Abstract

We present experimental investigations, accompanied by numerical simulations on third harmonic generation microscopy at interfaces. In particular we study the variation of the emitted third harmonic intensity profile with the interface orientation. Our data confirm previous theoretical predications that only at interfaces perpendicular to the direction of the fundamental laser beam can the generated third harmonic profile exhibit a single spot in the forward direction. At interfaces parallel with the direction of the fundamental beam, the third harmonic intensity profile moves outside the forward direction and develops into a double-spot beam with a large opening angle. As an important consequence for implementations of harmonic generation microscopy, the numerical aperture of the double-spot third harmonic beam exceeds the numerical aperture of the fundamental beam.

© 2013 Optical Society of America

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  1. S. Yue, M. N. Slipchenko, and J.-X. Cheng, “Multimodal nonlinear optical microscopy,” Laser Photon. Rev. 5, 496–512 (2011).
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    [CrossRef]
  3. R. Selm, G. Krauss, A. Leitenstorfer, and A. Zumbusch, “Simultaneous second-harmonic generation, third-harmonic generation, and four-wave mixing microscopy with single sub-8 fs laser pulses,” Appl. Phys. Lett. 99, 181124 (2011).
    [CrossRef]
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    [CrossRef]
  5. S. Witte, A. Negrean, J. C. Lodder, C. P. J. de Kock, G. Testa Silva, H. D. Mansvelder, and M. Louise Groot, “Label-free live brain imaging and targeted patching with third-harmonic generation microscopy,” Proc. Natl. Acad. Sci. USA 108, 5970–5975 (2011).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  12. U. Petzold, A. Büchel, and T. Halfmann, “Effects of laser polarization and interface orientation in harmonic generation microscopy,” Opt. Express 20, 3654–3662 (2012).
    [CrossRef]
  13. J. Squier and M. Müller, “High resolution nonlinear microscopy: a review of sources and methods for achieving optimal imaging,” Rev. Sci. Instrum. 72, 2855–2867 (2001).
    [CrossRef]
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    [CrossRef]
  15. J. M. Schins, T. Schrama, J. Squier, G. J. Brakenhoff, and M. Müller, “Determination of material properties by use of third-harmonic generation microscopy,” J. Opt. Soc. Am. B 19, 1627–1634 (2002).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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2012 (2)

U. Petzold, A. Büchel, S. Hardt, and T. Halfmann, “Imaging diffusion in a microfluidic device by third harmonic microscopy,” Exp. Fluids 53, 777–782 (2012).
[CrossRef]

U. Petzold, A. Büchel, and T. Halfmann, “Effects of laser polarization and interface orientation in harmonic generation microscopy,” Opt. Express 20, 3654–3662 (2012).
[CrossRef]

2011 (3)

S. Witte, A. Negrean, J. C. Lodder, C. P. J. de Kock, G. Testa Silva, H. D. Mansvelder, and M. Louise Groot, “Label-free live brain imaging and targeted patching with third-harmonic generation microscopy,” Proc. Natl. Acad. Sci. USA 108, 5970–5975 (2011).
[CrossRef]

S. Yue, M. N. Slipchenko, and J.-X. Cheng, “Multimodal nonlinear optical microscopy,” Laser Photon. Rev. 5, 496–512 (2011).
[CrossRef]

R. Selm, G. Krauss, A. Leitenstorfer, and A. Zumbusch, “Simultaneous second-harmonic generation, third-harmonic generation, and four-wave mixing microscopy with single sub-8 fs laser pulses,” Appl. Phys. Lett. 99, 181124 (2011).
[CrossRef]

2010 (1)

N. Olivier, M. A. Luengo-Oroz, L. Duloquin, E. Faure, T. Savy, I. Veilleux, X. Solinas, D. Debarre, P. Bourgine, A. Santos, N. Peyrieras, and E. Beaurepaire, “Cell lineage reconstruction of early zebrafish embryos using label-free nonlinear microscopy,” Science 329, 967–971 (2010).
[CrossRef]

2009 (2)

R. Carriles, D. Schafer, K. Sheetz, J. Field, R. Cisek, V. Barzda, A. Sylvester, and J. Squier, “Invited review article: imaging techniques for harmonic and multiphoton absorption fluorescence microscopy,” Rev. Sci. Instrum. 80, 081101 (2009).
[CrossRef]

T. Minamikawa, M. Hashimoto, K. Fujita, S. Kawata, and T. Araki, “Multi-focus excitation coherent anti-Stokes Raman scattering (CARS) microscopy and its applications for real-time imaging,” Opt. Express 17, 9526–9536 (2009).
[CrossRef]

2008 (1)

2007 (1)

2006 (1)

2004 (1)

2002 (4)

2001 (2)

J. Squier and M. Müller, “High resolution nonlinear microscopy: a review of sources and methods for achieving optimal imaging,” Rev. Sci. Instrum. 72, 2855–2867 (2001).
[CrossRef]

L. Moreaux, O. Sandre, S. Charpak, M. Blanchard-Desce, and J. Mertz, “Coherent scattering in multi-harmonic light microscopy,” Biophys. J. 80, 1568–1574 (2001).
[CrossRef]

2000 (1)

1999 (1)

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)

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]

J. Squier, M. Müller, G. J. Brakenhoff, and K. R. Wilson, “Third harmonic generation microscopy,” Opt. Express 3, 315–324 (1998).
[CrossRef]

Araki, T.

Barad, Y.

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]

Barille, R.

Barzda, V.

R. Carriles, D. Schafer, K. Sheetz, J. Field, R. Cisek, V. Barzda, A. Sylvester, and J. Squier, “Invited review article: imaging techniques for harmonic and multiphoton absorption fluorescence microscopy,” Rev. Sci. Instrum. 80, 081101 (2009).
[CrossRef]

Beaurepaire, E.

N. Olivier, M. A. Luengo-Oroz, L. Duloquin, E. Faure, T. Savy, I. Veilleux, X. Solinas, D. Debarre, P. Bourgine, A. Santos, N. Peyrieras, and E. Beaurepaire, “Cell lineage reconstruction of early zebrafish embryos using label-free nonlinear microscopy,” Science 329, 967–971 (2010).
[CrossRef]

N. Olivier and E. Beaurepaire, “Third-harmonic generation microscopy with focus-engineered beams: a numerical study,” Opt. Express 16, 14703–14715 (2008).
[CrossRef]

D. Debarre, N. Olivier, and E. Beaurepaire, “Signal epidetection in third-harmonic generation microscopy of turbid media,” Opt. Express 15, 8913–8924 (2007).
[CrossRef]

Blanchard-Desce, M.

L. Moreaux, O. Sandre, S. Charpak, M. Blanchard-Desce, and J. Mertz, “Coherent scattering in multi-harmonic light microscopy,” Biophys. J. 80, 1568–1574 (2001).
[CrossRef]

Bourgine, P.

N. Olivier, M. A. Luengo-Oroz, L. Duloquin, E. Faure, T. Savy, I. Veilleux, X. Solinas, D. Debarre, P. Bourgine, A. Santos, N. Peyrieras, and E. Beaurepaire, “Cell lineage reconstruction of early zebrafish embryos using label-free nonlinear microscopy,” Science 329, 967–971 (2010).
[CrossRef]

Brakenhoff, G. J.

Brechet, F.

Büchel, A.

U. Petzold, A. Büchel, and T. Halfmann, “Effects of laser polarization and interface orientation in harmonic generation microscopy,” Opt. Express 20, 3654–3662 (2012).
[CrossRef]

U. Petzold, A. Büchel, S. Hardt, and T. Halfmann, “Imaging diffusion in a microfluidic device by third harmonic microscopy,” Exp. Fluids 53, 777–782 (2012).
[CrossRef]

Canioni, L.

Carriles, R.

R. Carriles, D. Schafer, K. Sheetz, J. Field, R. Cisek, V. Barzda, A. Sylvester, and J. Squier, “Invited review article: imaging techniques for harmonic and multiphoton absorption fluorescence microscopy,” Rev. Sci. Instrum. 80, 081101 (2009).
[CrossRef]

Charpak, S.

L. Moreaux, O. Sandre, S. Charpak, M. Blanchard-Desce, and J. Mertz, “Coherent scattering in multi-harmonic light microscopy,” Biophys. J. 80, 1568–1574 (2001).
[CrossRef]

Cheng, J.-X.

S. Yue, M. N. Slipchenko, and J.-X. Cheng, “Multimodal nonlinear optical microscopy,” Laser Photon. Rev. 5, 496–512 (2011).
[CrossRef]

J.-X. Cheng and X. Xie, “Green’s function formulation for third-harmonic generation microscopy,” J. Opt. Soc. Am. B 19, 1604–1610 (2002).
[CrossRef]

Cisek, R.

R. Carriles, D. Schafer, K. Sheetz, J. Field, R. Cisek, V. Barzda, A. Sylvester, and J. Squier, “Invited review article: imaging techniques for harmonic and multiphoton absorption fluorescence microscopy,” Rev. Sci. Instrum. 80, 081101 (2009).
[CrossRef]

de Kock, C. P. J.

S. Witte, A. Negrean, J. C. Lodder, C. P. J. de Kock, G. Testa Silva, H. D. Mansvelder, and M. Louise Groot, “Label-free live brain imaging and targeted patching with third-harmonic generation microscopy,” Proc. Natl. Acad. Sci. USA 108, 5970–5975 (2011).
[CrossRef]

Debarre, D.

N. Olivier, M. A. Luengo-Oroz, L. Duloquin, E. Faure, T. Savy, I. Veilleux, X. Solinas, D. Debarre, P. Bourgine, A. Santos, N. Peyrieras, and E. Beaurepaire, “Cell lineage reconstruction of early zebrafish embryos using label-free nonlinear microscopy,” Science 329, 967–971 (2010).
[CrossRef]

D. Debarre, N. Olivier, and E. Beaurepaire, “Signal epidetection in third-harmonic generation microscopy of turbid media,” Opt. Express 15, 8913–8924 (2007).
[CrossRef]

Duloquin, L.

N. Olivier, M. A. Luengo-Oroz, L. Duloquin, E. Faure, T. Savy, I. Veilleux, X. Solinas, D. Debarre, P. Bourgine, A. Santos, N. Peyrieras, and E. Beaurepaire, “Cell lineage reconstruction of early zebrafish embryos using label-free nonlinear microscopy,” Science 329, 967–971 (2010).
[CrossRef]

Faure, E.

N. Olivier, M. A. Luengo-Oroz, L. Duloquin, E. Faure, T. Savy, I. Veilleux, X. Solinas, D. Debarre, P. Bourgine, A. Santos, N. Peyrieras, and E. Beaurepaire, “Cell lineage reconstruction of early zebrafish embryos using label-free nonlinear microscopy,” Science 329, 967–971 (2010).
[CrossRef]

Field, J.

R. Carriles, D. Schafer, K. Sheetz, J. Field, R. Cisek, V. Barzda, A. Sylvester, and J. Squier, “Invited review article: imaging techniques for harmonic and multiphoton absorption fluorescence microscopy,” Rev. Sci. Instrum. 80, 081101 (2009).
[CrossRef]

Fujita, K.

Halfmann, T.

U. Petzold, A. Büchel, and T. Halfmann, “Effects of laser polarization and interface orientation in harmonic generation microscopy,” Opt. Express 20, 3654–3662 (2012).
[CrossRef]

U. Petzold, A. Büchel, S. Hardt, and T. Halfmann, “Imaging diffusion in a microfluidic device by third harmonic microscopy,” Exp. Fluids 53, 777–782 (2012).
[CrossRef]

Hardt, S.

U. Petzold, A. Büchel, S. Hardt, and T. Halfmann, “Imaging diffusion in a microfluidic device by third harmonic microscopy,” Exp. Fluids 53, 777–782 (2012).
[CrossRef]

Hashimoto, M.

Hecht, B.

L. Novotny and B. Hecht, Principles of Nano-Optics (Cambridge University, 2006), pp. 1–94.

Kaneko, T.

Kawata, S.

Kobayashi, M.

Krauss, G.

R. Selm, G. Krauss, A. Leitenstorfer, and A. Zumbusch, “Simultaneous second-harmonic generation, third-harmonic generation, and four-wave mixing microscopy with single sub-8 fs laser pulses,” Appl. Phys. Lett. 99, 181124 (2011).
[CrossRef]

Leitenstorfer, A.

R. Selm, G. Krauss, A. Leitenstorfer, and A. Zumbusch, “Simultaneous second-harmonic generation, third-harmonic generation, and four-wave mixing microscopy with single sub-8 fs laser pulses,” Appl. Phys. Lett. 99, 181124 (2011).
[CrossRef]

Lodder, J. C.

S. Witte, A. Negrean, J. C. Lodder, C. P. J. de Kock, G. Testa Silva, H. D. Mansvelder, and M. Louise Groot, “Label-free live brain imaging and targeted patching with third-harmonic generation microscopy,” Proc. Natl. Acad. Sci. USA 108, 5970–5975 (2011).
[CrossRef]

Louise Groot, M.

S. Witte, A. Negrean, J. C. Lodder, C. P. J. de Kock, G. Testa Silva, H. D. Mansvelder, and M. Louise Groot, “Label-free live brain imaging and targeted patching with third-harmonic generation microscopy,” Proc. Natl. Acad. Sci. USA 108, 5970–5975 (2011).
[CrossRef]

Luengo-Oroz, M. A.

N. Olivier, M. A. Luengo-Oroz, L. Duloquin, E. Faure, T. Savy, I. Veilleux, X. Solinas, D. Debarre, P. Bourgine, A. Santos, N. Peyrieras, and E. Beaurepaire, “Cell lineage reconstruction of early zebrafish embryos using label-free nonlinear microscopy,” Science 329, 967–971 (2010).
[CrossRef]

Mansvelder, H. D.

S. Witte, A. Negrean, J. C. Lodder, C. P. J. de Kock, G. Testa Silva, H. D. Mansvelder, and M. Louise Groot, “Label-free live brain imaging and targeted patching with third-harmonic generation microscopy,” Proc. Natl. Acad. Sci. USA 108, 5970–5975 (2011).
[CrossRef]

Mertz, J.

L. Moreaux, O. Sandre, S. Charpak, M. Blanchard-Desce, and J. Mertz, “Coherent scattering in multi-harmonic light microscopy,” Biophys. J. 80, 1568–1574 (2001).
[CrossRef]

L. Moreaux, O. Sandre, and J. Mertz, “Membrane imaging by second-harmonic generation microscopy,” J. Opt. Soc. Am. B 17, 1685–1694 (2000).
[CrossRef]

Minamikawa, T.

Moreaux, L.

L. Moreaux, O. Sandre, S. Charpak, M. Blanchard-Desce, and J. Mertz, “Coherent scattering in multi-harmonic light microscopy,” Biophys. J. 80, 1568–1574 (2001).
[CrossRef]

L. Moreaux, O. Sandre, and J. Mertz, “Membrane imaging by second-harmonic generation microscopy,” J. Opt. Soc. Am. B 17, 1685–1694 (2000).
[CrossRef]

Müller, M.

Nakamura, O.

Negrean, A.

S. Witte, A. Negrean, J. C. Lodder, C. P. J. de Kock, G. Testa Silva, H. D. Mansvelder, and M. Louise Groot, “Label-free live brain imaging and targeted patching with third-harmonic generation microscopy,” Proc. Natl. Acad. Sci. USA 108, 5970–5975 (2011).
[CrossRef]

Novotny, L.

L. Novotny and B. Hecht, Principles of Nano-Optics (Cambridge University, 2006), pp. 1–94.

Oh-e, M.

Olivier, N.

N. Olivier, M. A. Luengo-Oroz, L. Duloquin, E. Faure, T. Savy, I. Veilleux, X. Solinas, D. Debarre, P. Bourgine, A. Santos, N. Peyrieras, and E. Beaurepaire, “Cell lineage reconstruction of early zebrafish embryos using label-free nonlinear microscopy,” Science 329, 967–971 (2010).
[CrossRef]

N. Olivier and E. Beaurepaire, “Third-harmonic generation microscopy with focus-engineered beams: a numerical study,” Opt. Express 16, 14703–14715 (2008).
[CrossRef]

D. Debarre, N. Olivier, and E. Beaurepaire, “Signal epidetection in third-harmonic generation microscopy of turbid media,” Opt. Express 15, 8913–8924 (2007).
[CrossRef]

Oron, D.

Pagnoux, D.

Patel, J. S.

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]

Petzold, U.

U. Petzold, A. Büchel, S. Hardt, and T. Halfmann, “Imaging diffusion in a microfluidic device by third harmonic microscopy,” Exp. Fluids 53, 777–782 (2012).
[CrossRef]

U. Petzold, A. Büchel, and T. Halfmann, “Effects of laser polarization and interface orientation in harmonic generation microscopy,” Opt. Express 20, 3654–3662 (2012).
[CrossRef]

Peyrieras, N.

N. Olivier, M. A. Luengo-Oroz, L. Duloquin, E. Faure, T. Savy, I. Veilleux, X. Solinas, D. Debarre, P. Bourgine, A. Santos, N. Peyrieras, and E. Beaurepaire, “Cell lineage reconstruction of early zebrafish embryos using label-free nonlinear microscopy,” Science 329, 967–971 (2010).
[CrossRef]

Pillai, R. S.

Rivet, S.

Roy, P.

Sandre, O.

L. Moreaux, O. Sandre, S. Charpak, M. Blanchard-Desce, and J. Mertz, “Coherent scattering in multi-harmonic light microscopy,” Biophys. J. 80, 1568–1574 (2001).
[CrossRef]

L. Moreaux, O. Sandre, and J. Mertz, “Membrane imaging by second-harmonic generation microscopy,” J. Opt. Soc. Am. B 17, 1685–1694 (2000).
[CrossRef]

Santos, A.

N. Olivier, M. A. Luengo-Oroz, L. Duloquin, E. Faure, T. Savy, I. Veilleux, X. Solinas, D. Debarre, P. Bourgine, A. Santos, N. Peyrieras, and E. Beaurepaire, “Cell lineage reconstruction of early zebrafish embryos using label-free nonlinear microscopy,” Science 329, 967–971 (2010).
[CrossRef]

Sarger, L.

Savy, T.

N. Olivier, M. A. Luengo-Oroz, L. Duloquin, E. Faure, T. Savy, I. Veilleux, X. Solinas, D. Debarre, P. Bourgine, A. Santos, N. Peyrieras, and E. Beaurepaire, “Cell lineage reconstruction of early zebrafish embryos using label-free nonlinear microscopy,” Science 329, 967–971 (2010).
[CrossRef]

Schafer, D.

R. Carriles, D. Schafer, K. Sheetz, J. Field, R. Cisek, V. Barzda, A. Sylvester, and J. Squier, “Invited review article: imaging techniques for harmonic and multiphoton absorption fluorescence microscopy,” Rev. Sci. Instrum. 80, 081101 (2009).
[CrossRef]

Schins, J. M.

Schrama, T.

Selm, R.

R. Selm, G. Krauss, A. Leitenstorfer, and A. Zumbusch, “Simultaneous second-harmonic generation, third-harmonic generation, and four-wave mixing microscopy with single sub-8 fs laser pulses,” Appl. Phys. Lett. 99, 181124 (2011).
[CrossRef]

Sheetz, K.

R. Carriles, D. Schafer, K. Sheetz, J. Field, R. Cisek, V. Barzda, A. Sylvester, and J. Squier, “Invited review article: imaging techniques for harmonic and multiphoton absorption fluorescence microscopy,” Rev. Sci. Instrum. 80, 081101 (2009).
[CrossRef]

Silberberg, Y.

D. Oron and Y. Silberberg, “Third-harmonic generation with cylindrical Gaussian beams,” J. Opt. Soc. Am. B 21, 1964–1968 (2004).
[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]

Slipchenko, M. N.

S. Yue, M. N. Slipchenko, and J.-X. Cheng, “Multimodal nonlinear optical microscopy,” Laser Photon. Rev. 5, 496–512 (2011).
[CrossRef]

Solinas, X.

N. Olivier, M. A. Luengo-Oroz, L. Duloquin, E. Faure, T. Savy, I. Veilleux, X. Solinas, D. Debarre, P. Bourgine, A. Santos, N. Peyrieras, and E. Beaurepaire, “Cell lineage reconstruction of early zebrafish embryos using label-free nonlinear microscopy,” Science 329, 967–971 (2010).
[CrossRef]

Squier, J.

R. Carriles, D. Schafer, K. Sheetz, J. Field, R. Cisek, V. Barzda, A. Sylvester, and J. Squier, “Invited review article: imaging techniques for harmonic and multiphoton absorption fluorescence microscopy,” Rev. Sci. Instrum. 80, 081101 (2009).
[CrossRef]

J. M. Schins, T. Schrama, J. Squier, G. J. Brakenhoff, and M. Müller, “Determination of material properties by use of third-harmonic generation microscopy,” J. Opt. Soc. Am. B 19, 1627–1634 (2002).
[CrossRef]

J. Squier and M. Müller, “High resolution nonlinear microscopy: a review of sources and methods for achieving optimal imaging,” Rev. Sci. Instrum. 72, 2855–2867 (2001).
[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]

J. Squier, M. Müller, G. J. Brakenhoff, and K. R. Wilson, “Third harmonic generation microscopy,” Opt. Express 3, 315–324 (1998).
[CrossRef]

Sylvester, A.

R. Carriles, D. Schafer, K. Sheetz, J. Field, R. Cisek, V. Barzda, A. Sylvester, and J. Squier, “Invited review article: imaging techniques for harmonic and multiphoton absorption fluorescence microscopy,” Rev. Sci. Instrum. 80, 081101 (2009).
[CrossRef]

Takamatsu, T.

Testa Silva, G.

S. Witte, A. Negrean, J. C. Lodder, C. P. J. de Kock, G. Testa Silva, H. D. Mansvelder, and M. Louise Groot, “Label-free live brain imaging and targeted patching with third-harmonic generation microscopy,” Proc. Natl. Acad. Sci. USA 108, 5970–5975 (2011).
[CrossRef]

Veilleux, I.

N. Olivier, M. A. Luengo-Oroz, L. Duloquin, E. Faure, T. Savy, I. Veilleux, X. Solinas, D. Debarre, P. Bourgine, A. Santos, N. Peyrieras, and E. Beaurepaire, “Cell lineage reconstruction of early zebrafish embryos using label-free nonlinear microscopy,” Science 329, 967–971 (2010).
[CrossRef]

Wilson, K. R.

J. Squier, M. Müller, G. J. Brakenhoff, and K. R. Wilson, “Third harmonic generation microscopy,” Opt. Express 3, 315–324 (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]

Witte, S.

S. Witte, A. Negrean, J. C. Lodder, C. P. J. de Kock, G. Testa Silva, H. D. Mansvelder, and M. Louise Groot, “Label-free live brain imaging and targeted patching with third-harmonic generation microscopy,” Proc. Natl. Acad. Sci. USA 108, 5970–5975 (2011).
[CrossRef]

Xie, X.

Yelin, D.

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]

Yokoyama, H.

Yue, S.

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Supplementary Material (2)

» Media 1: MOV (208129 KB)     
» Media 2: MOV (60975 KB)     

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Figures (7)

Fig. 1.
Fig. 1.

Experimental setup of our homemade nonlinear optical microscope.

Fig. 2.
Fig. 2.

(left) Schematic sketch of the geometry of the fused silica capillary and the laser focus. In our experiments we monitor the outer surface of the capillary in the refractive index-matched liquid. For all experiments the linear polarization is along the x axis. (right) Image of an xz cut through the capillary (oriented with the symmetry axis in the y direction) recorded by THG microscopy. The fundamental beam propagates in the z direction. Red color indicates large THG intensity, and blue color indicates low THG intensity. We choose the origin of the coordinate system in the center of the capillary. The angle θ describes the orientation of the interface (i.e., given by the normal vector) in the xz plane, i.e., with regard to the optical axis defined by the fundamental laser beam. The angle θ=0° corresponds to an interface orientation perpendicular to the optical axis. The angle θ=90° corresponds to an interface orientation parallel to the optical axis. To indicate the experimental geometry for the determination of THG intensity profiles, we schematically depict the shape of the laser focus (red) at a specific data point in the upper right part of the image. The FWHM decreases from 30 μm at θ=0° to 2 μm at θ=90°. We provide a detailed study and interpretation of THG resolution at interfaces of varying orientation in our previous work [12]. A glass ring is attached to the microscope slide. The volume inside this setup contains approximately 3 mm of index-matching fluid with a flat surface.

Fig. 3.
Fig. 3.

Normalized measured THG intensity profiles in the xy plane for different interface orientations with respect to the optical axis, determined by the angle θ in the xz plane (see Fig. 2). The fundamental beam propagates in the z direction. Red color indicates large measured THG intensity, and white color indicates low measured THG intensity. To guide the eye of the reader, around each THG spot we added a black line indicating the 1/e2 intensity of the maximum THG intensity. This area around the maxima typically contains 80 data points. The dotted circle indicates the theoretical maximum deflection of the fundamental laser corresponding to a numerical aperture NAF=0.22. We note that the center position of the single pictures slightly fluctuates due to limited precision in the positioning of the capillary and the PH. However, this has no effect upon the general characteristics of THG emission. (Media 1)

Fig. 4.
Fig. 4.

Numerical simulation of the THG intensity profile I(3ω)(θ,φ) in the xy plane for different interface orientations with respect to the optical axis, determined by the angle θ in the xz plane (compare experimental data in Fig. 3). Blue color indicates large calculated THG intensity, and white color indicates low calculated THG intensity. For other details, please also see caption of Fig. 3. We calculated I(3ω)(θ,φ) as described in Appendix A, on a grid of 100×100 points. The parameters in the simulation are λ=810nm, NAF=0.22, NAC=0.65, focal length of the focusing lens f0=16mm, distance of detector from the focus L=17mm, indices of refraction nω=1.45315 and n3ω=1.498, and beam waist at the entrance surface of the objective w=1.8mm. The results of the numerical simulations are in very good agreement with the experimental data in Fig. 3.

Fig. 5.
Fig. 5.

(left) Schematic sketch of the geometry of the fused silica capillary and the laser focus. In our experiments we monitor the outer surface of the capillary in the refractive index-matched liquid. For all experiments the linear polarization is along the x axis. (right) Image of a xy cut through the capillary (oriented with the symmetry axis in the z direction) recorded by THG microscopy. The fundamental beam propagates in the z direction. Red color indicates large THG intensity, and blue color indicates low THG intensity. We choose the origin of the coordinate system in the center of the capillary. The angle φ describes the orientation of the interface (i.e., given by the normal vector) in the xy plane. To indicate the experimental geometry for the determination of THG intensity profiles, we schematically depict the shape of the laser focus (red) at a specific data point in the upper right part of the image. For discussion of further data below we also added a tangent (dark green line) at a specific image point. The image shows a slow signal modulation along the x direction due to alignment variations in the mirror-scanning setup. In addition, we have local in homogeneities in the sample.

Fig. 6.
Fig. 6.

Normalized measured THG intensity profiles in the xy plane for different interface orientations, determined by the angle φ in the xy plane (see Fig. 5). The fundamental beam propagates in the z direction. Red color indicates large measured THG intensity, and white color indicates zero THG intensity. To guide the eye of the reader, around each THG spot we added a black line indicating the 1/e2 intensity of the maximum THG intensity. The dotted circle indicates the theoretical maximum deflection of the fundamental laser corresponding to a numerical aperture NAF=0.22. We also added the measured orientation of the interface (green line; compare also tangent in Fig. 5) and the dashed connection line between the two third harmonic spots. In the measurement, the distance of the objective to the condenser is smaller compared to the experiment in Fig. 3. Therefore, the extension of the beam profiles is smaller compared to Fig. 3. We also note that the slightly asymmetric intensity distribution in the two THG spots in each graph is due to a small deviation (by 1.2°) of the capillary orientation in the x and y directions from perfect parallel alignment with the optical axis. For a more detailed series of the data, see supplementary material to this paper in Media 2.

Fig. 7.
Fig. 7.

Simulated THG intensity profiles I(3ω)(θ,φ) in the xy plane for different interface orientations, determined by the angle φ in the xy plane (see Fig. 5). Blue color indicates large calculated THG intensity, and white color indicates zero calculated THG intensity. For details on the numerical simulation, see Appendix A and compare captions of Figs. 4 and 6. The distance of the detector from the focus is L=8mm.

Equations (8)

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E⃗(r⃗)=E⃗(ρ,z)=E⃗0eikωz1+2iz/kωw02e(ρ2w0211+2iz/w02),
P⃗(3ω)(r⃗)=ε0e⃗iχijkl(3ω)(r⃗)Ej(r⃗)Ek(r⃗)El(r⃗),
P⃗(3ω)=(Px(3ω)Py(3ω)Pz(3ω))=ε0χ0(3ω)(Ex(3Ex2+Ey2+Ez2)Ey(Ex2+3Ey2+Ez2)Ez(Ex2+Ey2+3Ez2)).
∇⃗×(∇⃗×E⃗(3ω)(r⃗))+k3ω2E⃗(3ω)(r⃗)=(3ω)2ε0c2P⃗(3ω)(r⃗),
E⃗(3ω)(r⃗)=VdVG^(r⃗r⃗)P⃗(3ω)(r⃗)=VdVe⃗(δijninj)G0Pj(3ω)(r⃗),
(Er3ω(r⃗)Eθ3ω(r⃗)Eφ3ω(r⃗))=T(Er3ω(r⃗)Ey3ω(r⃗)Ez3ω(r⃗))=VdVT·G^(r⃗r⃗)·P⃗(3ω)(r⃗)=exp(ik3ωr)4πr(000cosθcosφcosθsinφsinφsinφcosφ0)×VdVexp(ik3ωn⃗·r⃗)(Px(3ω)(r⃗)Py(3ω)(r⃗)Pz(3ω)(r⃗)).
Π(3ω)=cε0r2202πdφ0θmaxdθsinθ|E⃗(3ω)(r⃗)|2I(3ω)(θ,φ)dΩ,
I(3ω)(θ,φ)=cε0r22|E⃗(3ω)(r⃗)|2,

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