Abstract

We describe improvements to the Kleinman-disallowed hyper-Rayleigh scattering (HRS) measurement technique, which can be used to measure all of the rotationally invariant figures of merit for the first molecular nonlinear optical hyperpolarizability tensor βijk. As multiphoton excited fluorescence continues to be an accuracy-limiting factor in any HRS experiment, we have implemented time-resolved single photon counting in HRS using a Ti:sapphire laser. We show, however, that spectral analysis is necessary to ensure that the fluorescence and second harmonic are emitted on different time scales in order to allow temporal separation and thus improved accuracy. We also demonstrate how an electrically controlled liquid-crystal phase retarder can be used to vary the polarization state of the probe light in order to determine the second-order nonlinear response tensor. It was found that results agree with those obtained using a rotating quarter-wave plate to control the polarization state and demonstrate improved precision and reproducibility.

© 2008 Optical Society of America

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References

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  1. K. D. Singer and A. F. Garito, “Measurements of molecular 2nd order optical susceptibilities using dc induced 2nd harmonic-generation,” J. Chem. Phys. 75, 3572-3580 (1981).
    [CrossRef]
  2. A. Persoons, K. Clays, M. Kauranen, E. Hendrickx, E. Put, and W. Bijnens, “Characterization of nonlinear-optical properties by hyper-scattering techniques,” Synth. Met. 67, 31-38 (1994).
    [CrossRef]
  3. S. F. Hubbard, R. G. Petschek, K. D. Singer, N. D'Sidocky, C. Hudson, L. C. Chien, C. C. Henderson, and P. A. Cahill, “Measurements of Kleinman-disallowed hyperpolarizability in conjugated chiral molecules,” J. Opt. Soc. Am. B 15, 289-301 (1998).
    [CrossRef]
  4. K. D. Singer, J. E. Sohn, and S. J. Lalama, “Second harmonic-generation in poled polymer-films,” Appl. Phys. Lett. 49, 248-250 (1986).
    [CrossRef]
  5. T. Verbiest, K. Clays, C. Samyn, J. Wolff, D. Reinhoudt, and A. Persoons, “Investigations of the hyperpolarizability in organic-molecules from dipolar to octopolar systems,” J. Am. Chem. Soc. 116, 9320-9323 (1994).
    [CrossRef]
  6. J. Zyss, T. C. Van, C. Dhenaut, and I. Ledoux, “Harmonic Rayleigh-scattering from nonlinear octupolar molecular media--the case of crystal violet,” Chem. Phys. 177, 281-296 (1993).
    [CrossRef]
  7. V. Ostroverkhov, R. G. Petschek, K. D. Singer, L. Sukhomlinova, R. J. Twieg, S. X. Wang, and L. C. Chien, “Measurements of the hyperpolarizability tensor by means of hyper-Rayleigh scattering,” J. Opt. Soc. Am. B 17, 1531-1542 (2000).
    [CrossRef]
  8. K. Clays and A. Persoons, “Hyper-Rayleigh scattering in solution,” Rev. Sci. Instrum. 63, 3286-3289 (1992).
    [CrossRef]
  9. K. Clays and A. Persoons, “Hyper-Rayleigh scattering in solution,” Phys. Rev. Lett. 66, 2980-2983 (1991).
    [CrossRef] [PubMed]
  10. V. Ostroverkhov, O. Ostroverkhova, R. G. Petschek, K. D. Singer, L. Sukhomlinova, and R. J. Twieg, “Prospects for chiral nonlinear optical media,” IEEE J. Sel. Top. Quantum Electron. 7, 781-792 (2001).
    [CrossRef]
  11. K. D. Singer, R. G. Petschek, V. Ostroverkhov, R. J. Twieg, and L. Sukhomlinova, “Nonpolar second-order nonlinear and electrooptic materials: axially ordered chiral polymers and liquid crystals,” J. Polym. Sci., Part B: Polym. Phys. 41, 2744-2754 (2003).
    [CrossRef]
  12. P. Lemaillet, F. Pellen, S. Rivet, B. Le Jeune, and J. Cariou, “Optimization of a dual-rotating-retarder polarimeter designed for hyper-Rayleigh scattering,” J. Opt. Soc. Am. B 24, 609-614 (2007).
    [CrossRef]
  13. S. F. Hubbard, R. G. Petschek, and K. D. Singer, “Spectral content and dispersion of hyper-Rayleigh scattering,” Opt. Lett. 21, 1774-1776 (1996).
    [CrossRef] [PubMed]
  14. G. Olbrechts, R. Strobbe, K. Clays, and A. Persoons, “High-frequency demodulation of multi-photon fluorescence in hyper-Rayleigh scattering,” Rev. Sci. Instrum. 69, 2233-2241 (1998).
    [CrossRef]
  15. O. F. J. Noordman and N. F. van Hulst, “Time-resolved hyper-Rayleigh scattering: measuring first hyperpolarizabilities β of fluorescent molecules,” Chem. Phys. Lett. 253, 145-150 (1996).
    [CrossRef]
  16. See, for example, H. Weyl, The Classical Groups: Their Invariants and Representations (Princeton U. Press, 1997).
  17. Pr. Cvitanovi', Group Theory Birdtracks, Lie's, and Exceptional Groups, http://www.nbi.dk/GroupTheory/(Princeton U. Press, 2007).
  18. G. Olbrechts, K. Wostyn, K. Clays, and A. Persoons, “High-frequency demodulation of multiphoton fluorescence in long-wavelength hyper-Rayleigh scattering,” Opt. Lett. 24, 403-405 (1999).
    [CrossRef]
  19. D. V. O'Conner and D. Phillips, Time-Correlated Single Photon Counting (Academic, 1984).
  20. L. M. Loew, “Potentiometric dyes: imaging electrical activity of cell membranes,” Pure Appl. Chem. 68, 1405-1409 (1996).
    [CrossRef]
  21. K. A. Selanger, J. Falnes, and T. Sikkeland, “Fluorescence lifetime studies of Rhodamine 6G in methanol,” J. Phys. Chem. 81, 1960-1963 (1977).
    [CrossRef]
  22. Y. Rao, X.-m. Guo, Y.-S. Tao, and H.-f. Wang, “Observation of the direct S2-->S0 two-photon fluorescence between 370 and 480nm and the hyperpolarizability of crystal violet (CV) from spectrally resolved hyper-Rayleigh scattering measurement, J. Phys. Chem. A 108, 7977-7982 (2004).
    [CrossRef]

2007 (1)

2004 (1)

Y. Rao, X.-m. Guo, Y.-S. Tao, and H.-f. Wang, “Observation of the direct S2-->S0 two-photon fluorescence between 370 and 480nm and the hyperpolarizability of crystal violet (CV) from spectrally resolved hyper-Rayleigh scattering measurement, J. Phys. Chem. A 108, 7977-7982 (2004).
[CrossRef]

2003 (1)

K. D. Singer, R. G. Petschek, V. Ostroverkhov, R. J. Twieg, and L. Sukhomlinova, “Nonpolar second-order nonlinear and electrooptic materials: axially ordered chiral polymers and liquid crystals,” J. Polym. Sci., Part B: Polym. Phys. 41, 2744-2754 (2003).
[CrossRef]

2001 (1)

V. Ostroverkhov, O. Ostroverkhova, R. G. Petschek, K. D. Singer, L. Sukhomlinova, and R. J. Twieg, “Prospects for chiral nonlinear optical media,” IEEE J. Sel. Top. Quantum Electron. 7, 781-792 (2001).
[CrossRef]

2000 (1)

1999 (1)

1998 (2)

S. F. Hubbard, R. G. Petschek, K. D. Singer, N. D'Sidocky, C. Hudson, L. C. Chien, C. C. Henderson, and P. A. Cahill, “Measurements of Kleinman-disallowed hyperpolarizability in conjugated chiral molecules,” J. Opt. Soc. Am. B 15, 289-301 (1998).
[CrossRef]

G. Olbrechts, R. Strobbe, K. Clays, and A. Persoons, “High-frequency demodulation of multi-photon fluorescence in hyper-Rayleigh scattering,” Rev. Sci. Instrum. 69, 2233-2241 (1998).
[CrossRef]

1996 (3)

O. F. J. Noordman and N. F. van Hulst, “Time-resolved hyper-Rayleigh scattering: measuring first hyperpolarizabilities β of fluorescent molecules,” Chem. Phys. Lett. 253, 145-150 (1996).
[CrossRef]

L. M. Loew, “Potentiometric dyes: imaging electrical activity of cell membranes,” Pure Appl. Chem. 68, 1405-1409 (1996).
[CrossRef]

S. F. Hubbard, R. G. Petschek, and K. D. Singer, “Spectral content and dispersion of hyper-Rayleigh scattering,” Opt. Lett. 21, 1774-1776 (1996).
[CrossRef] [PubMed]

1994 (2)

T. Verbiest, K. Clays, C. Samyn, J. Wolff, D. Reinhoudt, and A. Persoons, “Investigations of the hyperpolarizability in organic-molecules from dipolar to octopolar systems,” J. Am. Chem. Soc. 116, 9320-9323 (1994).
[CrossRef]

A. Persoons, K. Clays, M. Kauranen, E. Hendrickx, E. Put, and W. Bijnens, “Characterization of nonlinear-optical properties by hyper-scattering techniques,” Synth. Met. 67, 31-38 (1994).
[CrossRef]

1993 (1)

J. Zyss, T. C. Van, C. Dhenaut, and I. Ledoux, “Harmonic Rayleigh-scattering from nonlinear octupolar molecular media--the case of crystal violet,” Chem. Phys. 177, 281-296 (1993).
[CrossRef]

1992 (1)

K. Clays and A. Persoons, “Hyper-Rayleigh scattering in solution,” Rev. Sci. Instrum. 63, 3286-3289 (1992).
[CrossRef]

1991 (1)

K. Clays and A. Persoons, “Hyper-Rayleigh scattering in solution,” Phys. Rev. Lett. 66, 2980-2983 (1991).
[CrossRef] [PubMed]

1986 (1)

K. D. Singer, J. E. Sohn, and S. J. Lalama, “Second harmonic-generation in poled polymer-films,” Appl. Phys. Lett. 49, 248-250 (1986).
[CrossRef]

1981 (1)

K. D. Singer and A. F. Garito, “Measurements of molecular 2nd order optical susceptibilities using dc induced 2nd harmonic-generation,” J. Chem. Phys. 75, 3572-3580 (1981).
[CrossRef]

1977 (1)

K. A. Selanger, J. Falnes, and T. Sikkeland, “Fluorescence lifetime studies of Rhodamine 6G in methanol,” J. Phys. Chem. 81, 1960-1963 (1977).
[CrossRef]

Appl. Phys. Lett. (1)

K. D. Singer, J. E. Sohn, and S. J. Lalama, “Second harmonic-generation in poled polymer-films,” Appl. Phys. Lett. 49, 248-250 (1986).
[CrossRef]

Chem. Phys. (1)

J. Zyss, T. C. Van, C. Dhenaut, and I. Ledoux, “Harmonic Rayleigh-scattering from nonlinear octupolar molecular media--the case of crystal violet,” Chem. Phys. 177, 281-296 (1993).
[CrossRef]

Chem. Phys. Lett. (1)

O. F. J. Noordman and N. F. van Hulst, “Time-resolved hyper-Rayleigh scattering: measuring first hyperpolarizabilities β of fluorescent molecules,” Chem. Phys. Lett. 253, 145-150 (1996).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron. (1)

V. Ostroverkhov, O. Ostroverkhova, R. G. Petschek, K. D. Singer, L. Sukhomlinova, and R. J. Twieg, “Prospects for chiral nonlinear optical media,” IEEE J. Sel. Top. Quantum Electron. 7, 781-792 (2001).
[CrossRef]

J. Am. Chem. Soc. (1)

T. Verbiest, K. Clays, C. Samyn, J. Wolff, D. Reinhoudt, and A. Persoons, “Investigations of the hyperpolarizability in organic-molecules from dipolar to octopolar systems,” J. Am. Chem. Soc. 116, 9320-9323 (1994).
[CrossRef]

J. Chem. Phys. (1)

K. D. Singer and A. F. Garito, “Measurements of molecular 2nd order optical susceptibilities using dc induced 2nd harmonic-generation,” J. Chem. Phys. 75, 3572-3580 (1981).
[CrossRef]

J. Opt. Soc. Am. B (3)

J. Phys. Chem. (1)

K. A. Selanger, J. Falnes, and T. Sikkeland, “Fluorescence lifetime studies of Rhodamine 6G in methanol,” J. Phys. Chem. 81, 1960-1963 (1977).
[CrossRef]

J. Phys. Chem. A (1)

Y. Rao, X.-m. Guo, Y.-S. Tao, and H.-f. Wang, “Observation of the direct S2-->S0 two-photon fluorescence between 370 and 480nm and the hyperpolarizability of crystal violet (CV) from spectrally resolved hyper-Rayleigh scattering measurement, J. Phys. Chem. A 108, 7977-7982 (2004).
[CrossRef]

J. Polym. Sci., Part B: Polym. Phys. (1)

K. D. Singer, R. G. Petschek, V. Ostroverkhov, R. J. Twieg, and L. Sukhomlinova, “Nonpolar second-order nonlinear and electrooptic materials: axially ordered chiral polymers and liquid crystals,” J. Polym. Sci., Part B: Polym. Phys. 41, 2744-2754 (2003).
[CrossRef]

Opt. Lett. (2)

Phys. Rev. Lett. (1)

K. Clays and A. Persoons, “Hyper-Rayleigh scattering in solution,” Phys. Rev. Lett. 66, 2980-2983 (1991).
[CrossRef] [PubMed]

Pure Appl. Chem. (1)

L. M. Loew, “Potentiometric dyes: imaging electrical activity of cell membranes,” Pure Appl. Chem. 68, 1405-1409 (1996).
[CrossRef]

Rev. Sci. Instrum. (2)

K. Clays and A. Persoons, “Hyper-Rayleigh scattering in solution,” Rev. Sci. Instrum. 63, 3286-3289 (1992).
[CrossRef]

G. Olbrechts, R. Strobbe, K. Clays, and A. Persoons, “High-frequency demodulation of multi-photon fluorescence in hyper-Rayleigh scattering,” Rev. Sci. Instrum. 69, 2233-2241 (1998).
[CrossRef]

Synth. Met. (1)

A. Persoons, K. Clays, M. Kauranen, E. Hendrickx, E. Put, and W. Bijnens, “Characterization of nonlinear-optical properties by hyper-scattering techniques,” Synth. Met. 67, 31-38 (1994).
[CrossRef]

Other (3)

D. V. O'Conner and D. Phillips, Time-Correlated Single Photon Counting (Academic, 1984).

See, for example, H. Weyl, The Classical Groups: Their Invariants and Representations (Princeton U. Press, 1997).

Pr. Cvitanovi', Group Theory Birdtracks, Lie's, and Exceptional Groups, http://www.nbi.dk/GroupTheory/(Princeton U. Press, 2007).

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Figures (7)

Fig. 1
Fig. 1

Schematic of the KD-HRS. The angle θ = 45 ° was chosen for alignment convenience.

Fig. 2
Fig. 2

TCSPC-KD-HRS (including TCSPC-HRS) setup: The components are denoted by BS, beam splitter; A, analyzer; LCR, liquid crystal retarder; D2040, LCR controller D2040; L, lens; T-cell, triangular sample cell; F, color and 400 nm narrowband filter; QWP, quarter-wave plate; P, polarizer; PD, high-speed SI photodiode; PMA, single photon detector, PMA185 (from PicoQuant Corp.); TH200, photon counting chip TimeHarp200 (from PicoQuant Corp.).

Fig. 3
Fig. 3

Studied compounds: (a) DR1, (b) Di-8, (c) MG.

Fig. 4
Fig. 4

Histograms from TCSPC measurements. (a) is the typical fluorescence time-domain spectrum of a fluorescent dye (Rhodamine 6G). (b) is the time-domain spectrum of MG and DR1. (c) is the time-domain spectrum of Di-8, which has a strong fluorescence tail.

Fig. 5
Fig. 5

Polar data plots and fits for KD-HRS measurements. (a)–(c) correspond to DR1, Di-8, and MG, respectively. The leftmost curves correspond to the output polarization settings: α o = 20.8 ° , γ o = 15.9 ° , while the rightmost curves correspond to the output polarization settings: α o = 73.1 ° , γ o = 60.0 ° .

Fig. 6
Fig. 6

Theoretical polar plots of the indicated rotational invariants Δ L . The leftmost curves correspond to the output polarization settings: α o = 20.8 ° , γ o = 15.9 ° , while the rightmost curves correspond to the output polarization settings: α o = 73.1 ° , γ o = 60.0 ° .

Fig. 7
Fig. 7

(a) Time-resolved HRS signal for CV pumped at 790 nm using two notch filters, one at the second-harmonic wavelength and one spectrally displaced. (b) Spectrum of scattering light of CV in acetone confirming significant fluorescence when pumped with a nanosecond pulse at 780 nm .

Tables (1)

Tables Icon

Table 1 Rotational Invariant Figures of Merit for the Hyperpolarizability, β a

Equations (22)

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I I L ω 3 = G N B I J K L M N 2 ( ω 3 , ω 1 , ω 2 ) E J ω 1 E K ω 2 ( E M ω 1 ) * ( E N ω 2 ) * ,
B I J K , L M N 2 β I J K β L M N * = L Δ ( L ) I J K , L M N β 2 ( L ) .
M = R ( γ ) M wave plate R ( γ ) R ( α ) M polarizer R ( α ) ,
M wave plate = [ 1 0 0 t ] , M polarizer = [ 1 0 0 0 ] ,
R ( α ) = [ cos ( α ) sin ( α ) sin ( α ) cos ( α ) ] .
e ̑ i = cos ( γ i α i ) ( x ̂ sin γ i + y ̂ cos γ i ) + t i sin ( γ i α i ) ( x ̂ cos γ i + y ̂ sin γ i ) .
e ̑ o = cos ( γ o α o ) ( ( x ̂ cos θ + z ̂ sin θ ) sin γ o + y ̂ cos γ o ) + t o sin ( γ o α o ) ( ( x ̂ cos θ + z ̂ sin θ ) cos γ o + y ̂ sin γ o ) .
e ̑ o = a z ̂ + b [ cos κ ( x ̂ cos ϕ + y ̂ sin ϕ ) + i sin κ ( x ̂ sin ϕ + y ̂ cos ϕ ) ] ,
e ̑ i = 1 2 [ ( 1 + cos r ) x ̂ + ( 1 cos r ) y ̂ + i sin r ( x ̂ y ̂ ) ] ,
Δ 1 ss = c 1 ss 1 9 [ A A * + 4 B B * + 4 Re ( B A * C ) ] = 1 9 c 1 ss ( 1 2 + 3 b 2 + 4 b 2 cos r cos 2 κ cos 2 ϕ + cos 2 r ( 1 2 + b 2 ) 2 b 2 sin r sin 2 κ ) ,
Δ 1 mm = c 1 mm 4 9 [ A A * + B B * 2 Re ( B A * C ) ] = 4 9 c 1 mm ( 1 2 + 1 b 2 2 cos 2 r b 2 2 sin r sin 2 κ b 2 2 cos r cos 2 κ cos 2 ϕ ) ,
Δ 1 sm + = c 1 sm + 4 9 [ A A * 2 B B * + Re ( B A * C ) ] = 4 9 c 1 sm + ( 1 2 3 b 2 4 b 2 2 cos r cos 2 κ cos 2 ϕ + ( 1 2 + b 2 4 ) cos 2 r + b 2 sin r sin 2 κ ) ,
Δ 1 sm = c 1 sm 4 i 3 [ Im ( B A * C ) ] = 4 3 c 1 sm ( b 2 4 ) sin 2 r cos 2 κ sin 2 ϕ ,
Δ 2 mm = 4 9 c 2 mm [ A A * + 2 B B * 2 Re ( B A * C ) ] + 2 3 c 2 mm [ 1 C C * ] = 4 9 c 2 mm ( 1 2 + 1 b 2 2 cos 2 r b 2 2 sin r sin 2 κ b 2 2 cos r cos 2 κ cos 2 ϕ ) + 2 3 c 2 mm ( 1 b 2 2 b 2 2 cos r cos 2 κ cos 2 ϕ b 2 2 sin r sin 2 κ ) ,
Δ 3 ss = 1 3 c 3 ss [ 1 + 2 C C * ] + 1 9 c 3 s s [ A A * + 4 B B * + 4 Re ( B A * C ) ] = 1 3 c 3 ss ( 1 + b 2 + b 2 cos r cos 2 κ cos 2 ϕ + b 2 sin r sin 2 κ ) + 1 9 c 3 ss ( 1 2 + 3 b 2 + 4 b 2 cos r cos 2 κ cos 2 ϕ + cos 2 r ( 1 2 + b 2 ) 2 b 2 sin r sin 2 κ ) ,
A = e i e o = cos 2 r 2 e i r + sin 2 r 2 e i ( r π ) = e i r ( cos 2 r 2 sin 2 r 2 ) = e i r cos r ,
B = e i e o * = ( cos r 2 e i r 2 , sin r 2 e i ( r π ) 2 ) ( cos κ cos ϕ + i sin κ sin ϕ cos κ sin ϕ i sin κ cos ϕ ) b = b 2 ( 1 + cos r + i sin r , 1 cos r i sin r ) ( cos κ cos ϕ + i sin κ sin ϕ cos κ sin ϕ i sin κ cos ϕ ) = b 2 ( ( 1 + cos r ) cos κ cos ϕ sin r sin κ sin ϕ + ( 1 cos r ) cos κ sin ϕ sin r sin κ cos ϕ + i ( ( 1 + cos r ) sin κ sin ϕ + sin r cos κ cos ϕ ( 1 cos r ) sin κ cos ϕ sin r cos κ sin ϕ ) ) ,
C = e i e o = b 2 ( 1 + cos r + i sin r , cos r i sin r ) ( cos κ cos ϕ + i sin κ sin ϕ cos κ sin ϕ i sin κ cos ϕ ) = b 2 ( ( 1 + cos r ) cos κ cos ϕ + sin r sin κ sin ϕ + ( 1 cos r ) cos κ sin ϕ + sin r sin κ cos ϕ + i ( ( 1 + cos r ) sin κ sin ϕ + sin r cos κ cos ϕ + ( 1 cos r ) sin κ cos ϕ sin r cos κ sin ϕ ) ) .
I 2 ω = L Δ L β L = n ( L A n , L β L sin n r + L B n , L β L cos n r ) .
χ 2 = n ( q n A n , L β L 2 ) 2 + n ( q n A n , L β L 2 ) 2 ,
0 = χ 2 β j 2 = 2 M i j β i 2 + 2 M i j β i 2 2 q n A n , j 2 q n A n , j ,
( M i j + M i j ) β i 2 = q n A n j + q n A n j ,

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