Abstract

The nature of the third-harmonic generation (THG) process in a nematic liquid crystal is investigated for the case of tightly focused, low intensity, laser beams. Colloidal particle induced topological defects in a liquid crystal are visualized in three-dimensions using the dependence of the THG signal on both changes in non-linear susceptibility and the orientation of the liquid crystal director relative to the incident laser polarization state. We have found that the interpretation of THG images in a liquid crystal is complicated not only by the change in polarisation of the electric field as it propagates through the medium but also by anisotropic refractive index mismatch induced aberrations.

© 2006 Optical Society of America

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  1. M. Schadt, "Liquid crystal materials and liquid crystal displays," Annu. Rev. Mater. Sci. 27, 305-379 (1997).
    [CrossRef]
  2. A. M. Weiner, "Femtosecond pulse shaping using spatial light modulators," Rev. Sci. Instrum. 71, 1929-1960 (2000).
    [CrossRef]
  3. I. Musevic, M. Skarabot, U. Tkalec, M. Ravnik, and S. Zumer, "Two-dimensional nematic colloidal crystals self-assembled by topological defects," Science 313, 954-958 (2006).
    [CrossRef]
  4. P. Poulin, and D. A. Weitz, "Inverted and multiple nematic emulsions," Phys. Rev. E 57, 626 - 637 (1998).
    [CrossRef]
  5. Y. Gu, and N. L. Abbott, "Observation of saturn-ring defects around solid microspheres in nematic liquid crystals," Phys. Rev. Lett. 85, 4719 - 4722 (2000).
    [CrossRef]
  6. P. Poulin, H. Stark, T. C. Lubensky, and D. A. Weitz, "Novel colloidal interactions in anisotropic fluids," Science 275, 1770 - 1773 (1997).
    [CrossRef]
  7. D. Yelin, Y. Silberberg, Y. Barad, and J. S. Patel, "Depth-resolved imaging of nematic liquid crystals by third-harmonic microscopy," Appl. Phys. Lett. 74, 3107-3109 (1999).
    [CrossRef]
  8. D. Yelin, Y. Silberberg, Y. Barad, and J. S. Patel, "Phase-matched third-harmonic generation in a nematic liquid crystal cell," Phys. Rev. Lett. 82, 3046 - 3049 (1999).
    [CrossRef]
  9. J.-I. Kosugi, and K. Kajikawaa, "Phase-matched third-harmonic generation from nematic liquid crystals," Appl. Phys. Lett. 84, 5013-5015 (2004).
    [CrossRef]
  10. R. W. Boyd, Nonlinear optics (Academic Press, Inc., New York, 1992).
  11. J. F. Reintjes, Nonlinear optical parametric processes in liquids and gases (Academic Press, Inc., Orlando, 1984).
  12. T. Tsang, "Optical third-harmonic generation at interfaces," Phys. Rev. A 52, 4116-4125 (1995).
    [CrossRef]
  13. 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]
  14. D. Debarre, W. Supatto, A. M. Pena, A. Fabre, T. Tordjmann, L. Combettes, M. C. Schanne-Klein, and E. Beaurepaire, "Imaging lipid bodies in cells and tissues using third-harmonic generation microscopy," Nature Methods 3, 47-53 (2006).
    [CrossRef]
  15. W. Supatto, D. Débarre, B. Moulia, E. Brouzés, J.-L. Martin, E. Farge, and E. Beaurepaire, "In vivo modulation of morphogenetic movements in Drosophila emryos with femtosecond laser pulses," PNAS 102, 1047-1052 (2005).
    [CrossRef]
  16. M. Müller, J. Squier, K. R. Wilson, and G. J. Brakenhoff, "3D Microscopy of transparent objects using third-harmonic generation," J. Microsc. 191, 266-274 (1998).
    [CrossRef]
  17. S.-W. Chu, S.-Y. Chen, T.-H. Tsai, T.-M. Liu, C.-Y. Lin, H.-J. Tsai, and C.-K. Sun, "In vivo developmental biology study using noninvasive multi-harmonic generation microscopy," Opt. Express 11, 3093 - 3099 (2003).
  18. S.-P. Tai, W.-J. Lee, D.-B. Shieh, P.-C. Wu, H.-Y. Huang, C.-H. Yu, and C.-K. Sun, "In vivo optical biopsy of hamster oral cavity with epi-third-harmonic generation microscopy," Opt. Express 14, 6178-6187 (2006).
    [CrossRef]
  19. D. Oron, E. Tal, and Y. Silberberg, "Depth-resolved multiphoton polarisation microscopy by third-harmonic generation," Opt. Lett. 28, 2315-2317 (2003).
  20. R. S. Pillai, G. J. Brakenhoff, and M. Müller, "Analysis of the influence of spherical aberration from focusing through a dielectric slab in quantitative nonlinear optical susceptibility measurements using third-harmonic generation," Opt. Express 14, 260-269 (2006).
    [CrossRef]

2006 (4)

I. Musevic, M. Skarabot, U. Tkalec, M. Ravnik, and S. Zumer, "Two-dimensional nematic colloidal crystals self-assembled by topological defects," Science 313, 954-958 (2006).
[CrossRef]

D. Debarre, W. Supatto, A. M. Pena, A. Fabre, T. Tordjmann, L. Combettes, M. C. Schanne-Klein, and E. Beaurepaire, "Imaging lipid bodies in cells and tissues using third-harmonic generation microscopy," Nature Methods 3, 47-53 (2006).
[CrossRef]

S.-P. Tai, W.-J. Lee, D.-B. Shieh, P.-C. Wu, H.-Y. Huang, C.-H. Yu, and C.-K. Sun, "In vivo optical biopsy of hamster oral cavity with epi-third-harmonic generation microscopy," Opt. Express 14, 6178-6187 (2006).
[CrossRef]

R. S. Pillai, G. J. Brakenhoff, and M. Müller, "Analysis of the influence of spherical aberration from focusing through a dielectric slab in quantitative nonlinear optical susceptibility measurements using third-harmonic generation," Opt. Express 14, 260-269 (2006).
[CrossRef]

2005 (1)

W. Supatto, D. Débarre, B. Moulia, E. Brouzés, J.-L. Martin, E. Farge, and E. Beaurepaire, "In vivo modulation of morphogenetic movements in Drosophila emryos with femtosecond laser pulses," PNAS 102, 1047-1052 (2005).
[CrossRef]

2004 (1)

J.-I. Kosugi, and K. Kajikawaa, "Phase-matched third-harmonic generation from nematic liquid crystals," Appl. Phys. Lett. 84, 5013-5015 (2004).
[CrossRef]

2003 (2)

2000 (2)

A. M. Weiner, "Femtosecond pulse shaping using spatial light modulators," Rev. Sci. Instrum. 71, 1929-1960 (2000).
[CrossRef]

Y. Gu, and N. L. Abbott, "Observation of saturn-ring defects around solid microspheres in nematic liquid crystals," Phys. Rev. Lett. 85, 4719 - 4722 (2000).
[CrossRef]

1999 (2)

D. Yelin, Y. Silberberg, Y. Barad, and J. S. Patel, "Depth-resolved imaging of nematic liquid crystals by third-harmonic microscopy," Appl. Phys. Lett. 74, 3107-3109 (1999).
[CrossRef]

D. Yelin, Y. Silberberg, Y. Barad, and J. S. Patel, "Phase-matched third-harmonic generation in a nematic liquid crystal cell," Phys. Rev. Lett. 82, 3046 - 3049 (1999).
[CrossRef]

1998 (2)

P. Poulin, and D. A. Weitz, "Inverted and multiple nematic emulsions," Phys. Rev. E 57, 626 - 637 (1998).
[CrossRef]

M. Müller, J. Squier, K. R. Wilson, and G. J. Brakenhoff, "3D Microscopy of transparent objects using third-harmonic generation," J. Microsc. 191, 266-274 (1998).
[CrossRef]

1997 (3)

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]

M. Schadt, "Liquid crystal materials and liquid crystal displays," Annu. Rev. Mater. Sci. 27, 305-379 (1997).
[CrossRef]

P. Poulin, H. Stark, T. C. Lubensky, and D. A. Weitz, "Novel colloidal interactions in anisotropic fluids," Science 275, 1770 - 1773 (1997).
[CrossRef]

1995 (1)

T. Tsang, "Optical third-harmonic generation at interfaces," Phys. Rev. A 52, 4116-4125 (1995).
[CrossRef]

Abbott, N. L.

Y. Gu, and N. L. Abbott, "Observation of saturn-ring defects around solid microspheres in nematic liquid crystals," Phys. Rev. Lett. 85, 4719 - 4722 (2000).
[CrossRef]

Barad, Y.

D. Yelin, Y. Silberberg, Y. Barad, and J. S. Patel, "Depth-resolved imaging of nematic liquid crystals by third-harmonic microscopy," Appl. Phys. Lett. 74, 3107-3109 (1999).
[CrossRef]

D. Yelin, Y. Silberberg, Y. Barad, and J. S. Patel, "Phase-matched third-harmonic generation in a nematic liquid crystal cell," Phys. Rev. Lett. 82, 3046 - 3049 (1999).
[CrossRef]

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]

Beaurepaire, E.

D. Debarre, W. Supatto, A. M. Pena, A. Fabre, T. Tordjmann, L. Combettes, M. C. Schanne-Klein, and E. Beaurepaire, "Imaging lipid bodies in cells and tissues using third-harmonic generation microscopy," Nature Methods 3, 47-53 (2006).
[CrossRef]

W. Supatto, D. Débarre, B. Moulia, E. Brouzés, J.-L. Martin, E. Farge, and E. Beaurepaire, "In vivo modulation of morphogenetic movements in Drosophila emryos with femtosecond laser pulses," PNAS 102, 1047-1052 (2005).
[CrossRef]

Brakenhoff, G. J.

Brouzés, E.

W. Supatto, D. Débarre, B. Moulia, E. Brouzés, J.-L. Martin, E. Farge, and E. Beaurepaire, "In vivo modulation of morphogenetic movements in Drosophila emryos with femtosecond laser pulses," PNAS 102, 1047-1052 (2005).
[CrossRef]

Chen, S.-Y.

Chu, S.-W.

Combettes, L.

D. Debarre, W. Supatto, A. M. Pena, A. Fabre, T. Tordjmann, L. Combettes, M. C. Schanne-Klein, and E. Beaurepaire, "Imaging lipid bodies in cells and tissues using third-harmonic generation microscopy," Nature Methods 3, 47-53 (2006).
[CrossRef]

Debarre, D.

D. Debarre, W. Supatto, A. M. Pena, A. Fabre, T. Tordjmann, L. Combettes, M. C. Schanne-Klein, and E. Beaurepaire, "Imaging lipid bodies in cells and tissues using third-harmonic generation microscopy," Nature Methods 3, 47-53 (2006).
[CrossRef]

Débarre, D.

W. Supatto, D. Débarre, B. Moulia, E. Brouzés, J.-L. Martin, E. Farge, and E. Beaurepaire, "In vivo modulation of morphogenetic movements in Drosophila emryos with femtosecond laser pulses," PNAS 102, 1047-1052 (2005).
[CrossRef]

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]

Fabre, A.

D. Debarre, W. Supatto, A. M. Pena, A. Fabre, T. Tordjmann, L. Combettes, M. C. Schanne-Klein, and E. Beaurepaire, "Imaging lipid bodies in cells and tissues using third-harmonic generation microscopy," Nature Methods 3, 47-53 (2006).
[CrossRef]

Farge, E.

W. Supatto, D. Débarre, B. Moulia, E. Brouzés, J.-L. Martin, E. Farge, and E. Beaurepaire, "In vivo modulation of morphogenetic movements in Drosophila emryos with femtosecond laser pulses," PNAS 102, 1047-1052 (2005).
[CrossRef]

Gu, Y.

Y. Gu, and N. L. Abbott, "Observation of saturn-ring defects around solid microspheres in nematic liquid crystals," Phys. Rev. Lett. 85, 4719 - 4722 (2000).
[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]

Huang, H.-Y.

Kajikawaa, K.

J.-I. Kosugi, and K. Kajikawaa, "Phase-matched third-harmonic generation from nematic liquid crystals," Appl. Phys. Lett. 84, 5013-5015 (2004).
[CrossRef]

Kosugi, J.-I.

J.-I. Kosugi, and K. Kajikawaa, "Phase-matched third-harmonic generation from nematic liquid crystals," Appl. Phys. Lett. 84, 5013-5015 (2004).
[CrossRef]

Lee, W.-J.

Lin, C.-Y.

Liu, T.-M.

Lubensky, T. C.

P. Poulin, H. Stark, T. C. Lubensky, and D. A. Weitz, "Novel colloidal interactions in anisotropic fluids," Science 275, 1770 - 1773 (1997).
[CrossRef]

Martin, J.-L.

W. Supatto, D. Débarre, B. Moulia, E. Brouzés, J.-L. Martin, E. Farge, and E. Beaurepaire, "In vivo modulation of morphogenetic movements in Drosophila emryos with femtosecond laser pulses," PNAS 102, 1047-1052 (2005).
[CrossRef]

Moulia, B.

W. Supatto, D. Débarre, B. Moulia, E. Brouzés, J.-L. Martin, E. Farge, and E. Beaurepaire, "In vivo modulation of morphogenetic movements in Drosophila emryos with femtosecond laser pulses," PNAS 102, 1047-1052 (2005).
[CrossRef]

Müller, M.

Musevic, I.

I. Musevic, M. Skarabot, U. Tkalec, M. Ravnik, and S. Zumer, "Two-dimensional nematic colloidal crystals self-assembled by topological defects," Science 313, 954-958 (2006).
[CrossRef]

Oron, D.

Patel, J. S.

D. Yelin, Y. Silberberg, Y. Barad, and J. S. Patel, "Depth-resolved imaging of nematic liquid crystals by third-harmonic microscopy," Appl. Phys. Lett. 74, 3107-3109 (1999).
[CrossRef]

D. Yelin, Y. Silberberg, Y. Barad, and J. S. Patel, "Phase-matched third-harmonic generation in a nematic liquid crystal cell," Phys. Rev. Lett. 82, 3046 - 3049 (1999).
[CrossRef]

Pena, A. M.

D. Debarre, W. Supatto, A. M. Pena, A. Fabre, T. Tordjmann, L. Combettes, M. C. Schanne-Klein, and E. Beaurepaire, "Imaging lipid bodies in cells and tissues using third-harmonic generation microscopy," Nature Methods 3, 47-53 (2006).
[CrossRef]

Pillai, R. S.

Poulin, P.

P. Poulin, and D. A. Weitz, "Inverted and multiple nematic emulsions," Phys. Rev. E 57, 626 - 637 (1998).
[CrossRef]

P. Poulin, H. Stark, T. C. Lubensky, and D. A. Weitz, "Novel colloidal interactions in anisotropic fluids," Science 275, 1770 - 1773 (1997).
[CrossRef]

Ravnik, M.

I. Musevic, M. Skarabot, U. Tkalec, M. Ravnik, and S. Zumer, "Two-dimensional nematic colloidal crystals self-assembled by topological defects," Science 313, 954-958 (2006).
[CrossRef]

Schadt, M.

M. Schadt, "Liquid crystal materials and liquid crystal displays," Annu. Rev. Mater. Sci. 27, 305-379 (1997).
[CrossRef]

Schanne-Klein, M. C.

D. Debarre, W. Supatto, A. M. Pena, A. Fabre, T. Tordjmann, L. Combettes, M. C. Schanne-Klein, and E. Beaurepaire, "Imaging lipid bodies in cells and tissues using third-harmonic generation microscopy," Nature Methods 3, 47-53 (2006).
[CrossRef]

Shieh, D.-B.

Silberberg, Y.

D. Oron, E. Tal, and Y. Silberberg, "Depth-resolved multiphoton polarisation microscopy by third-harmonic generation," Opt. Lett. 28, 2315-2317 (2003).

D. Yelin, Y. Silberberg, Y. Barad, and J. S. Patel, "Phase-matched third-harmonic generation in a nematic liquid crystal cell," Phys. Rev. Lett. 82, 3046 - 3049 (1999).
[CrossRef]

D. Yelin, Y. Silberberg, Y. Barad, and J. S. Patel, "Depth-resolved imaging of nematic liquid crystals by third-harmonic microscopy," Appl. Phys. Lett. 74, 3107-3109 (1999).
[CrossRef]

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]

Skarabot, M.

I. Musevic, M. Skarabot, U. Tkalec, M. Ravnik, and S. Zumer, "Two-dimensional nematic colloidal crystals self-assembled by topological defects," Science 313, 954-958 (2006).
[CrossRef]

Squier, J.

M. Müller, J. Squier, K. R. Wilson, and G. J. Brakenhoff, "3D Microscopy of transparent objects using third-harmonic generation," J. Microsc. 191, 266-274 (1998).
[CrossRef]

Stark, H.

P. Poulin, H. Stark, T. C. Lubensky, and D. A. Weitz, "Novel colloidal interactions in anisotropic fluids," Science 275, 1770 - 1773 (1997).
[CrossRef]

Sun, C.-K.

Supatto, W.

D. Debarre, W. Supatto, A. M. Pena, A. Fabre, T. Tordjmann, L. Combettes, M. C. Schanne-Klein, and E. Beaurepaire, "Imaging lipid bodies in cells and tissues using third-harmonic generation microscopy," Nature Methods 3, 47-53 (2006).
[CrossRef]

W. Supatto, D. Débarre, B. Moulia, E. Brouzés, J.-L. Martin, E. Farge, and E. Beaurepaire, "In vivo modulation of morphogenetic movements in Drosophila emryos with femtosecond laser pulses," PNAS 102, 1047-1052 (2005).
[CrossRef]

Tai, S.-P.

Tal, E.

Tkalec, U.

I. Musevic, M. Skarabot, U. Tkalec, M. Ravnik, and S. Zumer, "Two-dimensional nematic colloidal crystals self-assembled by topological defects," Science 313, 954-958 (2006).
[CrossRef]

Tordjmann, T.

D. Debarre, W. Supatto, A. M. Pena, A. Fabre, T. Tordjmann, L. Combettes, M. C. Schanne-Klein, and E. Beaurepaire, "Imaging lipid bodies in cells and tissues using third-harmonic generation microscopy," Nature Methods 3, 47-53 (2006).
[CrossRef]

Tsai, H.-J.

Tsai, T.-H.

Tsang, T.

T. Tsang, "Optical third-harmonic generation at interfaces," Phys. Rev. A 52, 4116-4125 (1995).
[CrossRef]

Weiner, A. M.

A. M. Weiner, "Femtosecond pulse shaping using spatial light modulators," Rev. Sci. Instrum. 71, 1929-1960 (2000).
[CrossRef]

Weitz, D. A.

P. Poulin, and D. A. Weitz, "Inverted and multiple nematic emulsions," Phys. Rev. E 57, 626 - 637 (1998).
[CrossRef]

P. Poulin, H. Stark, T. C. Lubensky, and D. A. Weitz, "Novel colloidal interactions in anisotropic fluids," Science 275, 1770 - 1773 (1997).
[CrossRef]

Wilson, K. R.

M. Müller, J. Squier, K. R. Wilson, and G. J. Brakenhoff, "3D Microscopy of transparent objects using third-harmonic generation," J. Microsc. 191, 266-274 (1998).
[CrossRef]

Wu, P.-C.

Yelin, D.

D. Yelin, Y. Silberberg, Y. Barad, and J. S. Patel, "Depth-resolved imaging of nematic liquid crystals by third-harmonic microscopy," Appl. Phys. Lett. 74, 3107-3109 (1999).
[CrossRef]

D. Yelin, Y. Silberberg, Y. Barad, and J. S. Patel, "Phase-matched third-harmonic generation in a nematic liquid crystal cell," Phys. Rev. Lett. 82, 3046 - 3049 (1999).
[CrossRef]

Yu, C.-H.

Zumer, S.

I. Musevic, M. Skarabot, U. Tkalec, M. Ravnik, and S. Zumer, "Two-dimensional nematic colloidal crystals self-assembled by topological defects," Science 313, 954-958 (2006).
[CrossRef]

Annu. Rev. Mater. Sci. (1)

M. Schadt, "Liquid crystal materials and liquid crystal displays," Annu. Rev. Mater. Sci. 27, 305-379 (1997).
[CrossRef]

Appl. Phys. Lett. (3)

D. Yelin, Y. Silberberg, Y. Barad, and J. S. Patel, "Depth-resolved imaging of nematic liquid crystals by third-harmonic microscopy," Appl. Phys. Lett. 74, 3107-3109 (1999).
[CrossRef]

J.-I. Kosugi, and K. Kajikawaa, "Phase-matched third-harmonic generation from nematic liquid crystals," Appl. Phys. Lett. 84, 5013-5015 (2004).
[CrossRef]

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]

J. Microsc. (1)

M. Müller, J. Squier, K. R. Wilson, and G. J. Brakenhoff, "3D Microscopy of transparent objects using third-harmonic generation," J. Microsc. 191, 266-274 (1998).
[CrossRef]

Nature Methods (1)

D. Debarre, W. Supatto, A. M. Pena, A. Fabre, T. Tordjmann, L. Combettes, M. C. Schanne-Klein, and E. Beaurepaire, "Imaging lipid bodies in cells and tissues using third-harmonic generation microscopy," Nature Methods 3, 47-53 (2006).
[CrossRef]

Opt. Express (3)

Opt. Lett. (1)

Phys. Rev. A (1)

T. Tsang, "Optical third-harmonic generation at interfaces," Phys. Rev. A 52, 4116-4125 (1995).
[CrossRef]

Phys. Rev. E (1)

P. Poulin, and D. A. Weitz, "Inverted and multiple nematic emulsions," Phys. Rev. E 57, 626 - 637 (1998).
[CrossRef]

Phys. Rev. Lett. (2)

Y. Gu, and N. L. Abbott, "Observation of saturn-ring defects around solid microspheres in nematic liquid crystals," Phys. Rev. Lett. 85, 4719 - 4722 (2000).
[CrossRef]

D. Yelin, Y. Silberberg, Y. Barad, and J. S. Patel, "Phase-matched third-harmonic generation in a nematic liquid crystal cell," Phys. Rev. Lett. 82, 3046 - 3049 (1999).
[CrossRef]

PNAS (1)

W. Supatto, D. Débarre, B. Moulia, E. Brouzés, J.-L. Martin, E. Farge, and E. Beaurepaire, "In vivo modulation of morphogenetic movements in Drosophila emryos with femtosecond laser pulses," PNAS 102, 1047-1052 (2005).
[CrossRef]

Rev. Sci. Instrum. (1)

A. M. Weiner, "Femtosecond pulse shaping using spatial light modulators," Rev. Sci. Instrum. 71, 1929-1960 (2000).
[CrossRef]

Science (2)

I. Musevic, M. Skarabot, U. Tkalec, M. Ravnik, and S. Zumer, "Two-dimensional nematic colloidal crystals self-assembled by topological defects," Science 313, 954-958 (2006).
[CrossRef]

P. Poulin, H. Stark, T. C. Lubensky, and D. A. Weitz, "Novel colloidal interactions in anisotropic fluids," Science 275, 1770 - 1773 (1997).
[CrossRef]

Other (2)

R. W. Boyd, Nonlinear optics (Academic Press, Inc., New York, 1992).

J. F. Reintjes, Nonlinear optical parametric processes in liquids and gases (Academic Press, Inc., Orlando, 1984).

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