Spectroscopic Line Shapes Of Spectroscopic Line Shapes Of Broad Band Sum Frequency Broad Band Sum Frequency GenerationGeneration

Himali JayathilakeIgor Stiopkin, Champika Weeraman, Achani Yatawara and

Alexander BenderskiiDepartment of Chemistry, Wayne State University

Detroit, MI

Interfacial StudiesInterfacial Studies

• Biological ProcessesBiological Processes• Molecular ElectronicsMolecular Electronics• NanotechnologyNanotechnology

Molecular OrganizationMolecular Organizationat the Surfaceat the Surface

FunctionFunction

Surface SelectiveSurface SelectiveSpectroscopySpectroscopy

Nature

Living Organisms(Cell membrane)

Industry(LCD Displays)

OutlineOutline Spectroscopic Spectroscopic Line ShapesLine Shapes1.1. AmplitudeAmplitude2. Line Width2. Line Width3. Transition frequency3. Transition frequency

Information extracted from Line shapes1. Molecular organization

i. Orientationii. Conformational orderiii. Packing

2. Molecular Dynamics

Frequency A

mpl

itud

e

Spectroscopic Signal

(0) (1) (2) (3)

(0) (1) (2) (3)

( ) ...

: : ...

P t P P P P

P E EE EEE

PolarizationPolarization

1( )E 2( )E

outE

( )P t

Second Order Non-linear Susceptibility

Surface-Selective Non-Linear OpticalSurface-Selective Non-Linear OpticalSpectroscopySpectroscopy

)()( 21)2()2(

EEP

0)2(

0)2(

Surface selectivity: (2) = 0 in isotropic media (bulk)

Vibrational Sum Frequency Generation (SFG)Vibrational Sum Frequency Generation (SFG)Broad-Band Vibrational SFGBroad-Band Vibrational SFG

(Broad-band IR pulse + Spectrally narrow (Broad-band IR pulse + Spectrally narrow visvis pulse) pulse)

|v=0

|v=1

visvis

vis

IRIR

IR

SFG= IR+ vis

SFGSFG

vis

IR

(2)

2(2)

(2)( ) ( ) (

) ( )

( ) )

(

SFG IR IR vis vis IR

SFG SFG S

I

G

R

F

P E E d

I P

SFGSFG

van der Ham, Vrehen, Eliel Opt. Lett. 21, 1448 (1996) Richter; Petralli-Mallow; Stephenson, Opt. Lett. 23, 1594 (1998)

Experimental Set-upExperimental Set-up

PumpPumpLasersLasers

AmplifierAmplifier OPAOPA

OscillatorOscillator

11 22

SFGSFG

MonochromatorMonochromator

CCDCCD

IR

visSampleSample

SFG SpectrumSFG Spectrum

IR output: 3-8 IR output: 3-8 m 65-75 fs m 65-75 fs 300 cm300 cm-1-1 bandwidth bandwidth1-2 1-2 J/pulseJ/pulse

800 nm800 nm40 nm bandwidth40 nm bandwidth

803 nm 26 nm bandwidth 803 nm 26 nm bandwidth 40 fs40 fs2 mJ/pulse, 1 kHz2 mJ/pulse, 1 kHz

Shaped vis pulseShaped vis pulsei. Stretcheri. Stretcherii. Etalonii. Etalon

EtalonOPA

To the sample

Grating

Tunable slit

Stretcher and Etalon

Spectroscopic Line Shapes in SFGSpectroscopic Line Shapes in SFG

Peaks are Peaks are asymmetricasymmetric--interference of the resonant and the interference of the resonant and the nonresonant SFGnonresonant SFG

Peaks are Peaks are broadbroad--convolution of the molecular response convolution of the molecular response with the visible up-converted pulse with the visible up-converted pulse

800

600

400

200

0

SF

G I

nte

nsi

ty (

a.u

.)

2300220021002000

IR Frequency (cm-1

)b=23G=13 cm-1Phi=1.36Om= 2134cm-1 omIR1=2115cm-1omIR2=2220cm-1TauIR1=129fsTauIR2=137fsNR1=6NR2=7.5

Propiolic acid Propiolic acid At air- water interfaceAt air- water interface

VisibleIR IR IR

Time0

E f

ield

Frequency

SFG

Sig

nal

Frequency

SFG

Sig

nal

Frequency

SFG

Sig

nal

VisibleIR IR IR

Time0

E f

ield

Frequency

SFG

Sig

nal

Frequency

SFG

Sig

nal

Frequency

SFG

Sig

nal

How Time Delay Affects SFG Spectra?How Time Delay Affects SFG Spectra?

(-) ve Time Delay (+) ve Time Delay

1. Stretcher Based Visible Pulses1. Stretcher Based Visible Pulses

350x103

300

250

200

150

100

50

0

Int

ensi

ty (

a.u.

)

-6000 -4000 -2000 0 2000 4000 6000

Time (fs)

400

300

200

100

0

x103

-4000 -2000 0 2000 4000

8000

6000

4000

2000

0

12.60x103

12.5512.5012.45

Visible frequency (cm-1

)10x10

3

8

6

4

2

0 Vis

. In

ten

sity

(a.

u.)

12.60x103

12.5512.5012.45

Visible frequency (cm-1

)

(a)

(d)

(b)

(c)Inte

nsit

y (a

.u.)

350x103

300

250

200

150

100

50

0

Int

ensi

ty (

a.u.

)

-6000 -4000 -2000 0 2000 4000 6000

Time (fs)

400

300

200

100

0

x103

-4000 -2000 0 2000 4000

8000

6000

4000

2000

0

12.60x103

12.5512.5012.45

Visible frequency (cm-1

)10x10

3

8

6

4

2

0 Vis

. In

ten

sity

(a.

u.)

12.60x103

12.5512.5012.45

Visible frequency (cm-1

)

(a)

(d)

(b)

(c)350x10

3

300

250

200

150

100

50

0

Int

ensi

ty (

a.u.

)

-6000 -4000 -2000 0 2000 4000 6000

Time (fs)

400

300

200

100

0

x103

-4000 -2000 0 2000 4000

8000

6000

4000

2000

0

12.60x103

12.5512.5012.45

Visible frequency (cm-1

)10x10

3

8

6

4

2

0 Vis

. In

ten

sity

(a.

u.)

12.60x103

12.5512.5012.45

Visible frequency (cm-1

)

350x103

300

250

200

150

100

50

0

Int

ensi

ty (

a.u.

)

-6000 -4000 -2000 0 2000 4000 6000

Time (fs)

400

300

200

100

0

x103

-4000 -2000 0 2000 4000

8000

6000

4000

2000

0

12.60x103

12.5512.5012.45

Visible frequency (cm-1

)10x10

3

8

6

4

2

0 Vis

. In

ten

sity

(a.

u.)

12.60x103

12.5512.5012.45

Visible frequency (cm-1

)

(a)

(d)

(b)

(c)Inte

nsit

y (a

.u.)

Vis. Width=17 cm-1

Vis. Width=37 cm-1

dtiEtE

o

o

visvis

2

2

)}(exp{)()(

2

)(sin

)(

)(exp2)(

t

t

titE o

vis

Electric field of time domain visible pulse

SFG Spectra From Stretcher Based VisibleSFG Spectra From Stretcher Based Visible

4000

3000

2000

1000

0

SFG

Int

ensi

ty (

a.u.

)

2300225022002150210020502000

IR Frequency (cm-1

)

666 fs

366 fs

66 fs

-234 fs

-534 fs

-834 fs

-1134 fs

-1434 fs

-1734 fs

2000

1500

1000

500

0

SFG

Int

ensi

ty (

a.u.

)

2300225022002150210020502000

IR Frequency (cm-1

)

600 fs

0 fs

-300 fs

-733 fs

-900 fs

-600 fs

Vis. Width=17 cmVis. Width=17 cm-1-1 Vis. Width=37 cmVis. Width=37 cm-1-1

Fitting ProcedureFitting Procedure

Time domainTime domain

Molecular response function

( )( ) ( ) i it i tNR i i

i

t A t iS t B e e

(1) ( ' ') ')) (( IR SE t t dttP t

)(2) (1 (), ) )( (visEt t PP t

The 1st order polarization

The 2nd order polarization

Frequency domainFrequency domain2nd order susceptibility

(2)

IR i

( )( ) i

i iIR NR

i i

BA

The BB-SFG Spectrum

Fourier Transform

2)2( ),()( PI SFG

dttitPP )exp(),(),( )2()2( FFT

2145

2140

2135

2130

Pea

k F

reque

ncy

(cm-1

)

-1500 -1000 -500 0 500

Time Delay (fs)

40

20

0

FW

HM

(cm

-1)

2Г

1000

800

600

400

200

0

Pea

k I

nte

nsi

ty (

a.u.

)

Visible 37 cm-1

Visible 17 cm-1

AnalysisAnalysis

Peak Intensity get Peak Intensity get maximized at negative maximized at negative time delaystime delays

FWHM get minimized at FWHM get minimized at negative time delaysnegative time delays

2. Etalon Based Visible Pulse2. Etalon Based Visible Pulse

3000

2500

2000

1500

1000

500

0

Vis

. in

ten

sity

(a.

u.)

12.45x103

12.4012.3512.3012.25

Visible Frequency (cm-1

)

800x103

600

400

200

0

Int

ensi

ty (

a.u.

)

3000200010000

Time (fs)

(a) (b)3000

2500

2000

1500

1000

500

0

Vis

. in

ten

sity

(a.

u.)

12.45x103

12.4012.3512.3012.25

Visible Frequency (cm-1

)

800x103

600

400

200

0

Int

ensi

ty (

a.u.

)

3000200010000

Time (fs)

3000

2500

2000

1500

1000

500

0

Vis

. in

ten

sity

(a.

u.)

12.45x103

12.4012.3512.3012.25

Visible Frequency (cm-1

)

800x103

600

400

200

0

Int

ensi

ty (

a.u.

)

3000200010000

Time (fs)

(a) (b)

12332 cm-1ωEtalon

42.5 fsτL

800 nmωL

6N

54n

0.955R

valueparameter

12332 cm-1ωEtalon

42.5 fsτL

800 nmωL

6N

54n

0.955R

valueparameter

2

0

/))(2(exp)2exp()( LLn

nvis tnTinTRtE

Nc

LEtalon

exact

2

2

Electric field of time domain visible pulse

SFG Spectra From Etalon Based VisibleSFG Spectra From Etalon Based Visible

1000

800

600

400

200

0

SFG

Inte

nsity

(a.u

.)

230022502200215021002050

IR frequency (cm-1

)

+199 fs

+33 fs

-33 fs

-99 fs

-199 fs

-233 fs

60

40

20

0

FWH

M (

cm-1)

2Г

2200

2150

2100

2050Peak

Fre

quen

cy (

cm-1

)

-400 -300 -200 -100 0 100 200

Time Delay (fs)

300

200

100

0Peak

Int

ensi

ty (

a.u.

)

60

40

20

0

FWH

M (

cm-1)

2Г

2200

2150

2100

2050Peak

Fre

quen

cy (

cm-1

)

-400 -300 -200 -100 0 100 200

Time Delay (fs)

300

200

100

0Peak

Int

ensi

ty (

a.u.

)

60

40

20

0

FWH

M (

cm-1)

2Г

2200

2150

2100

2050Peak

Fre

quen

cy (

cm-1

)

-400 -300 -200 -100 0 100 200

Time Delay (fs)

300

200

100

0Peak

Int

ensi

ty (

a.u.

)

π/2±0.2π/2±0.2π/2±0.2Phase, φ

2135±32135±52136±0.2Transition

Frequency, ω(cm-1)

13.5±0.513.5±0.513.5±0.5Line width, Г

(cm-1)

EtalonStretcher

FWHM=37 cm-1Stretcher

FWHM=17 cm-1

Narrowing method of visible

spectrum

π/2±0.2π/2±0.2π/2±0.2Phase, φ

2135±32135±52136±0.2Transition

Frequency, ω(cm-1)

13.5±0.513.5±0.513.5±0.5Line width, Г

(cm-1)

EtalonStretcher

FWHM=37 cm-1Stretcher

FWHM=17 cm-1

Narrowing method of visible

spectrum

Fitting Results

SummarySummary

Visible pulse shape and time delay can be used toVisible pulse shape and time delay can be used to eenhance the SFG signal intensitynhance the SFG signal intensity and obtain the and obtain the desired desired line shapeline shape without sacrificing the spectral resolution without sacrificing the spectral resolution

Combining theoretical modeling with experimental Combining theoretical modeling with experimental measurementsmeasurements,

i. information such as true line width can be extracted ii. observed line shapes can be described

AcknowledgementsAcknowledgementsThe Group

Adib J. SaminFunding

Wayne State University

ACS-PRF

NSF

http://chem.wayne.edu/benderskii-group/

4

3

2

1

0 SF

G I

nten

sity

(a.

u.)

23002250220021502100205020001950

(d)

(c)

(b)

(a)

10

8

6

4

2

0

Ele

ctri

c F

ield

(a.

u.)

23002250220021502100205020001950

IR Frequency (cm-1)

4

3

2

1

0 SF

G I

nten

sity

(a.

u.)

23002250220021502100205020001950

(d)

(c)

(b)

(a)

10

8

6

4

2

0

Ele

ctri

c F

ield

(a.

u.)

23002250220021502100205020001950

IR Frequency (cm-1)

4

3

2

1

0 SF

G I

nten

sity

(a.

u.)

23002250220021502100205020001950

(d)

(c)

(b)

(a)

10

8

6

4

2

0

Ele

ctri

c F

ield

(a.

u.)

23002250220021502100205020001950

IR Frequency (cm-1)

Modeled homodyne detected SFG spectrum

Asymmetric homodyne detectedSFG spectrum

Symmetric real part of the resonant contribution

Asymmetric imaginarypart of the resonant contribution

Non-resonant contribution

Visible Pulse Shape From Stretcher

slit

OPA

To the sample

Grating

Tunable slit

slit

OPA

To the sample

Grating

Tunable slit

Incoming beam

Outgoing beam

Incoming beam

Outgoing beam

Front view of grating

Visible

The inset shows the front view of the grating

EtalonOPA

To the sample

Grating

Tunable slit

Stretcher and Etalon