Transcript MolSpec2007 - Ohio State University Knowledge Bank

Fast Polarization Analysis by Nonlinear
Optical Stokes Ellipsometry
SFG
SHG
Nathan J. Begue, Andrew J. Moad,
Victoria J. Hall and Garth J. Simpson
Purdue University
vis

L
R
2
ir
sum
62nd Ohio State University International
Symposium on Molecular Spectroscopy
June 21, 2007
1
The Goal: Routine Polarization Analysis by SHG
(or any other Nonlinear Optical methods)
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).
2
Polarization analysis: The devil is in the details.
I
2
p
 2  s5 ZXX  s7  ZZZ  s3 XXZ  s6 XXZ  cos   2s6 ZXX
2
2
But Near Resonance…
1. Intensity-based
polarization analyses are
generally inapplicable on
resonance.
n

2

0
I p2 
  Re  s6  Re   ZXX   Im  s6  Im   ZXX  




  Re  s3  Re   XXZ   Re  s5  Re   ZXX   Re  s6  Re   ZXX   Re  s7  Re   ZZZ   
2

 cos  
  Im  s3  Im   XXZ   Im  s5  Im   ZXX   Im  s6  Im   ZXX   Im  s7  Im   ZZZ   

Re  s6  Im   ZXX   Im  s6  Re   ZXX 



  Re  s3  Im   XXZ   Re  s5  Im   ZXX   Re  s6  Im   ZXX   Re  s7  Im   ZZZ   

2

 cos  

  Im  s3  Re   XXZ   Im  s5  Re   ZXX   Im  s6  Re   ZXX   Im  s7  Re   ZZZ   
2
…the complex-valued tensor
element ratios often cannot be
uniquely determined by
comparing intensities acquired
at a single angle of incidence.
3
2
Top Down Approach:
Pilfer ideas from linear ellipsometry
1. The change in polarization upon reflection or transmission at a
surface is measured.
Pol
Pol
λ/4
2. The change in ellipticity of the incident beam is used to calculate the
complex-valued elements of the Jones matrix describing reflection.
Eout
 Rp

0
0
 Ein

Rs 

Rp
Rs

Rp
Rs
ei 
3. The measured complex ratio of the Jones matrix elements are then
related back to thin film properties using a given interfacial model. 4
Nonlinear
Film
1064 nm
PMT #2
Nonlinear Optical Null Ellipsometry (NONE)
532 nm
Nd:YAG
PMT #1
Pol
Waveplate rotation angle:
λ/2 λ/4
aH -45o
λ/4 λ/2 Pol
aQ2 aH2
Instead of measuring intensity, measure the
complete polarization state of the exigent beam.
(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.
5
Determine the (2) using analytical expressions
Experimentally measure the
complete polarization state:
 pol 
2
p
2
s
e
e
 ppp  ep   2  psp ep es   pss  es 
2

 spp  e p   2  ssp e p es   sss  es
 2
2

 2
 
Calculate (2) analytically:
 pss
  45  i  LCP
 ssp
o
 ppp
  45  i  LCP
 ssp
o
The Problem: Time consuming!
To get full (2) with sign and phase
information can take up to 8 hrs!
(2) Plocinik, R. M.; Everly, R. M., Simpson, G. J., Phys. Rev. B. 2005, 72, 125409.
6
The goal: Complete polarization analysis in less than
a second!
PMT
5W
532 nm
Half wave
plate at 22.5o
1W
PMT
800 nm
Sample
Ti:Sapphire fs Laser
PEM
Partially
polarizing
beam splitter
Quarter wave
plate at 45o
-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)
7
using a photoelastic modulator (PEM).
Extracting the (2) tensors from NOSE
Global Least
Squares
Minimization
DATA
 ppp
 pps   psp
 pss
Counts
 spp
 sps   ssp
s
RCP
p
RCP
s
LCP
p
LCP
s
Theoretical
Fits
 sss
Incident Polarization
Alternatively, one can apply thin film optics and Fresnel factors,
and fit to the angle independent 3x3x3 Cartesian surface (2)
tensor elements.
(3) Begue, N. J.; Moad, A. J.; Hall, V. J.; Simpson, G. J. in preparation.
8
Nonlinear Optical Stokes Ellipsometry (NOSE)
2
Quartz Sample
2
PM
T
Cellobiose Sample
PMT
PM
T
5W
532 nm
Half wave
plate at 22.5o
1W
PMT
800 nm
Sample
Ti:Sapphire fs Laser
PEM
Partially
polarizing
beam splitter
9
Quarter wave
plate at 45o
Fast Nonlinear Optical Ellipsometry
2
Disperse Yellow 7
ppp = 2.73(5) + 5.293(7)i
pps = psp = 0
pss = 5.91(3) – 3.75(6)i
spp = 0
sps = ssp = 1
sss = 0
The full complex valued (2) tensor elements were extracted
10
with 3-4 significant digits and an acquisition time of ~1 second.
How about a biomolecule?
NOSE of a crystalline disaccharide, cellobiose.
1 ms
NOE of a dye film
(disperse red 19) using 3
different methods based
on the physical motion of
optical elements
0.1 s
(3) Begue, N. J.; Hall, V. J.; Moad, A. J.; Simpson, G. J. in preparation.
(1) Plocinik, R. M.; Everly, R. M.; Moad, A. J.;
Simpson, G. J. Phys. Rev. B 2005, 72, 125409.
(2) Plocinik, R. M.; Simpson, G. J. Anal. Chim.
Acta 2003, 496, 133.
(4) Dehen, C. J.; Everly, R. M.; Plocinik, R. M.;
11Sci. Instr.
Hedderich, H. G.; Simpson, G. J. Rev.
2007, 78, 013106.
Bottom Up Approach:
Start from quantum mechanics and turn the crank
1.
Optimize molecular structures and calculate electronic excited
states in Gaussian
2. Working under the electric dipole approximation and within the
two state limit
n


2
i
jk


a

1  Iq qI 2PA 

(2)
ijk  2; ,     

2 q  qI  2 


(2)
 xxx
 48.2
(2)
(2)
 xxy
  xyx
 60.4
(2)
 xyy
 18.7
(5) Moad, A. J.; Simpson, G. J., Journal of Physical Chemistry A 2005, 109, (7), 1316-1323.
12
Bottom Up Continued:
3. NLOPredict (a tool developed for Chimera in collaboration with
Indiana University) allows for simple visualization of the χ(2)
tensor elements and predictions of molecular orientation at an
interface.
(2) = tensor for the
chromophore
(2) = surface tensor
y
q
z'
y'
x'
Y

( 2)
IJK


i ' j ' k ' x ' y ' z '
N s RIi ' RJj ' RKk ' 
(2)
i ' j 'k '
f
X
13
(6) Moad, A. J.; Moad, C. W.; Perry, J.M; Wampler, R.D.; Goeken, G.S.; Begue, N.J.; Shen, T; Heiland, R.; Simpson, G. J. Comp. Chem. 2007
DY7 Thin Film Orientation
y
q
z'
y'
x'
Y
f
X
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).
2
Half wave
plate at 22.5o
PMT
PM
T
5W
532 nm
PM
T

1W
PMT
800 nm
Sample
Ti:Sapphire fs Laser
PEM
Partially
polarizing
beam splitter
Quarter wave
plate at 45o
-Simultaneous twophoton Absorption
(including polarization15
dependence).
Cellobiose Image
Crystalline cellobiose film
S/N > 105
LDR > 106
Full set of
tensor elements
to ~3
significant
figures for 1 ms
acquisitions.
WJ11
16
Cellobiose Image
Crystalline cellobiose film
S/N > 105
LDR > 106
Full set of
tensor elements
to ~3
significant
figures for 1 ms
acquisitions.
17
This instrumental approach demonstrates
remarkable selectivity for chiral crystals.
NaCl (SHG-inactive
crystal)
Sucrose (SHG-active
chiral crystal)
18
Conclusions
•Nonlinear Optical Stokes Ellipsometry (NOSE)
has several advantages over previous Nonlinear
Optical Ellipsometry techniques
•Gain of 1-2 orders of magnitude in precision
•Reduction of data acquisition time by over 4
orders of magnitude
•While SHG was presented, NOSE is applicable to
any NLO techniques; Vib-SFG, CARS…
Future Work
•Investigation of theory of thin film optics
•Kinetics of nucleation, cellulous degradation
•What ever “brilliant” ideas Garth comes up with…
19
Kyle Jacobson, Ryan Plocinik, Chris Dehen, Nathan Begue, Scott Goeken, Victoria Hall, Zhi
Dr. Andy Moad (NIST), Garth Simpson, Brian Lynch and Nick Ingram
Not picture: Ron Wampler, Ellen Gilson, Debbie Wanapun, Ryan Davis and David Kissick
The Simpson Group
Funding
-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
20
21
Generalization to Nonlinear Optical Ellipsometry
1. The complete polarization state of the nonlinear beam is measured.

ep sum
essum

cos(2a H  2aQ )  i cos(2a H )
 sin(2a H  2aQ )  i sin(2a H )
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
222.
 : e e   pps : e p es   psp : es e p   pss : es es
eout   (2) : e1in e2in
  ppp p p
 spp : e p e p   sps : e p es   ssp : es e p   sss : es es
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.






 ppp  s3 q, n31 , n32 , n33 , d  XXZ  s5 q, n31 , n32 , n33 , d  ZXX  s7 q, n31 , n32 , n33 , d  ZZZ
22
Polarization analysis: The devil is in the details.
I
2
p
 2  s5 ZXX  s7  ZZZ  s3 XXZ  s6 XXZ  cos   2s6 ZXX
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
ZXX
2
 sin 2 q cos q   z ' z ' z '   cos q   z ' x ' x '   z ' y ' y ' 



 sin 2 q cos q sin 2 y   y ' y ' z '   y ' z ' y '   z ' y ' y ' 



 sin 2 q cos q cos 2 y   x ' x ' z '   x ' z ' x '   z ' x ' x ' 



 sin 2 q cos q sin y cos y  x ' y ' z '   x ' z ' y '   y ' x ' z '   y ' z ' x '   z ' x ' y '   z ' y ' x '  


 sin q sin y  y ' y ' y '   y ' x ' x '   z ' y ' z '   z ' z ' y ' 



 12 N s 

 sin q cos y   x ' x ' x '   x ' y ' y '   z ' x ' z '   z ' z ' x ' 



3
 sin q sin y   x ' x ' y '   x ' y ' x '   y ' x ' x '   y ' z ' z '   z ' y ' z '   z ' z ' y ' 



3
 sin q cos y   x ' y ' y '   y ' x ' y '   y ' y ' x '   x ' z ' z '   z ' x ' z '   z ' z ' x ' 



3
3
 sin q sin y   y ' y ' y '   x ' x ' y '   x ' y ' x '   y ' x ' x ' 



3
3
 sin q cos y   x ' x ' x '   x ' y ' y '   y ' x ' y '   y ' y ' x ' 

23
Step 1: What are the Key Molecular
Properties Driving Optical Nonlinearity?
sum
a b
ijk  sum ; a , b  
1
4 2

n

m 

From time-dependent perturbation
theory assuming a “frozen matrix”:


1
1
k

 nj 0 
i0 m mn

  m  sum  i m  n  a  i n   m  sum  i m  n  a  i n  


1
1

 0j m kmnin 0 

  m  a  i m  n  sum  i n   m  a  i m  n  sum  i n  


1
1
j


 nk 0 
i0 m mn

i





i





i





i







  m
n 
b
n
m
sum
m
n
b
m  n
sum



1
1
j

in 0 
 0k m mn

  m  b  i m  n  sum  i n   m  b  i m  n  sum  i n  


1
1

 0k mimn nj 0 

  m  b  i m  n  a  i n   m  b  i m  n  a  i n  
 

1
1
k
i
j

 0 m mn n 0 

  m  a  i m  n  b  i n   m  a  i m  n  b  i n   
24
Rigorous, correct, but with few obvious chemical insights!
Just by grouping terms and performing substitutions, the
complete sum-over-states expression for SFG can be
rewritten identically in a more intuitive form.
2 IIijk  sum ; 1 , 2  
1

2 n
j
ik
k
ij
 a Injk  nIi


a

a




In
nI
In
nI
SR
SR
2 PA




 n  sum  i n  n  1  i n  n  2  i n  


i
jk
ik
j
ij
k
 In a nI 2 PA
a In  AR nI
a In  AR nI 











i





i





i







n
sum
n
n
1
n
n
2
n 

n
1
sum
2
sum n
1
2
0
0
1
sum
2
n
0
SHG and two-photon absorption are directly linked!
(1)
(2)
Moad, A. J.; Simpson, G. J. J. Phys. Chem. A. 2005, 109, 1316.
Moad, A. J.; Simpson, G. J. J. Phys. Chem. B. 2004, 108, 3548.
25
Real-time measurement of unlabeled bovine serum
albumin (BSA) adsorption kinetics
Right circularly polarized incident beam
(I2)2(normalized)
0.4
BSA solution
introduced
0.3
0.2
0.1
0.0
-2
0
2
4
6
8
10
Time (min.)
PMT #1
532 nm
λ/4 λ/2 Pol

(3) Polizzi, M. A.; Plocinik, R. M.; Simpson, G. J., J. Am. Chem. Soc., 2004, 126, 5001.
26
2
Real-time measurement of unlabeled bovine serum
albumin (BSA) adsorption kinetics
(I2)2(normalized)
1.5
BSA solution
introduced
NONE-SI (p-pol.)
1.0
NONE-SI (RCP)
0.5
0.0
-2
0
2
4
6
8
Chiral-specific!!
Ispp2 depends
exclusively on
YXZ, providing a
simple route to
selectively and
sensitively
measure the
emergence of
surface chirality.
10
Time (min.)
Predicted Enhancement: 26
Measured Enhancement: 25  4
(3) Polizzi, M. A.; Plocinik, R. M.; Simpson, G. J., J. Am. Chem. Soc., 2004, 126, 5001.
27
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.
 XYZ
 sin 2 q sin y cos y   z ' y ' y '   z ' x ' x '  


1
 2 N s   sin q cos q sin y   x ' y ' y '   x ' z ' z '  


  sin q cos q cos y  y ' x ' x '   y ' z ' z '  


q and y are the Euler angles
describing polar tilt and planar
twist, respectively.
Macroscopic
Coordinates
q
x' y
Chromophore
Coordinates z'
(6)
(7)
(8)
(9)
(10)
(11)
Z
Y
Perry, J. M.; Moad, A. J.; Begue, N. J.; Wampler, R. D.; Simpson, G. J.; J. Phys. Chem. B.2005, 109, 20009.
Simpson, G. J. ChemPhysChem 2004, 5, 1301.
Simpson, G. J.; Moad, A. J.; Wampler, R. D. submitted.
Simpson, G. J., Perry, J. M.; Moad, A. J.; Wampler, R. D. Chem. Phys. Lett. 2004, 399, 26.
28
Simpson, G. J.; Perry, J. M.; Ashmore-Good, C. L. Phys. Rev. B. 2002, 66, 165437.
Simpson, G. .J. J. Chem. Phys. 2002, 117, 3398.
X