Fast Polarization Analysis by Nonlinear Optical Stokes Ellipsometry
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 62 nd 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. But Near Resonance… 1. Intensity-based polarization analyses are generally inapplicable on resonance. n w w 2 w 0 …the complex-valued tensor element ratios often cannot be uniquely determined by comparing intensities acquired at a single angle of incidence. 3
Top Down Approach: Pilfer ideas from linear ellipsometry 1. The change in polarization upon reflection or transmission at a surface is measured. Lig ht s r o t c e Det our ce 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. 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 Nd: YAG Pol Waveplate rotation angle: λ/2 λ/4 a. Hw -45 o PMT #2 Nonlinear Optical Null Ellipsometry (NONE) 532 nm PMT #1 λ/4 λ/2 Pol a. Q 2 w a. H 2 w 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 c(2) using analytical expressions Experimentally measure the complete polarization state: Calculate c(2) analytically: The Problem: Time consuming! To get full c(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
1 W PMT 800 nm Sample Ti: Sapphire fs Laser PMT PM T Half wave plate at 22. 5 o PM 5 W 532 nm T The goal: Complete polarization analysis in less than a second! PEM Partially polarizing beam splitter Quarter wave plate at 45 o -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 k. Hz) 7 using a photoelastic modulator (PEM).
Extracting the c(2) tensors from NOSE DATA Global Least Squares Minimization Theoretical Fits Alternatively, one can apply thin film optics and Fresnel factors, and fit to the angle independent 3 x 3 x 3 Cartesian surface c(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 w Quartz Sample 2 w Cellobiose Sample 9
Fast Nonlinear Optical Ellipsometry 2 w 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 c(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. ; 11 Sci. 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 w 2 w w 12 (5) Moad, A. J. ; Simpson, G. J. , Journal of Physical Chemistry A 2005, 109, (7), 1316 -1323.
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. b(2) = tensor for the chromophore c(2) = surface tensor y q z' y' x' Y X f 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
DY 7 Thin Film Orientation y q z' y' x' Y X f 14
SHG and TPA Polarization Microscopy -Complete polarization analysis (including chiral information) on samples in the m. L - p. L range. w 2 w w -SHG imaging with full ellipsometric characterization at each pixel (protein identification from polarization). -Simultaneous twophoton Absorption (including polarization 15 dependence).
Cellobiose Image Crystalline cellobiose film S/N > 105 LDR > 106 Full set of tensor elements to ~3 significant figures for 1 ms acquisitions. WJ 11 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. Na. Cl (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
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Generalization to Nonlinear Optical Ellipsometry 1. The complete polarization state of the nonlinear beam is measured. 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. 3. The measured complex ratios of the Jones tensor elements are then related back to the set of surface c(2) tensor elements using an interfacial model. 22
Polarization analysis: The devil is in the details. 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. 23
Step 1: What are the Key Molecular Properties Driving Optical Nonlinearity? wsum wa wb From time-dependent perturbation theory assuming a “frozen matrix”: 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. n w 1 wsum w 2 0 w 2 wsum n w 1 0 w 1 wsum w 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 BSA solution introduced PMT #1 532 nm λ/4 λ/2 Pol w (3) Polizzi, M. A. ; Plocinik, R. M. ; Simpson, G. J. , J. Am. Chem. Soc. , 2004, 126, 5001. 26 2 w
Real-time measurement of unlabeled bovine serum albumin (BSA) adsorption kinetics BSA solution introduced Predicted Enhancement: 26 Chiral-specific!! Ispp 2 depends exclusively on c. YXZ, providing a simple route to selectively and sensitively measure the emergence of surface chirality. 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. Z q and y are the Euler angles describing polar tilt and planar twist, respectively. (6) (7) (8) (9) (10) (11) q x' y Chromophore Coordinates z' Macroscopic Coordinates 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. Chem. Phys. Chem 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
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