College
Noisy Light Spectroscopy
U Toronto, February 18, 2011
Theory
Noisy Light Spectroscopy
Optical
coherence
theory
Perturbation
theory:
Density
operator
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Darin J. Ulness, Concordia College
Noisy Light Spectroscopy
U Toronto, February 18, 2011
Theoretical Challenges
•Complicated Mathematics
•Complicated Physical Interpretation
Difficulty
•The cw nature requires all field action
permutations. The light is always on.
•The proper treatment of the noise
cross-correlates chromophores.
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Darin J. Ulness, Concordia College
Noisy Light Spectroscopy
U Toronto, February 18, 2011
Bichromophoric Model
a
Noisy
light
(3)
P(t)
(3)*
b
P(s)
Solution
•Factorized time correlation (FTC)
diagram analysis
<>
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Darin J. Ulness, Concordia College
Noisy Light Spectroscopy
U Toronto, February 18, 2011
FTC Diagram Analysis
Messy integration and algebra
Set of intensity
level terms
(pre-evaluated)
Construction
Rules
Set of FTC
diagrams
Evaluation
Rules
Set of evaluated
intensity level
terms
easy
hard
hard
Physics
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Darin J. Ulness, Concordia College
Noisy Light Spectroscopy
Example:
a
b
U Toronto, February 18, 2011
(2)
I CARS
P(t,{ti})
arrow segments: t-dependent
correlation
line segments:
P(s,{si})
t-independent
correlation
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Darin J. Ulness, Concordia College
Noisy Light Spectroscopy
U Toronto, February 18, 2011
Experiment
•Coherent Raman Scattering: e.g., CARS
•Frequency resolved signals
•Spectrograms
•Molecular liquids
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Darin J. Ulness, Concordia College
Noisy Light Spectroscopy
U Toronto, February 18, 2011
Nonlinear Optics
Material
Signal
P= c E
Light field
Perturbation series approximation
P(t) = P(1) + P(2) + P(3) …
P(1) = c (1)E,
P(2) = c (2)EE,
P(3) = c (3)EEE
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Darin J. Ulness, Concordia College
Noisy Light Spectroscopy
U Toronto, February 18, 2011
CARS
Coherent Anti-Stokes Raman Scattering
w1
wR
w2
w1
wCARS
w1-w2= wR
wCARS= w1 +wR
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Darin J. Ulness, Concordia College
Noisy Light Spectroscopy
U Toronto, February 18, 2011
CARS with Noisy Light
•I(2)CARS
•We need twin noisy beams B and B’.
•We also need a narrowband beam, M.
•The frequency of B (B’) and M differ by
roughly the Raman frequency of the sample.
•The I(2)CARS signal has a frequency that is
anti-Stokes shifted from that of the noisy
beams.
B
M
B’
I(2)CARS
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Darin J. Ulness, Concordia College
Noisy Light Spectroscopy
(2)
I CARS:
U Toronto, February 18, 2011
Experiment
Computer
CCD
Interferometer
Monochromator
B’
Sample
t
B
I(2)CARS
M
Lens
Narrowband
Source
Broadband
Source
(noisy light)
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Darin J. Ulness, Concordia College
Noisy Light Spectroscopy
(2)
I CARS:
Spectrogram
Computer
CCD
Interferometer
Monochromator
B’
Sample
t
B
I(2)CARS
M
Lens
Narrowband
Source
U Toronto, February 18, 2011
Broadband
Source
•Signal is dispersed onto the
CCD
•Entire Spectrum is taken at
each delay
•2D data set: the Spectrogram
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Darin J. Ulness, Concordia College
Noisy Light Spectroscopy
(2)
I CARS:
U Toronto, February 18, 2011
Spectrogram
A
Pixel A
Pixel
B
B
C
Pixel C
Dark regions: high intensity
Light regions: low intensity
Oscillations: downconversion
of Raman frequency.
Decay: Lineshape function
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Darin J. Ulness, Concordia College
Noisy Light Spectroscopy
U Toronto, February 18, 2011
Spectrogram
No new information can
be extracted.
However…
•Huge oversampling gives much
enhanced precision.
•Visually appealing presentation of
data gives much insight.
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Darin J. Ulness, Concordia College
Noisy Light Spectroscopy
(2)
I CARS:
U Toronto, February 18, 2011
Data Processing
BenzeneT22
BenzeneT22
150
2
125
1
Fourier
0
100
75
-1
Transformation
-2
50
25
18000
18100
18200
18300
18400
0
0
100
200
300
200
400
600
800
400
0.8
0.6
0.4
0.2
X-Marginal
1000
1200
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Darin J. Ulness, Concordia College
Noisy Light Spectroscopy
Virtues of
U Toronto, February 18, 2011
(2)
I CARS
•Less expensive.
•Easier experiment to perform.
•Signals are more robust.
•Immune to dispersion effects.
•Exquisitely sensitive to relative changes in
the vibrational frequency and dephasing
rate constant.
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Darin J. Ulness, Concordia College
Noisy Light Spectroscopy
U Toronto, February 18, 2011
Pyridine and Water
Pyridine
Pyridine
Neat
Pyridine
400
400
200
200
0
0
FT
-200
-200
-400
-400
17300
17400
17500
17600
17300
ave x .45 pyr_water
400
Pyridine/
Water
Xw= 0.55
200
0
-200
-400
17300
17400
17500
17600
17400
17500
17600
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Darin J. Ulness, Concordia College
Noisy Light Spectroscopy
U Toronto, February 18, 2011
Pyridine and Water
1.2
1
0.8
pure pyr
0.6
x=.15
x=0.3
0.4
x=0.45
x=0.75
0.2
0
955
-0.2
975
995
1015
Wavenumber / cm-1
1035
1055
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Darin J. Ulness, Concordia College
Noisy Light Spectroscopy
U Toronto, February 18, 2011
Pyridine and Water
1 .0
P y rid in e /w a te r s o lu tio n : X (p y )= 0 .6
0 .8
N orm alized X -m arginal
T = -4
T = 3
o
o
T = 23
0 .6
T = 32
T = 42
T = 52
0 .4
T = 62
T = 72
T = 76
o
o
o
o
o
o
o
0 .2
0 .0
960
970
980
990
1000
1010
W avenum ber / cm
-1
1020
1030
1040
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Darin J. Ulness, Concordia College
Noisy Light Spectroscopy
26
U Toronto, February 18, 2011
Halogen bonding
3.5
0.2
3
0.3
3
0.4
2.5
0.5
2
2.5
2
1.5
0.6
1
0.7
C6F13I and Pyridine
4
0.1
3.5
Neat
Normalized Intesity
Normalized Intensity
Pyridine and C3F7I
4
0.1
0.2
0.3
0.4
0.5
1.5
0.6
0.7
1
.8
0.9
0.5
0.8
0
900
920
940
960
980
1000
1020
Frequency (cm-1)
1040
1060
1080
1100
0.9
Neat
0.5
0
900
920
940
960
980
1000
1020
Frequency (cm-1)
1040
1060
1080
1100
Darin J. Ulness, Concordia College
Noisy Light Spectroscopy
U Toronto, February 18, 2011
Prospectus
Summary:
•Noisy light provides an alternative
method for probing ultrafast dynamics of
the condensed phase.
•Experimentally it is relatively easy.
•Theoretically it is relatively hard.
•FTC diagram analysis helps with
theoretical understanding.
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Darin J. Ulness, Concordia College
Noisy Light Spectroscopy
U Toronto, February 18, 2011
Prospectus
Future of noisy light at Concordia:
•I(2)CARS is an exquisitely sensitive
probe of vibrational frequency shifts
•A principle goal is to explore halogen
bonding. I(2)CARS is one tool available
to us.
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Darin J. Ulness, Concordia College
Noisy Light Spectroscopy
U Toronto, February 18, 2011
Connections
Coherent Energy Transfer:
•Noisy light can produce a nonlinear
response.
•Noisy light is “incoherent.”
•Amplitude level correlation.
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Darin J. Ulness, Concordia College
Noisy Light Spectroscopy
U Toronto, February 18, 2011
Connections
Stimulus
P(s)
P(t)
“Reaction
Center”
<>
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Darin J. Ulness, Concordia College
Noisy Light Spectroscopy
U Toronto, February 18, 2011
Acknowledgements
Former Students
Theory
Jahan Dawlaty
Dan Biebighauser
John Gregiore
Duffy Turner
Method Development
Pye Phyo Aung
Tanner Schulz
Lindsay Weisel
Krista Cosert
Perrie Cole
Alex Harsh
Britt Berger
Zach Johnson
Thao Ta
Hydrogen/Halogen bonding
Eric Berg
Jeff Eliason
Diane Moliva
Jason Olson
Scott Flancher
Danny Green
Other Group Members
Funding
NSF CAREER Grant CHE-0341087
Henry Dreyfus Teacher/Scholar program
Concordia Chemistry Research Fund
Dr. Mark Gealy, Department of Physics
Dr. Eric Booth, Post-doctoral researcher
Dr. Haiyan Fan, Post-doctoral researcher
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Darin J. Ulness, Concordia College
Noisy Light Spectroscopy
U Toronto, February 18, 2011
Darin J. Ulness, Concordia College
Noisy Light Spectroscopy
U Toronto, February 18, 2011
Utility of FTC Diagrams
•Organize lengthy calculations
•Error checking
•Identification of important terms
•Immediate information of about features
of spectrograms
•Much physical insight that transcends
the choice of mathematical model.
A1
Darin J. Ulness, Concordia College
Noisy Light Spectroscopy
Example:
U Toronto, February 18, 2011
(2)
I CARS
FTC analysis
•Each diagram with arrows
has a topologically
equivalent partner diagram
containing only lines: 2:1
dynamic range
•Each diagram with arrows
has a topologically
equivalent partner diagram
that has arrows pointing in
the opposite direction: signal
must be symmetric in t
a
P(t,{ti})
b
P(s,{si})
arrow segments: B, B’ correlation
t-dependent
line segments: B, B or B’,B’ correlation
t-independent
A2
Darin J. Ulness, Concordia College
Noisy Light Spectroscopy
Example:
U Toronto, February 18, 2011
(2)
I CARS
A
Pixel A
Pixel
B
B
C
Pixel C
The I(2)CARS data shows
• 2:1 dynamics range
• t symmetry
A3
Darin J. Ulness, Concordia College
(a)
Noisy Light Spectroscopy
U Toronto, February 18, 2011
0.30
0.25
sg
0.20
0.15
0.10
0.05
(b)
0.25
0.00
0
0.20
1
2
3
S/N
sw
0
D
0.15
0.10
0.05
0.00
0
1
2
3
S/N
4
5
4
5
A4
Darin J. Ulness, Concordia College
Noisy Light Spectroscopy
U Toronto, February 18, 2011
A5
Darin J. Ulness, Concordia College
Noisy Light Spectroscopy
U Toronto, February 18, 2011
A6
Darin J. Ulness, Concordia College
Noisy Light Spectroscopy
U Toronto, February 18, 2011
1 .5
F it R e s u lts :
Free pyr. to H -bound pyr
1 .4
ra tio = 0 .0 0 7 8 3 T + 0 .9 0 5
R = 0 .9 9 4 2
1 .3
1 .2
1 .1
1 .0
0 .9
0 .8
-2 0
0
20
40
60
o
T e m p e ra tu re (C )
- ∆G° Product Favored
- ∆H° Exothermic
- ∆S° Entropically unfavorable
80
A7
Darin J. Ulness, Concordia College
pyridine
Noisy Light Spectroscopy
A8
U Toronto, February 18, 2011
with .4g AgNO3
1 .0
P y rid in e / A g N O 3
400
g A g N O 3 /m l p y
0 .0 0
0 .8
N o rm a lize d X -m a rg in a l
0 .0 6 1
200
0
-200
-400
0 .0 9 7
0 .1 2 1
0 .6
0 .1 7 0
0 .2 3 8
0 .2 9 8
0 .3 4 1
0 .4
0 .4 0 9
0 .2
0 .0
17300
17400
17500
-0 .2
17600
960
970
980
990
1000
1010
W avenum ber / cm
1 .4
P y rid in e /A g N O 3
R a tio
Free pyridined
C om plexed pyridine to
2 7 .1 X e ff
0 .8
2
1030
1040
-1
c(3)complex = Icomplex c(3)free xfree
Icomplex = Ifree at 0.21 mole fraction
c(3)complex = 1 c(3)free .79
1 .2
1 .0
1020
-.9 7 X e ff + 0 .0 1 3
c(3)complex = 3.76 c(3)free
0 .6
0 .4
0 .2
0 .0
-0 .2
0 .0 0
0 .0 5
0 .1 0
0 .1 5
0 .2 0
E ffe c tiv e m o le fra c tio n A g N O 3
0 .2 5

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