u toronto, february 18, 2011darin j. ulness, concordia college 1 noisy light spectroscopy noisy...

U Toronto, February 18, 2011Darin J. Ulness, Concordia College 1Noisy Light Spectroscopy

Noisy LightSpectroscopy:

Putting noise to good use

Darin J. UlnessDepartment of Chemistry

Concordia CollegeMoorhead, MN


OutlineI. IntroductionII.TheoryIII. Experiment

• Coherent Raman Scattering

IV. Connections


SpectroscopyUsing light to gain information about matter

• Lineshape function• Transition frequencies• Cross-sections• Susceptibilities

Information Uses of information• In Chemistry• In Biology• In Engineering


Modern SpectroscopyFrequency Domain• Measure Spectra• Examples• IR, UV-VIS, Raman

• Material response• Spectrally narrow• Temporally slow

Time Domain• Response to light pulse• Examples• PE, transient abs.

• Material response• Spectrally broad• Temporally fast


Modern SpectroscopyFrequency Domain• Measure Spectra• Examples• IR, UV-VIS, Raman

• Material response• Spectrally narrow• Temporally slow

Time Domain• Response to light pulse• Examples• PE, transient abs.

• Material response• Spectrally broad• Temporally fast

Is there another useful technique?Noisy light? YES!


Light

frequency

Spectrum

time

One frequency (or color)

Electromagnetic radiation•Focus on electric field part


Noisy Light: Definition• Broadband• Phase incoherent• Quasi continuous wave

Ele

tric

Fie

ld S

tren

gth

Time

Noi

sy L

ight

Spe

ctru

m

Frequency

Time resolution onthe order of the correlation time, tc


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…


Theory

Optical coherence theory

Perturbation theory: Density operator

Noisy Light Spectroscopy


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.


Bichromophoric Model

a

b

Noisy light

P(t)(3)

P(s)(3)*

< >

Solution•Factorized time correlation (FTC) diagram analysis


FTC Diagram Analysis

Set of intensity level terms

(pre-evaluated)

Set of evaluated intensity level

terms

Messy integration and algebra

Set of FTC diagrams

ConstructionRules

EvaluationRules

Physicshard hard

easy


Example: I(2)CARS

a

b

P(t,{ti})

P(s,{si})

arrow segments: t-dependent correlation

line segments: t-independent

correlation


Experiment•Coherent Raman Scattering: e.g., CARS•Frequency resolved signals•Spectrograms•Molecular liquids


Nonlinear Optics

P= c ESignal

Material

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


CARSCoherent Anti-Stokes Raman Scattering

wR

w1

w1w2

wCARS

w1-w2= wR

wCARS= w1 +wR


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

B’M

I(2)CARS


I(2)CARS: Experiment

Monochromator

NarrowbandSource

BroadbandSource(noisy light)

Lens

Sample

Interferometer

t

B

B’

MI(2)CARS

ComputerCCD


I(2)CARS: SpectrogramMonochromator

NarrowbandSource

BroadbandSource

Lens

Sample

Interferometer

t

B

B’

MI(2)CARS

ComputerCCD

• Signal is dispersed onto the CCD

• Entire Spectrum is taken at each delay

• 2D data set: the Spectrogram


I(2)CARS: Spectrogram

Pixel A

A

Pixel B

B

Pixel C

C

Dark regions: high intensityLight regions: low intensity

Oscillations: downconversion of Raman frequency.Decay: Lineshape function


SpectrogramNo new information can be extracted.

However…

• Huge oversampling gives much enhanced precision.

• Visually appealing presentation of data gives much insight.


I(2)CARS: Data Processing

18000 18100 18200 18300 18400

-2

-1

0

1

2

BenzeneT22

0 200 400 600 800 1000 1200

0

25

50

75

100

125

150

BenzeneT22

100 200 300 400

0.2

0.4

0.6

0.8

Fourier

Transformation

X-Marginal


Virtues of I(2)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.


17300 17400 17500 17600

-400

-200

0

200

400

Pyridine

Pyridine and Water

17300 17400 17500 17600

-400

-200

0

200

400

Pyridine

17300 17400 17500 17600

-400

-200

0

200

400

ave x.45 pyr_water

FT

NeatPyridine

Pyridine/Water Xw= 0.55


Pyridine and Water

-0.2

0

0.2

0.4

0.6

0.8

1

1.2

955 975 995 1015 1035 1055

pure pyr

x=.15

x=0.3

x=0.45

x=0.75

Wavenumber / cm-1


Pyridine and Water

960 970 980 990 1000 1010 1020 1030 1040

0.0

0.2

0.4

0.6

0.8

1.0 Pyridine/water solution: X(py)=0.6

T = -4o

T = 3o

T = 23o

T = 32o

T = 42o

T = 52o

T = 62o

T = 72o

T = 76o

No

rma

lize

d X

-ma

rgin

al

Wavenumber / cm-1


Halogen bondingPyridine and C3F7I

0

0.5

1

1.5

2

2.5

3

3.5

4

900 920 940 960 980 1000 1020 1040 1060 1080 1100

Frequency (cm-1)

Norma

lized In

tensity

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

Neat

C6F13I and Pyridine

0

0.5

1

1.5

2

2.5

3

3.5

4

900 920 940 960 980 1000 1020 1040 1060 1080 1100Frequency (cm-1)

Norma

lized In

tesity

Neat

0.1

0.2

0.3

0.4

0.5

0.6

0.7

.8

0.9


ProspectusSummary:•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.


ProspectusFuture 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.


ConnectionsCoherent Energy Transfer:•Noisy light can produce a nonlinear response.

•Noisy light is “incoherent.” •Amplitude level correlation.


Connections

< >

P(t) P(s)

Stimulus

“ReactionCenter”


AcknowledgementsFormer StudentsTheoryJahan DawlatyDan BiebighauserJohn GregioreDuffy Turner

Other Group MembersDr. Mark Gealy, Department of PhysicsDr. Eric Booth, Post-doctoral researcherDr. Haiyan Fan, Post-doctoral researcher

FundingNSF CAREER Grant CHE-0341087Henry Dreyfus Teacher/Scholar programConcordia Chemistry Research Fund

Method DevelopmentPye Phyo AungTanner SchulzLindsay WeiselKrista CosertPerrie ColeAlex HarshBritt BergerZach JohnsonThao Ta

Hydrogen/Halogen bondingEric BergJeff EliasonDiane MolivaJason OlsonScott FlancherDanny Green

U Toronto, February 18, 2011Darin J. Ulness, Concordia College Noisy Light Spectroscopy

U Toronto, February 18, 2011Darin J. Ulness, Concordia College A1Noisy Light Spectroscopy

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.


Example: I(2)CARS

a

b

P(t,{ti})

P(s,{si})

arrow segments: B, B’ correlation

t-dependentline segments: B, B or B’,B’ correlation

t-independent

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


Example: I(2)CARS

Pixel A

A

Pixel B

B

Pixel C

C

The I(2)CARS data shows • 2:1 dynamics range• t symmetry


0 1 2 3 4 50.00

0.05

0.10

0.15

0.20

0.25

0.30

s g

S/N

(a)

0 1 2 3 4 50.00

0.05

0.10

0.15

0.20

0.25

0s w

D

S/N

(b)


-20 0 20 40 60 800.8

0.9

1.0

1.1

1.2

1.3

1.4

1.5

Fit Results:ratio =0.00783 T + 0.905R = 0.9942

Fre

e p

yr.

to

H-b

ou

nd

pyr

Temperature (Co)

- ∆G° Product Favored

- ∆H° Exothermic

- ∆S° Entropically unfavorable


17300 17400 17500 17600

-400

-200

0

200

400

pyridine with .4g AgNO3

960 970 980 990 1000 1010 1020 1030 1040-0.2

0.0

0.2

0.4

0.6

0.8

1.0Pyridine / AgNO

3

g AgNO3/ml py

0.00 0.061 0.097 0.121 0.170 0.238 0.298 0.341 0.409

No

rma

lize

d X

-ma

rgin

al

Wavenumber / cm-1

0.00 0.05 0.10 0.15 0.20 0.25-0.2

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4 Pyridine/AgNO3

Ratio

27.1 Xeff

2 -.97 X

eff + 0.013

Co

mp

lexe

d p

yri

din

e t

o

Fre

e p

yri

din

ed

Effective mole fraction AgNO3

c(3)complex = Icomplex c(3)

free xfree

Icomplex = Ifree at 0.21 mole fraction

c(3)complex = 1 c(3)

free .79

c(3)complex = 3.76 c(3)

free

u toronto, february 18, 2011darin j. ulness, concordia college 1 noisy light spectroscopy noisy...

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