1

Polarization in Nonlinear Optics:

Rethinking Old Ideas

Nathan J. BeguePurdue University

RL

2RL

2 ir sum

vis

Second harmonic generation (SHG) and sum-frequency generation (SFG) are symmetry forbidden in isotropic media but allowed at the interface between two such media.

SHG SFG

2

Polarization Effects in Nonlinear Optics: Chirality

RL

2

In SHG, RCD approaches 100%

22

21

22

RL

RLCD II

IIR

L R

CD

L R

A AR

A A

In absorbance, RCD is typically ~0.1% to 1%.

R L

Objective: Develop a predictive framework for interpreting the chiral-specific second-order nonlinear optical properties of oriented and isotropic systems.

3

22 25 7 3 6 62 cos 2p ZXX ZZZ XXZ XXZ ZXXI s s s s s

2

6 6

23 5 6 72

3 5 6 7

6 6

3 52

Re Re Im Im

Re Re Re Re Re Re Re Recos

Im Im Im Im Im Im Im Im

Re Im Im Re

Re Im Re Im Recos

ZXX ZXX

p XXZ ZXX ZXX ZZZ

XXZ ZXX ZXX ZZZ

ZXX ZXX

XXZ ZXX

s s

I s s s s

s s s s

s s

s s

2

6 7

3 5 6 7

Im Re Im

Im Re Im Re Im Re Im Re

ZXX ZZZ

XXZ ZXX ZXX ZZZ

s s

s s s s

…the complex-valued tensor element ratios often cannot be uniquely determined by comparing intensities acquired at a single angle of incidence.

But Near Resonance…1. Intensity-based polarization analyses are generally inapplicable on resonance.

n

0

Polarization analysis: The devil is in the details.

4

Four major hurdles must be overcome.

1. Development of an intuitive framework for interpreting the molecular properties that drive optical activity in SHG and SFG.

2. Simplification of the relationships connecting molecular and surface nonlinearity.

3. Improvement in the instrumental methods used for polarization analysis.

4. Construction of reliable models for treating the thin film optics in SHG and SFG (i.e., Fresnel factors).

The Goal: Routine Polarization Analysis by SHG

5

2. The change in ellipticity of the incident beam is used to calculate the complex-valued elements of the Jones matrix describing reflection.

3. The measured complex ratio of the Jones matrix elements are then related back to thin film properties using a given interfacial model.

0

0p

out ins

RE E

R

p p i

s s

R Re

R R

1. The change in polarization upon reflection or transmission at a surface is measured.

Polλ/4

Light source Detector

Pol

Our approach: Pilfer ideas from linear ellipsometry

6(1) Plocinik, R. M.; Simpson, G. J., Anal. Chim. Acta 2003, 496, 133. (2) Plocinik, R. M.; Everly, R. M., Simpson, G. J., Phys. Rev. B. 2005, 72, 125409.

Nd:YAG

λ/2PolPMT #1

Pol

Nonlinear Film

λ/4 λ/4 λ/2H Q H-45o

1064 nm 532 nm

Waveplate rotation angle:

PM

T #

2

Instead of measuring intensity, measure the complete polarization state of the exigent

beam.

Nonlinear Optical Null Ellipsometry (NONE)

7

Label-free measurement of binding

AB

-SHG and SFG are very sensitive to surface orientation.

Time (min.)-2 0 2 4 6 8 10

(I2

) (n

orm

aliz

ed)

0.0

0.5

1.0

1.5

NONE-SI (p-pol.)

NONE-SI (RCP)

BSA solution introduced

Nd:YAG

λ/2PolPMT #1

Pol

Nonlinear Film

λ/4 λ/4 λ/2H Q H-45o

1064 nm 532 nm

Waveplate rotation angle:

PMT

#2

Nd:YAG

λ/2PolPMT #1

Pol

Nonlinear Film

λ/4 λ/4 λ/2H Q H-45o

1064 nm 532 nm

Waveplate rotation angle:

PMT

#2

(3) Polizzi, M.A.; Plocinik, R. M.; Simpson, G. J., JACS 2004, 126, 5001.

8

Generalized Nonlinear Optical Ellipsometry (NOE)-null ellipsometry-rotating quarter wave plate ellipsometry-rotating half wave plate ellipsometry

-0.4 -0.2 0.0 0.2 0.4

-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

Re(ρ)

ρ-22.5

ρ0

ρ22.5

ρ45

Im(ρ)

(2) Plocinik, R. M.; Everly, R. M., Simpson, G. J., Phys. Rev. B. 2005, 72, 125409.

rhodamine labeled dextran

9

IrisKG3

Flipper Mounts

λ/2 λ/222.5o

λ/445o-45o

PBCCL

Iris

PMT

532 nmKG3

532IF

VB

Flipper Mounts

FL

λ/2λ/2

22.5o

λ/4

45o -45o

PBC

1064 nm

sample

IrisKG3

Flipper Mounts

λ/2 λ/222.5o

λ/445o-45o

PBCCL

Iris

PMT

532 nmKG3

532IFIris

KG3

Flipper Mounts

λ/2 λ/222.5o

λ/445o-45o

PBCCL

Iris

PMTPMT

532 nmKG3

532IF

VB

Flipper Mounts

FL

λ/2λ/2

22.5o

λ/4

45o -45o

PBC

1064 nm VB

Flipper Mounts

FL

λ/2λ/2

22.5o

λ/4

45o -45o

PBC

1064 nm

samplesample

ρ R

ρL

ρ -45

ρ 45

RQW (1 hr)Flipper (8 min)

Auto-NONE (8 hr)Manual-NONE (30 min)

010 011 100 101

001

( ) ( )

2

H H H H

H

I I i I I

I

(4) Dehen, C. J.; Simpson, G. J. in preparation.

The second generation instrument: Maximum flexibility!

10

-Stokes ellipsometry approach allows complete polarization determination with every laser pulse.-A fs laser with a high (~90 MHz) repetition rate.-The incident polarization state is rapidly cycled (50 kHz) using a photoelastic modulator (PEM).

5 W532 nm

1 W

800 nm

PMT

PMT

Sample

PEMTi:Sapphire fs Laser

Partially polarizing beam splitter

PMT

PM

T

Quarter wave plate at 45o

Half wave plate at 22.5o

The goal: Complete polarization analysis in less than a second!

11Time (s)

0 5 10 15 20

Cou

nts

1e+1

1e+2

1e+3

1e+4

1e+5

200 s

10 ms

100 ms

5 W532 nm

1 W

800 nm

PMT

PMT

Sample

PEMTi:Sapphire fs Laser

Partially polarizing beam splitter

PMT

PM

T

Quarter wave plate at 45o

Half wave plate at 22.5o

5 W532 nm

1 W

800 nm

PMT

PMT

Sample

PEMTi:Sapphire fs Laser

Partially polarizing beam splitter

PMT

PM

T

Quarter wave plate at 45o

Half wave plate at 22.5o

Quartz Sample

2

Nonlinear Optical Stokes Ellipsometry (NOSE)

12

Malachite Green Monolayer

25 W532 nm

1 W

800 nm

PMT

PMT

Sample

PEMTi:Sapphire fs Laser

Partially polarizing beam splitter

PMT

PM

T

Quarter wave plate at 45o

Half wave plate at 22.5o

5 W532 nm

1 W

800 nm

PMT

PMT

Sample

PEMTi:Sapphire fs Laser

Partially polarizing beam splitter

PMT

PM

T

Quarter wave plate at 45o

Half wave plate at 22.5o

Time (s)

0 5 10 15 20

Cou

nts

100

1000

10000 1 s

Fast Nonlinear Optical Ellipsometry

13

ppp = 8.84 (0.01) + 81.22i (0.02)

pss = 109.30 (0.02) + 83.90i (0.02)

ssp = 52.68 (0.01) – 5.36i (0.01)

DATAGlobal Least Squares Minimization

Theoretical Fits

NOSE yields the full set of complex-valued (2) tensor elements to four significant figures for total acquisition times of ~1 sec.

(5) Moad, A. J.; Begue, N. J.; Hall, V. J.; Simpson, G. J. in preparation.

Extracting the (2) Jones tensors from NOSE

14

SHG and TPA Polarization Microscopy-Complete

polarization analysis (including chiral information) on samples in the mL - pL range.

-SHG imaging with full ellipsometric characterization at each pixel (protein identification from polarization).

-Simultaneous two-photon Absorption (including polarization-dependence).

5 W532 nm

1 W

800 nm

PMT

PMT

Sample

PEMTi:Sapphire fs Laser

Partially polarizing beam splitter

PMT

PM

T

Quarter wave plate at 45o

Half wave plate at 22.5o

5 W532 nm

1 W

800 nm

PMT

PMT

Sample

PEMTi:Sapphire fs Laser

Partially polarizing beam splitter

PMT

PM

T

Quarter wave plate at 45o

Half wave plate at 22.5o

15

Funding

The Simpson Group

-NSF-Research Corporation (Cottrell Teacher-Scholar Award, Research Innovation Award)-Eli Lilly (Analytical Chemistry Academic Contact Committee New Faculty Award)-Sloan Foundation (Sloan Fellowship)

-Beckman Foundation (Young Investigator Award)-Camille and Henry Dreyfus Foundation (New Faculty Award)-ACS-PRF Type G-Showalter Trust Organization

Garth Simpson, Kyle Jacobson, Nathan Begue, Al Hilton, Ryan Plocinik, Ron Wampler, Scott Goeken

Elizabeth Faust, Andy Moad, Brian Lynch, Chris Dehen, Tian Shen, John Perry, Rachel IspasNot pictured: Victoria Hall, Nick Isaps

16

17

Generalization to Nonlinear Optical Ellipsometry

2. The polarization-dependence of the exigent beam is used to calculate the complex-valued elements of a generalized Jones tensor describing the nonlinear optical process. For SHG and SFG, the Jones tensor is 222.

3. The measured complex ratios of the Jones tensor elements are then related back to the set of surface (2) tensor elements using an interfacial model.

1. The complete polarization state of the nonlinear beam is measured.

(2) : 1 2out in ine e e: : : :

: : : :ppp p p pps p s psp s p pss s s

spp p p sps p s ssp s p sss s s

e e e e e e e e

e e e e e e e e

1 2 3 1 2 3 1 2 33 3 3 3 5 3 3 3 7 3 3 3, , , , , , , , , , , ,ppp XXZ ZXX ZZZs n n n d s n n n d s n n n d

cos(2 2 ) cos(2 )

sin(2 2 ) sin(2 )

sum

sum

p H Q H

s H Q H

e i

e i

18

22 25 7 3 6 62 cos 2ZXX ZZZ XXZ XXZ ZXXpI s s s s s

1. Intensity-based polarization analyses are generally inapplicable on resonance.2. The optical constants of the ultrathin interfacial layer are unknown.3. The relationships connecting the macroscopic and molecular nonlinearity are nontrivial.

2' ' ' ' ' ' ' ' '

2 2' ' ' ' ' ' ' ' '

2 2' ' ' ' ' ' ' ' '

2' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' '

' '12

sin cos cos

sin cos sin

sin cos cos

sin cos sin cos

sin sin

z z z z x x z y y

y y z y z y z y y

x x z x z x z x x

x y z x z y y x z y z x z x y z y x

y y

ZXX sN

' ' ' ' ' ' ' ' ' '

' ' ' ' ' ' ' ' ' ' ' '

3' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' '

3' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' '

3 3' '

sin cos

sin sin

sin cos

sin sin

y y x x z y z z z y

x x x x y y z x z z z x

x x y x y x y x x y z z z y z z z y

x y y y x y y y x x z z z x z z z x

y y y

' ' ' ' ' ' ' ' ' '

3 3' ' ' ' ' ' ' ' ' ' ' 'sin cos

x x y x y x y x x

x x x x y y y x y y y x

Polarization analysis: The devil is in the details.

19

Step 1: What are the Key Molecular Properties Driving Optical Nonlinearity?

2

0 0

0 0

0 0

1; ,

4

1 1

1 1

1 1

ijksum a b

n m

i k jm mn n

m sum m n a n m sum m n a n

j k im mn n

m a m n sum n m a m n sum n

i j km mn n

m summ sum m n b n

i i i i

i i i i

ii i

0 0

0 0

0 0

1 1

1 1

1 1

m n b n

k j im mn n

m b m n sum n m b m n sum n

k i jm mn n

m b m n a n m b m n a n

j i km mn n

m a m n b n m a m n b n

i

i i i i

i i i i

i i i i

Rigorous, correct, but with few obvious chemical insights!

From time-dependent perturbation theory assuming a “frozen matrix”:

sum a b

20

2

1 2

1 2

2

21

12 ; ,

2ijkII sum

n

i jk ij k

j ik k ijjk iIn nI In nIIn nI SR SRPA

n sum n n n n n

ik jIn nIn nI In nIPA AR

n sum n n n

IAR

n n

i i i

ii i

2

1sum

0

n 2

1

sum

0

n

2

1sum

0n

Just by grouping terms and performing substitutions, the complete sum-over-states expression for SFG can be rewritten identically in a more intuitive form.

(1) Moad, A. J.; Simpson, G. J. J. Phys. Chem. A. 2005, 109, 1316.(2) Moad, A. J.; Simpson, G. J. J. Phys. Chem. B. 2004, 108, 3548.

SHG and two-photon absorption are directly linked!

21

Time (min.)-2 0 2 4 6 8 10

(I2

) (n

orm

aliz

ed)

0.0

0.1

0.2

0.3

0.4

BSA solution introduced

Real-time measurement of unlabeled bovine serum albumin (BSA) adsorption kinetics

PMT #1

Polλ/4532 nm

λ/2

Right circularly polarized incident beam

(3) Polizzi, M. A.; Plocinik, R. M.; Simpson, G. J., J. Am. Chem. Soc., 2004, 126, 5001.

22

Time (min.)-2 0 2 4 6 8 10

(I2

) (n

orm

aliz

ed)

0.0

0.5

1.0

1.5

NONE-SI (p-pol.)

NONE-SI (RCP)

BSA solution introduced

Predicted Enhancement: 26 Measured Enhancement: 25 4

Chiral-specific!!Ispp

2 depends exclusively on YXZ, providing a simple route to selectively and sensitively measure the emergence of surface chirality.

(3) Polizzi, M. A.; Plocinik, R. M.; Simpson, G. J., J. Am. Chem. Soc., 2004, 126, 5001.

Real-time measurement of unlabeled bovine serum albumin (BSA) adsorption kinetics

23

' ' '

1'

2' ' '

' '2

' ' ' '

' ' '

' 'sin cos c

sin sin cos

sin cos sin

os

z y y

s x y yXYZ

y x x y z z

z x x

x z zN

and are the Euler angles describing polar tilt and planar twist, respectively.

X

Z

Yz'

x'

Macroscopic Coordinates

ChromophoreCoordinates

Because the NLO properties of the amide chromophore are dominated by interactions within a plane, macromolecular chirality can arise through an orientational mechanism analogous to that in a propeller. This chiral mechanism has no simple analog in absorbance spectroscopy, since absorption is described by a vector (within the E-dipole approx.) rather than a tensor.

(6) Perry, J. M.; Moad, A. J.; Begue, N. J.; Wampler, R. D.; Simpson, G. J.; J. Phys. Chem. B.2005, 109, 20009.(7) Simpson, G. J. ChemPhysChem 2004, 5, 1301.(8) Simpson, G. J.; Moad, A. J.; Wampler, R. D. submitted.(9) Simpson, G. J., Perry, J. M.; Moad, A. J.; Wampler, R. D. Chem. Phys. Lett. 2004, 399, 26. (10) Simpson, G. J.; Perry, J. M.; Ashmore-Good, C. L. Phys. Rev. B. 2002, 66, 165437. (11) Simpson, G. .J. J. Chem. Phys. 2002, 117, 3398.