Abstract

A four-wave mixing (FWM) microscopy that is designed to probe third-order nonlinear susceptibilities, χ(3) of target materials with femtosecond light pulses has been constructed and investigated. Nondegenerate FWM signals (at 1500 and 639 nm) were produced in samples by a femtosecond Ti:sapphire laser (790 nm) and a femtosecond optical parametric oscillator (1035 nm). While the effect of electronic and vibrational molecular resonances on the visible FWM signal has been extensively studied, little attention has been paid to the infrared (IR) signal. This IR signal should exhibit a different dependence on the spectrum of molecular electronic resonances, and thus potentially offers a new mechanism for image contrast in microscopy. We have therefore constructed a FWM microscope to characterize these signals in a focused geometry. In polymeric films and beads containing a solute with a resonant (or near-resonant) optical response, the nonresonant polymer background signal was effectively suppressed using polarization-sensitive detection. Longitudinal scans of the beam foci through films were used to determine relative nonlinear third-order susceptibilities and second hyperpolarizabilities of selected solvents and the Rhodamine 6G dye molecule, for both the visible and IR FWM wavelengths.

© 2010 Optical Society of America

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2009 (1)

2008 (1)

C. Freudiger, W. Min, B. Saar, S. Lu, G. Holtom, C. He, J. Tsai, J. Kang, and X. S. Xie, “Label-free biomedical imaging with high sensitivity by stimulated Raman scattering microscopy,” Science 322, 1857-1861 (2008).
[CrossRef] [PubMed]

2007 (1)

E. Ploetz, S. Laimgruber, S. Berner, W. Zinth, and P. Gilch, “Femtosecond stimulated Raman microscopy,” Appl. Phys. B 87, 389-393 (2007).
[CrossRef]

2006 (2)

2003 (1)

W. Rudolph, P. Dorn, X. Liu, N. Vretenar, and R. Stock, “Microscopy with femtosecond laser pulses,” Appl. Surf. Sci. 208-209, 327-332 (2003).
[CrossRef]

2002 (1)

2001 (1)

2000 (3)

1999 (1)

A. Zumbusch, G. R. Holtom, and X. S. Xie, “Three-dimensional vibrational imaging by coherent anti-Stokes Raman scattering,” Phys. Rev. Lett. 82, 4142-4145 (1999).
[CrossRef]

1997 (1)

Y. Barad, H. Eisenberg, M. Horowitz, and Y. Silberberg, “Nonlinear scanning laser microscopy by third harmonic generation,” Appl. Phys. Lett. 70, 922-924 (1997).
[CrossRef]

1996 (1)

1990 (1)

W. Denk, J. H. Strickler, and W. W. Webb, “Two-photon laser scanning fluorescence microscopy,” Science 248, 73-76 (1990).
[CrossRef] [PubMed]

1987 (1)

1985 (2)

W. Leupacher and A. Penzkofer, “Third-order nonlinear susceptibilities of dye solutions determined by third-harmonic generation,” Appl. Phys. B 36, 25-31 (1985).
[CrossRef]

F. Kajzar and J. Messier, “Third harmonic generation in liquids,” Phys. Rev. A 32, 2352-2363 (1985).
[CrossRef] [PubMed]

1982 (1)

1979 (1)

J.-L. Oudar, R. W. Smith, and Y.-R. Shen, “Polarization-sensitive coherent anti-Stokes Raman spectroscopy,” Appl. Phys. Lett. 34, 758-760 (1979).
[CrossRef]

1978 (1)

J. N. Gannaway and C. J. R. Sheppard, “Second harmonic imaging in the scanning optical microscope,” Opt. Quantum Electron. 10, 435-439 (1978).
[CrossRef]

1977 (1)

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

1976 (1)

H. Lotem, R. R. Lynch, and N. Bloembergen, “Interference between Raman resonances in four-wave difference mixing,” Phys. Rev. A 14, 1748-1755 (1976).
[CrossRef]

1975 (1)

G. C. Bjorklund, “Effects of focusing on third-order nonlinear processes in isotropic media,” IEEE J. Quantum Electron. 11, 287-296 (1975).
[CrossRef]

1972 (1)

J. Selwyn and J. Steinfeld, “Aggregation equilibria of xanthene dyes,” J. Phys. Chem. 76, 762-774 (1972).
[CrossRef]

1962 (2)

D. A. Kleinman, “Nonlinear dielectric polarization in optical media,” Phys. Rev. 126, 1977-1979 (1962).
[CrossRef]

E. G. Baranova, “Study of the association of Rhodamine 6G in ethanol and glycerol solutions,” Opt. Spectrosc. 13, 452-456 (1962).

1959 (1)

O. H. Wheeler, “Near infrared spectra of organic compounds,” Chem. Rev. (Washington, D.C.) 59, 629-666 (1959).
[CrossRef]

Araki, T.

Barad, Y.

Y. Barad, H. Eisenberg, M. Horowitz, and Y. Silberberg, “Nonlinear scanning laser microscopy by third harmonic generation,” Appl. Phys. Lett. 70, 922-924 (1997).
[CrossRef]

Baranova, E. G.

E. G. Baranova, “Study of the association of Rhodamine 6G in ethanol and glycerol solutions,” Opt. Spectrosc. 13, 452-456 (1962).

Berner, S.

E. Ploetz, S. Laimgruber, S. Berner, W. Zinth, and P. Gilch, “Femtosecond stimulated Raman microscopy,” Appl. Phys. B 87, 389-393 (2007).
[CrossRef]

Bjorklund, G. C.

G. C. Bjorklund, “Effects of focusing on third-order nonlinear processes in isotropic media,” IEEE J. Quantum Electron. 11, 287-296 (1975).
[CrossRef]

Bloembergen, N.

H. Lotem, R. R. Lynch, and N. Bloembergen, “Interference between Raman resonances in four-wave difference mixing,” Phys. Rev. A 14, 1748-1755 (1976).
[CrossRef]

Book, L. D.

Boyd, R. W.

R. W. Boyd, Nonlinear Optics, 1st ed. (Academic, 1992), p. 439.

Brakenhoff, G. J.

M. Müller, J. Squier, C. A. de Lange, and G. J. Brakenhoff, “CARS microscopy with folded BoxCARS phasematching,” J. Microsc. 197, 150-158 (2000).
[CrossRef] [PubMed]

Cheng, J. X.

de Boeij, W.

de Lange, C. A.

M. Müller, J. Squier, C. A. de Lange, and G. J. Brakenhoff, “CARS microscopy with folded BoxCARS phasematching,” J. Microsc. 197, 150-158 (2000).
[CrossRef] [PubMed]

Denk, W.

W. Denk, J. H. Strickler, and W. W. Webb, “Two-photon laser scanning fluorescence microscopy,” Science 248, 73-76 (1990).
[CrossRef] [PubMed]

Dorn, P.

W. Rudolph, P. Dorn, X. Liu, N. Vretenar, and R. Stock, “Microscopy with femtosecond laser pulses,” Appl. Surf. Sci. 208-209, 327-332 (2003).
[CrossRef]

Duncan, M. D.

Eisenberg, H.

Y. Barad, H. Eisenberg, M. Horowitz, and Y. Silberberg, “Nonlinear scanning laser microscopy by third harmonic generation,” Appl. Phys. Lett. 70, 922-924 (1997).
[CrossRef]

Falnes, J.

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

Fischer, M.

T. Ye, M. Fischer, G. Yurtsever, and W. S. Warren, “Two-photon absorption microscopy of tissue,” in Conference on Lasers and Electro-Optics (CLEO) (2005), Vol. 2, pp. 1512-1514.
[CrossRef]

Freudiger, C.

C. Freudiger, W. Min, B. Saar, S. Lu, G. Holtom, C. He, J. Tsai, J. Kang, and X. S. Xie, “Label-free biomedical imaging with high sensitivity by stimulated Raman scattering microscopy,” Science 322, 1857-1861 (2008).
[CrossRef] [PubMed]

Fukui, K.

Furtak, T.

M. Klein and T. Furtak, Optics (Wiley, 1986), p. 660.

Gannaway, J. N.

J. N. Gannaway and C. J. R. Sheppard, “Second harmonic imaging in the scanning optical microscope,” Opt. Quantum Electron. 10, 435-439 (1978).
[CrossRef]

Gilch, P.

E. Ploetz, S. Laimgruber, S. Berner, W. Zinth, and P. Gilch, “Femtosecond stimulated Raman microscopy,” Appl. Phys. B 87, 389-393 (2007).
[CrossRef]

Hashimoto, M.

He, C.

C. Freudiger, W. Min, B. Saar, S. Lu, G. Holtom, C. He, J. Tsai, J. Kang, and X. S. Xie, “Label-free biomedical imaging with high sensitivity by stimulated Raman scattering microscopy,” Science 322, 1857-1861 (2008).
[CrossRef] [PubMed]

Higashi, T.

Holtom, G.

C. Freudiger, W. Min, B. Saar, S. Lu, G. Holtom, C. He, J. Tsai, J. Kang, and X. S. Xie, “Label-free biomedical imaging with high sensitivity by stimulated Raman scattering microscopy,” Science 322, 1857-1861 (2008).
[CrossRef] [PubMed]

Holtom, G. R.

A. Zumbusch, G. R. Holtom, and X. S. Xie, “Three-dimensional vibrational imaging by coherent anti-Stokes Raman scattering,” Phys. Rev. Lett. 82, 4142-4145 (1999).
[CrossRef]

Horowitz, M.

Y. Barad, H. Eisenberg, M. Horowitz, and Y. Silberberg, “Nonlinear scanning laser microscopy by third harmonic generation,” Appl. Phys. Lett. 70, 922-924 (1997).
[CrossRef]

Ishigure, T.

Isobe, K.

Itoh, K.

Kajiyama, S.

Kajzar, F.

Kang, J.

C. Freudiger, W. Min, B. Saar, S. Lu, G. Holtom, C. He, J. Tsai, J. Kang, and X. S. Xie, “Label-free biomedical imaging with high sensitivity by stimulated Raman scattering microscopy,” Science 322, 1857-1861 (2008).
[CrossRef] [PubMed]

Kataoka, S.

Kawakami, S.

Kawasumi, T.

Kawata, S.

Klein, M.

M. Klein and T. Furtak, Optics (Wiley, 1986), p. 660.

Kleinman, D. A.

D. A. Kleinman, “Nonlinear dielectric polarization in optical media,” Phys. Rev. 126, 1977-1979 (1962).
[CrossRef]

Koike, Y.

Laimgruber, S.

E. Ploetz, S. Laimgruber, S. Berner, W. Zinth, and P. Gilch, “Femtosecond stimulated Raman microscopy,” Appl. Phys. B 87, 389-393 (2007).
[CrossRef]

Leupacher, W.

W. Leupacher and A. Penzkofer, “Third-order nonlinear susceptibilities of dye solutions determined by third-harmonic generation,” Appl. Phys. B 36, 25-31 (1985).
[CrossRef]

Liu, X.

X. Liu, W. Rudolph, and J. L. Thomas, “Photobleaching resistance of parametric fluorescence in microscopy,” Opt. Lett. 34, 304-306 (2009).
[CrossRef] [PubMed]

W. Rudolph, P. Dorn, X. Liu, N. Vretenar, and R. Stock, “Microscopy with femtosecond laser pulses,” Appl. Surf. Sci. 208-209, 327-332 (2003).
[CrossRef]

Lotem, H.

H. Lotem, R. R. Lynch, and N. Bloembergen, “Interference between Raman resonances in four-wave difference mixing,” Phys. Rev. A 14, 1748-1755 (1976).
[CrossRef]

Lu, S.

C. Freudiger, W. Min, B. Saar, S. Lu, G. Holtom, C. He, J. Tsai, J. Kang, and X. S. Xie, “Label-free biomedical imaging with high sensitivity by stimulated Raman scattering microscopy,” Science 322, 1857-1861 (2008).
[CrossRef] [PubMed]

Lynch, R. R.

H. Lotem, R. R. Lynch, and N. Bloembergen, “Interference between Raman resonances in four-wave difference mixing,” Phys. Rev. A 14, 1748-1755 (1976).
[CrossRef]

Matsunaga, S.

Messier, J.

Min, W.

C. Freudiger, W. Min, B. Saar, S. Lu, G. Holtom, C. He, J. Tsai, J. Kang, and X. S. Xie, “Label-free biomedical imaging with high sensitivity by stimulated Raman scattering microscopy,” Science 322, 1857-1861 (2008).
[CrossRef] [PubMed]

Müller, M.

M. Müller, J. Squier, C. A. de Lange, and G. J. Brakenhoff, “CARS microscopy with folded BoxCARS phasematching,” J. Microsc. 197, 150-158 (2000).
[CrossRef] [PubMed]

Murase, R.

Nihei, E.

Oudar, J. -L.

J.-L. Oudar, R. W. Smith, and Y.-R. Shen, “Polarization-sensitive coherent anti-Stokes Raman spectroscopy,” Appl. Phys. Lett. 34, 758-760 (1979).
[CrossRef]

Ozeki, Y.

Pedrotti, F.

F. Pedrotti, L. S. Pedrotti, and L. M. Pedrotti, Introduction to Optics, 3rd ed. (Pearson Prentice Hall, 2007), p. 622.

Pedrotti, L. M.

F. Pedrotti, L. S. Pedrotti, and L. M. Pedrotti, Introduction to Optics, 3rd ed. (Pearson Prentice Hall, 2007), p. 622.

Pedrotti, L. S.

F. Pedrotti, L. S. Pedrotti, and L. M. Pedrotti, Introduction to Optics, 3rd ed. (Pearson Prentice Hall, 2007), p. 622.

Penzkofer, A.

W. Leupacher and A. Penzkofer, “Third-order nonlinear susceptibilities of dye solutions determined by third-harmonic generation,” Appl. Phys. B 36, 25-31 (1985).
[CrossRef]

Ploetz, E.

E. Ploetz, S. Laimgruber, S. Berner, W. Zinth, and P. Gilch, “Femtosecond stimulated Raman microscopy,” Appl. Phys. B 87, 389-393 (2007).
[CrossRef]

Potma, E.

Reintjes, J.

Rudolph, W.

X. Liu, W. Rudolph, and J. L. Thomas, “Photobleaching resistance of parametric fluorescence in microscopy,” Opt. Lett. 34, 304-306 (2009).
[CrossRef] [PubMed]

W. Rudolph, P. Dorn, X. Liu, N. Vretenar, and R. Stock, “Microscopy with femtosecond laser pulses,” Appl. Surf. Sci. 208-209, 327-332 (2003).
[CrossRef]

Saar, B.

C. Freudiger, W. Min, B. Saar, S. Lu, G. Holtom, C. He, J. Tsai, J. Kang, and X. S. Xie, “Label-free biomedical imaging with high sensitivity by stimulated Raman scattering microscopy,” Science 322, 1857-1861 (2008).
[CrossRef] [PubMed]

Selanger, K.

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

Selwyn, J.

J. Selwyn and J. Steinfeld, “Aggregation equilibria of xanthene dyes,” J. Phys. Chem. 76, 762-774 (1972).
[CrossRef]

Shen, Y. -R.

J.-L. Oudar, R. W. Smith, and Y.-R. Shen, “Polarization-sensitive coherent anti-Stokes Raman spectroscopy,” Appl. Phys. Lett. 34, 758-760 (1979).
[CrossRef]

Sheppard, C. J. R.

J. N. Gannaway and C. J. R. Sheppard, “Second harmonic imaging in the scanning optical microscope,” Opt. Quantum Electron. 10, 435-439 (1978).
[CrossRef]

Shimanouchi, T.

T. Shimanouchi, Tables of Molecular Vibrational Frequencies (U.S. Department of Commerce, National Bureau of Standards, 1967).

Sikkeland, T.

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

Silberberg, Y.

Y. Barad, H. Eisenberg, M. Horowitz, and Y. Silberberg, “Nonlinear scanning laser microscopy by third harmonic generation,” Appl. Phys. Lett. 70, 922-924 (1997).
[CrossRef]

Smith, R. W.

J.-L. Oudar, R. W. Smith, and Y.-R. Shen, “Polarization-sensitive coherent anti-Stokes Raman spectroscopy,” Appl. Phys. Lett. 34, 758-760 (1979).
[CrossRef]

Squier, J.

M. Müller, J. Squier, C. A. de Lange, and G. J. Brakenhoff, “CARS microscopy with folded BoxCARS phasematching,” J. Microsc. 197, 150-158 (2000).
[CrossRef] [PubMed]

Steinfeld, J.

J. Selwyn and J. Steinfeld, “Aggregation equilibria of xanthene dyes,” J. Phys. Chem. 76, 762-774 (1972).
[CrossRef]

Stock, R.

W. Rudolph, P. Dorn, X. Liu, N. Vretenar, and R. Stock, “Microscopy with femtosecond laser pulses,” Appl. Surf. Sci. 208-209, 327-332 (2003).
[CrossRef]

Strickler, J. H.

W. Denk, J. H. Strickler, and W. W. Webb, “Two-photon laser scanning fluorescence microscopy,” Science 248, 73-76 (1990).
[CrossRef] [PubMed]

Thomas, J. L.

Tian, P.

Tsai, J.

C. Freudiger, W. Min, B. Saar, S. Lu, G. Holtom, C. He, J. Tsai, J. Kang, and X. S. Xie, “Label-free biomedical imaging with high sensitivity by stimulated Raman scattering microscopy,” Science 322, 1857-1861 (2008).
[CrossRef] [PubMed]

Vretenar, N.

W. Rudolph, P. Dorn, X. Liu, N. Vretenar, and R. Stock, “Microscopy with femtosecond laser pulses,” Appl. Surf. Sci. 208-209, 327-332 (2003).
[CrossRef]

Warren, W. S.

P. Tian and W. S. Warren, “Ultrafast measurement of two-photon absorption by loss modulation,” Opt. Lett. 27, 1634-1636 (2002).
[CrossRef]

T. Ye, M. Fischer, G. Yurtsever, and W. S. Warren, “Two-photon absorption microscopy of tissue,” in Conference on Lasers and Electro-Optics (CLEO) (2005), Vol. 2, pp. 1512-1514.
[CrossRef]

Watanabe, W.

Webb, W. W.

W. Denk, J. H. Strickler, and W. W. Webb, “Two-photon laser scanning fluorescence microscopy,” Science 248, 73-76 (1990).
[CrossRef] [PubMed]

Wheeler, O. H.

O. H. Wheeler, “Near infrared spectra of organic compounds,” Chem. Rev. (Washington, D.C.) 59, 629-666 (1959).
[CrossRef]

Wiersma, D.

Wohlfarth, B.

C. Wohlfarth and B. Wohlfarth, Refractive Indices of Organic Liquids, Landolt-Börnstein (New Series) Volume Group III, M.D.Lechner, ed. (Springer-Verlag, 1996), Vol. 38, Subvol. B.

Wohlfarth, C.

C. Wohlfarth and B. Wohlfarth, Refractive Indices of Organic Liquids, Landolt-Börnstein (New Series) Volume Group III, M.D.Lechner, ed. (Springer-Verlag, 1996), Vol. 38, Subvol. B.

Xie, X. S.

C. Freudiger, W. Min, B. Saar, S. Lu, G. Holtom, C. He, J. Tsai, J. Kang, and X. S. Xie, “Label-free biomedical imaging with high sensitivity by stimulated Raman scattering microscopy,” Science 322, 1857-1861 (2008).
[CrossRef] [PubMed]

J. X. Cheng, L. D. Book, and X. S. Xie, “Polarization coherent anti-Stokes Raman scattering microscopy,” Opt. Lett. 26, 1341-1343 (2001).
[CrossRef]

A. Zumbusch, G. R. Holtom, and X. S. Xie, “Three-dimensional vibrational imaging by coherent anti-Stokes Raman scattering,” Phys. Rev. Lett. 82, 4142-4145 (1999).
[CrossRef]

Ye, T.

T. Ye, M. Fischer, G. Yurtsever, and W. S. Warren, “Two-photon absorption microscopy of tissue,” in Conference on Lasers and Electro-Optics (CLEO) (2005), Vol. 2, pp. 1512-1514.
[CrossRef]

Yurtsever, G.

T. Ye, M. Fischer, G. Yurtsever, and W. S. Warren, “Two-photon absorption microscopy of tissue,” in Conference on Lasers and Electro-Optics (CLEO) (2005), Vol. 2, pp. 1512-1514.
[CrossRef]

Zinth, W.

E. Ploetz, S. Laimgruber, S. Berner, W. Zinth, and P. Gilch, “Femtosecond stimulated Raman microscopy,” Appl. Phys. B 87, 389-393 (2007).
[CrossRef]

Zumbusch, A.

A. Zumbusch, G. R. Holtom, and X. S. Xie, “Three-dimensional vibrational imaging by coherent anti-Stokes Raman scattering,” Phys. Rev. Lett. 82, 4142-4145 (1999).
[CrossRef]

Appl. Opt. (1)

Appl. Phys. B (2)

E. Ploetz, S. Laimgruber, S. Berner, W. Zinth, and P. Gilch, “Femtosecond stimulated Raman microscopy,” Appl. Phys. B 87, 389-393 (2007).
[CrossRef]

W. Leupacher and A. Penzkofer, “Third-order nonlinear susceptibilities of dye solutions determined by third-harmonic generation,” Appl. Phys. B 36, 25-31 (1985).
[CrossRef]

Appl. Phys. Lett. (2)

J.-L. Oudar, R. W. Smith, and Y.-R. Shen, “Polarization-sensitive coherent anti-Stokes Raman spectroscopy,” Appl. Phys. Lett. 34, 758-760 (1979).
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Figures (11)

Fig. 1
Fig. 1

Schematic diagram of two-photon resonances that may enhance χ ( 3 ) . Each diagram corresponds to one or more terms in the perturbation expansion for the nonlinear material polarization [22]. Solid arrows represent input fields ( ω 1 corresponds to the 790 nm Ti:sapphire laser, while ω 2 corresponds to a 1035 nm OPO); wavy arrows represent the nonlinear signal. Two-photon resonant excited states are shown by dashed lines. A vibrational level at the difference energy can contribute to IR signals, through CSRS, and to visible signals, through CARS. However, an electronic excited state will contribute differently to the IR and visible signals.

Fig. 2
Fig. 2

Polarization geometry of parametric emission generation.

Fig. 3
Fig. 3

Schematic diagram of the FWM microscope: HWP, half-wave-plate; QWP, quarter-wave-plate; DBS, dichroic beam splitter; F, filter; A, analyzer; L, lens; PR, photoreceiver; APD, avalanche photodiode; OBJ, microscope objective.

Fig. 4
Fig. 4

IR SPE signal (S, in logarithm) as a function of the incident average power P ( P 1 , Ti:sapphire; P 2 , OPO, both in logarithm).

Fig. 5
Fig. 5

(a),(c) TPF and (b),(d) IR SPE images of mixed dyed and blank beads (Duke Scientific, Fremont, CA) taken as simultaneous pairs. (a) A TPF image of Rh6G-doped 7 μ m (diameter) and blank 6 μ m polysterene beads. (b) A nonresonant IR SPE image of the same field. The smaller undyed beads appear dimmer in the IR SPE image because of their size difference (the IR SPE signal depends on bead thickness, since the Rayleigh range is comparable to the bead size). (c) A second TPF image of the same field, taken synchronously with image (d). (d) A resonant IR SPE image of the same field. Intensity scale bars are shown for the SPE images (b) and (d), ×10 mV. Images of this field of beads were also used to demonstrate photobleaching resistance of the SPE signal [15].

Fig. 6
Fig. 6

Intensities of IR SPE signals as a function of analyzer angle β for an undoped (nonresonant) PMMA film (◻) and for a film doped with Rh6G (0.1 wt. %) (▲). Also shown is the ratio of these signals (right axis), which becomes quite large when the nonresonant signal is nearly extinguished at β = 135 ° .

Fig. 7
Fig. 7

IR FWM signal as a function of the position of the common focus of OPO and Ti:sapphire pulse for different liquids sandwiched between a glass substrate and a cover glass.

Fig. 8
Fig. 8

The molecular second hyperpolarizabilities | γ ( 2 ω 2 + ω 1 ; ω 2 , ω 2 , ω 1 ) | and | γ ( 2 ω 1 + ω 2 ; ω 1 , ω 1 , ω 2 ) | of several alcohols and hexane, normalized to the corresponding γ value of methanol, as a function of the number m of carbon atoms. Predictions for hexane ( m = 6 ) based on simple bond additivity (gray symbols) fall short of the measured second hyperpolarizabilities for both visible and IR signals.

Fig. 9
Fig. 9

FWM signals normalized to the signals from pure methanol ( C = 0 ) as a function of dye (Rh6G) concentration in methanol. A single second hyperpolarizability is unable to fit the data well over the entire concentration range. Solid lines are best fit curves to low concentration data, from which the monomeric Rh6G second hyperpolarizabilities were determined. Dashed lines show fits to an aggregation model; Rh6G aggregates have a smaller nonlinear response than monomers.

Fig. 10
Fig. 10

IR SPE signal normalized to the signal from undoped PMMA film as a function of dye (Rh6G) concentration in doped PMMA film. The curves are parabolic fits.

Fig. 11
Fig. 11

IR SPE signal of undoped and Rh6G doped (0.1 wt. %) PMMA films as a function of the analyzer orientation angle β.

Tables (2)

Tables Icon

Table 1 Refractive Indices of Solvents Calculated from the Three-Term Cauchy Dispersion Formula, at the Wavelengths Relevant to This Study

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Table 2 Molecular Number Densities N and Debye Field Enhancement Factors F, for the Solvents Used in This Study

Equations (35)

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P ( 3 ) = 3 χ ( 3 ) E 2 2 E 1 ,
χ ( 3 ) = ( 1 p ) χ N R + p χ R = ( 1 p ) χ N R + p A ω R 2 ω 2 i Γ ,
P ( 3 ) = P N R + P R .
χ ( 3 ) = ( 1 N D r ) χ N R + F N D γ D ,
F = ( n 2 ( ω 1 ) + 2 3 ) ( n 2 ( ω 2 ) + 2 3 ) 2 ( n 2 ( ω S ) + 2 3 ) ,
P N R = 3 E 2 2 E 1 ( 1 N D r ) ( x ̂ χ 1111 N R   cos   ϕ + y ̂ χ 2112 N R   sin   ϕ ) ,
P R = 3 E 2 2 E 1 ( x ̂ N D F γ 1   cos   ϕ + y ̂ N D F γ 2   sin   ϕ ) ,
tan   α = χ 2112 N R χ 1111 N R tan   ϕ = ρ N R   tan   ϕ ,
P = 3 E 2 2 E 1 { [ ( 1 N D r ) χ 1111 N R + N D F γ 1 ] cos   ϕ   cos   α + [ ( 1 N D r ) χ 2112 N R + N D F γ 2 ] sin   ϕ   sin   α } ,
P = 3 E 2 2 E 1 ( N D F γ 2   sin   ϕ   cos   α N D F γ 1   cos   ϕ   sin   α ) .
S = | 3 E 2 2 E 1 N D F ( γ 2 γ 1 ρ N R ) | 2 sin 2 ϕ 1 + ρ N R 2 tan 2 ϕ .
γ = χ ( 3 ) / N m F m = m ( 2 γ CH + γ CC ) + ( γ CH γ CC + γ CO + γ OH ) ,
P x = ( P N R + P R ) x = ( 3 E 2 2 E 1 F N H γ 1 H ) [ 1 + ( N D N H ) | γ 1 D γ 1 H | e i θ ] .
S x | 3 E 2 2 E 1 F N H γ 1 H | 2 = [ 1 + 2   cos   θ | γ 1 D γ 1 H | ( N D N H ) + | γ 1 D γ 1 H | 2 ( N D N H ) 2 ] .
| γ 1 D γ 1 H | 930 ,     θ 1 D 112 ° ± 10 ° .
| γ 1 D γ 1 H | 600 ± 70 ,     θ 1 D 117 ° ± 10 ° ,
S ( N D , β ) = q | [ ( 1 + r 1 ) cot   ϕ + ( ρ N R + r 2 ) ρ N R   tan   ϕ ] cos ( α β ) + ( r 2 r 1 ρ N R ) sin ( α β ) | 2 ,
S ( N D ) = q | r 2 r 1 ρ N R | 2 ,
S ( N D ) = q | ( 1 + r 1 ) cot   ϕ + ( ρ N R + r 2 ) ρ N R   tan   ϕ | 2 .
| γ 1 | ( 51 ± 5 ) × 10 34   esu ,     with   a   phase   angle   θ 1 126 ° ± 5 ° ,
| γ 2 | ( 12 ± 1 ) × 10 34   esu ,     with   a   phase   angle   θ 2 122 ° ± 5 ° .
E = E 0 e i θ P ,
E = E 0 e i θ P .
tan   2 ε = 2 E 0 E 0   cos   θ E 0 2 E 0 2 ,
χ = ( 1 N D r ) ( ρ N R χ 1111 N R + χ 2112 N R tan 2 α ) ,
γ = N D F ( γ 2 tan 2 α + ρ N R γ 1 ) ,
γ = N D F ( γ 2 ρ N R γ 1 ) .
E χ + γ ,
E γ   tan   α ,
tan   2 ε 2 E 0   cos   θ E 0 2   tan   α   Re   γ χ .
ε tan   α   Re   γ χ .
cos   2 η = cos   2 υ cos   2 ε ,
1 4 η 2 = 1 4 υ 2 + 4 ε 2 ,
η = υ 2 ε 2 = tan   α   Im   γ χ .
n λ = A + B λ 2 + C λ 4 ,

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