Polarization in Nonlinear Optics: Rethinking Old Ideas SFG

Polarization in Nonlinear Optics: Rethinking Old Ideas SFG

Polarization in Nonlinear Optics: Rethinking Old Ideas SFG SHG Nathan J. Begue Purdue University vis L R 2 ir sum Second harmonic generation (SHG) and sumfrequency generation (SFG) are symmetry forbidden in isotropic media but allowed at 1 the interface between two such media. Polarization Effects in Nonlinear Optics: Chirality L R RCD AL AR AL AR In absorbance, RCD is typically ~0.1% to 1%. R L 2 RCD I L2 I R2 1 2

2 I I L R 2 In SHG, RCD approaches 100% Objective: Develop a predictive framework for interpreting the chiral-specific second-order nonlinear optical properties of oriented and 2 isotropic systems. Polarization analysis: The devil is in the details. I 2 p 2 2 s5 ZXX s7 ZZZ s3 XXZ s6 XXZ cos 2s6 ZXX 1. Intensity-based polarization analyses are generally inapplicable on resonance. n 2 But Near Resonance 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 0 the complex-valued tensor element ratios often cannot be uniquely determined by comparing intensities acquired at a single angle of incidence. 3 2 The Goal: Routine Polarization Analysis by SHG 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). 4 Our approach: Pilfer ideas from linear ellipsometry 1. The change in polarization upon reflection or transmission at a surface is measured. Lig ht s

our c r o t c e Det e Pol Pol /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 5 then related back to thin film properties using a given interfacial model. Nonlinear Film 1064 nm

Nd:YAG Pol Waveplate rotation angle: /2 /4 H -45o PMT #2 Nonlinear Optical Null Ellipsometry (NONE) 532 nm PMT #1 /4 /2 Pol Q H 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. 6 Nonlinear Film 1064 nm Nd:YAG Pol Waveplate rotation angle: PMT #2 Label-free measurement of binding -SHG and SFG are very sensitive to surface orientation. 532 nm PMT #1 /4 /2 Pol Q H /2 /4 H -45o

B A (I2 ) (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 Time (min.) 7 (3) Polizzi, M.A.; Plocinik, R. M.; Simpson, G. J., JACS 2004, 126, 5001. 10 eneralized Nonlinear Optical Ellipsometry (NOE ull ellipsometry otating quarter wave plate ellipsometry otating half wave plate ellipsometry 1.5 45 1.0 0.5

Im() -22.5 0.0 -0.5 22.5 -1.0 0 -1.5 -0.4 -0.2 0.0 0.2 0.4 rhodamine labeled dextran Re() 8 (2) Plocinik, R. M.; Everly, R. M., Simpson, G. J., Phys. Rev. B. 2005, 72, 125409. The second generation instrument: Maximum flexibility! Flipper Mounts Flipper Mounts 1064 nm PBC /2 /2 /4 45o 22.5o -45o Iris

VB KG3 FL sample CL /4 /2 -45o 22.5o /2 45o 532 IF Iris PBC KG3 532 nm PMT Auto-NONE (8 hr) Manual-NONE (30 min) RQW (1 hr) Flipper (8 min) L 45 H H H H ( I 010 I 011 ) i ( I100 I101 ) H 2 I 001 -45 R

9 (4) Dehen, C. J.; Simpson, G. J. in preparation. Half wave plate at 22.5o 1W PMT 800 nm Sample Ti:Sapphire fs Laser PMT PM T 5W 532 nm PM T The goal: Complete polarization analysis in less than a second! 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 10 kHz) using a photoelastic modulator (PEM). Nonlinear Optical Stokes Ellipsometry (NOSE) PMT PM PM T

Half wave plate at 22.5o 1W 2 T 5W 532 nm PMT 800 nm Sample Ti:Sapphire fs Laser PEM Partially polarizing beam splitter Quartz Sample Quarter wave plate at 45o 1e+5 100 ms 1e+4 Counts 10 ms 1e+3 1e+2 200 s 1e+1 0 5 10 Time (s)

15 20 11 Fast Nonlinear Optical Ellipsometry T PMT PM T Half wave plate at 22.5o 1W PMT 800 nm Sample Malachite Green Monolayer Quarter wave plate at 45o Partially polarizing beam splitter PEM 1s 10000 Counts Ti:Sapphire fs Laser 2 PM 5W 532 nm 1000 100

0 5 10 Time (s) 15 20 12 Extracting the (2) Jones tensors from NOSE DATA Global Least Squares Minimizatio n 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) Theoretical Fits NOSE yields the full set of complex-valued (2) tensor elements to four significant figures for total acquisition times of ~1 sec. 13 (5) Moad, A. J.; Begue, N. J.; Hall, V. J.; Simpson, G. J. in preparation. SHG and TPA Polarization Microscopy -Complete polarization analysis (including chiral information) on samples in the mL pL range. 1W PMT 800 nm Sample Ti:Sapphire fs Laser

PMT PM T Half wave plate at 22.5o PM 5W 532 nm T PEM Partially polarizing beam splitter Quarter wave plate at 45o -SHG imaging with full ellipsometric characterization at each pixel (protein identification from polarization). -Simultaneous two14 photon Absorption The Simpson Group 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 Ispas Not pictured: Victoria Hall, Nick Isaps 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 15 16 Generalization to Nonlinear Optical Ellipsometry 1. The complete polarization state of the nonlinear beam is measured. ep sum essum cos(2 H 2 Q ) i cos(2 H ) sin(2 H 2 Q ) i sin(2 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 222. ppp : e p e p pps : e p es psp : es e p pss : es es eout (2) : e1in e2in 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 , n31 , n3 2 , n33 , d XXZ s5 , n31 , n32 , n33 , d ZXX s7 , n31 , n32 , n33 , d ZZZ 17 Polarization analysis: The devil is in the details. I 2 p 2 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. ZXX 2 sin 2 cos z ' z ' z ' cos z ' x ' x ' z ' y ' y ' sin 2 cos sin 2 y ' y ' z ' y ' z ' y ' z ' y ' y ' sin 2 cos cos 2 x ' x ' z ' x ' z ' x ' z ' x ' x ' sin 2 cos sin cos x ' y ' z ' x ' z ' y ' y ' x ' z ' y ' z ' x ' z ' x ' y ' z ' y ' x ' sin sin y ' y ' y ' y ' x ' x ' z ' y ' z ' z ' z ' y ' 12 N s sin cos x ' x ' x ' x ' y ' y ' z ' x ' z ' z ' z ' x ' 3 sin sin x ' x ' y ' x ' y ' x ' y ' x ' x ' y ' z ' z ' z ' y ' z ' z ' z ' y ' 3 sin cos x ' y ' y ' y ' x ' y ' y ' y ' x ' x ' z ' z ' z ' x ' z ' z ' z ' x ' 3 3 sin sin y ' y ' y ' x ' x ' y ' x ' y ' x ' y ' x ' x '

3 3 sin cos x ' x ' x ' x ' y ' y ' y ' x ' y ' y ' y ' x ' 18 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 i0 m mn nj 0 m sum im n a i n m sum i m n a i n 1 1 0j m kmnin 0 m a im n sum in m a im n sum i n 1 1 j

i0 m mn nk 0 i i i i m m sum m n b n sum m n b n 1 1 j 0k m mn in 0 m b im n sum in m b i m n sum i n

1 1 0k mimn nj 0 m b im n a i n m b i m n a i n 1 1 j i k 0 m mn n 0 m a im n b i n m a i m n b i n 19 gorous, correct, but with few obvious chemical insight 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 2 IIijk sum ; 1 , 2 2 n j ik k ij Injk nIi In nI In nI SR SR 2 PA

n sum in n 1 i n n 2 in i jk ik j ij k In nI 2 PA In AR nI 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. 20 Real-time measurement of unlabeled bovine serum albumin (BSA) adsorption kinetics Right circularly polarized incident beam (I2 ) (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 /4 /2 Pol (3) Polizzi, M. A.; Plocinik, R. M.; Simpson, G. J., J. Am. Chem. Soc., 2004, 126, 5001. 21 Real-time measurement of unlabeled bovine serum albumin (BSA) adsorption kinetics (I2 ) (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 Chiralspecific!! 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. 22 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 Edipole approx.) rather than a tensor. XYZ sin 2 sin cos z ' y ' y ' z ' x ' x ' 1 2 N s sin cos sin x ' y ' y ' x ' z ' z ' sin cos cos y ' x ' x ' y ' z ' z '

and are the Euler angles describing polar tilt and planar twist, respectively. Macroscopic Coordinates x' 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. 23 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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