Abstract

We use a finite-difference time-domain method to model the experiments of second-harmonic generation at the apex of a metallic tip used in a scanning near-field optical microscope. We calculate the linear diffracted field and the second-harmonic field. In the near field we compare the confinement of the two fields around the apex. In the far field we determine the spectral responses versus the sample tip coupling.

© 2005 Optical Society of America

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  1. S. I. Bozhevolnyi, K. Pedersen, T. Skettrup, X. Zhang, and M. Belmote, "Far- and near-field second-harmonic imaging of ferroelectric domain walls," Opt. Commun. 152, 221-224 (1998).
    [CrossRef]
  2. I. Smolyaninov, H. Y. Liang, C. H. Lee, C. C. Davis, V. Nagarajan, and R. Ramesh, "Near-field second harmonic imaging of c/a/c/a polydomain structure of epitaxial PbZrxTi1-xO3 thin films," J. Microsc. 202, 250-254 (2001).
    [CrossRef] [PubMed]
  3. A. V. Zayats, T. Kalkbrenner, V. Sandoghdar, and J. Mlynek, "Second harmonic generation from individual surface defects under local excitation," Phys. Rev. B 61, 4545-4548 (2000).
    [CrossRef]
  4. S. Takahashi and A. V. Zayats, "Near-field second-harmonic generation at a metal tip apex," Appl. Phys. Lett. 80, 3479-3481 (2002).
    [CrossRef]
  5. R. Fikri, D. Barchiesi, F. H'Dhili, R. Bachelot, A. Vial, and P. Royer, "Modeling recent experiments of apertureless near-field optical microscopy using 2d finite element method," Opt. Commun. 221, 13-22 (2003).
    [CrossRef]
  6. A. Bouhelier, M. Beverluis, A. Hartschuh, and L. Novotny, "Near-field second-harmonic generation induced by local field enhancement," Phys. Rev. Lett. 90, 013903/1-4 (2003).
    [CrossRef]
  7. A. V. Zayats and V. Sandoghdar, "Apertureless scanning near-field second-harmonic microscopy." Opt. Commun. 178, 245-249 (2000).
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    [CrossRef]
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  12. A. Bourgeade and E. Freysz, "Computational modeling of second-harmonic generation by solution of full-wave vector Maxwell equations," J. Opt. Soc. Am. B 17, 226-234 (2000).
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  13. W. Nakagawa, R. C. Tyan, and Y. Fainman, "Analysis of enhanced second-harmonic generation in periodic nanostructures using modified rigorous coupled-wave analysis in the undepleted-pump approximation," J. Opt. Soc. Am. A 19, 1919-1928 (2002).
    [CrossRef]
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  15. F. Raineri, Y. Dumeige, A. Levenson, and X. Letartre, "Nonlinear decoupled FDTD code: phase-matching in 2D defective photonic crystal," Electron. Lett. 38, 1704-1706 (2002).
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  18. E. Vasilyeva and A. Taflove, "Three-dimensional modeling of amplitude-object imaging in scanning near-field optical microscopy," Opt. Lett. 23, 1155-1157 (1998).
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  19. J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, "Interactions between light waves in nonlinear dielectric," Phys. Rev. 127, 1918-1939 (1962).
    [CrossRef]
  20. D. A. Kleinman, "Nonlinear dielectric polarization in optical media," Phys. Rev. 126, 1977-1979 (1962).
    [CrossRef]
  21. P. S. Pershan, "Nonlinear optical properties of solids: energy considerations," Phys. Rev. 130, 919-929 (1963).
    [CrossRef]
  22. N. Bloembergen, R. K. Chang, and C. H. Lee, "Second harmonic generation of light in reflexion from media with inversion symmetry," Phys. Rev. Lett. 16, 986-989 (1966).
    [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] [PubMed]
  31. G. Parent, D. Van-Labeke, and F. I. Baida, "Theoretical study of transient phenomena in near-field optics," J. Microsc. 202, 296-306 (2001).
    [CrossRef] [PubMed]
  32. J. P. Berenger, "A perfectly matched layer for the absorption of electromagnetic waves," J. Comput. Phys. 114, 185-200 (1994).
    [CrossRef]
  33. J. J. Greffet and C. Baylard, "Nonspecular astigmatic reflection of a 3D Gaussian beam on an interface," Opt. Commun. 93, 271-276 (1992).
    [CrossRef]
  34. W. Nasalski, "Longitudinal and transverse effects of nonspecular reflection," J. Opt. Soc. Am. A 13, 172-181 (1996).
    [CrossRef]
  35. F. I. Baida, D. Van Labeke, and J. M. Vigoureux, "Theoretical study of near-field surface plasmon excitation, propagation and diffraction," Opt. Commun. 171, 317-331 (1999).
    [CrossRef]
  36. F. I. Baida, D. Barchiesi, and D. Vanlabeke, "Near-field effects of focused illumination on periodic structures in scanning tunneling optical microscopy," Opt. Lett. 24, 1587-1589 (1999).
    [CrossRef]
  37. F. I. Baida, D. Van Labeke, and J.-M. Vigoureux, "Numerical study of the displacement of a three-dimensional Gaussian beam transmitted at total internal reflection. Near-field applications," J. Opt. Soc. Am. A 17, 858-866 (2000).
  38. L. Novotny, R. X. Bian, and X. S. Xie, "Theory of nanometric optical tweezers," Phys. Rev. Lett. 79, 645-648 (1997).
    [CrossRef]
  39. A. Madrazo, R. Carminati, M. Nieto-Vesperinas, and J. J. Greffet, "Polarization effects in the optical interaction between a nanoparticle and a corrugated surface: implications for apertureless near-field microscopy," J. Opt. Soc. Am. A 15, 109-119 (1998).
    [CrossRef]
  40. F. I. Baida and D. Van Labeke, "Light transmission by subwavelength annular aperture arrays in metallic films," Opt. Commun. 209, 17-22 (2002).
    [CrossRef]
  41. F. I. Baida and D. Van Labeke, "Three-dimensional structures for enhanced transmission through a metallic film: annular aperture arrays," Phys. Rev. B 67, 155314/1-7 (2003).
    [CrossRef]
  42. F. I. Baida, D. Van Labeke, and G. Granet, "Origin of the super-enhanced light transmission through a 2-D metallic annular aperture array: a study of photonic bands," Appl. Phys. B: Lasers Opt. 79, 1-8 (2004).
    [CrossRef]

2004 (1)

F. I. Baida, D. Van Labeke, and G. Granet, "Origin of the super-enhanced light transmission through a 2-D metallic annular aperture array: a study of photonic bands," Appl. Phys. B: Lasers Opt. 79, 1-8 (2004).
[CrossRef]

2003 (3)

F. I. Baida and D. Van Labeke, "Three-dimensional structures for enhanced transmission through a metallic film: annular aperture arrays," Phys. Rev. B 67, 155314/1-7 (2003).
[CrossRef]

R. Fikri, D. Barchiesi, F. H'Dhili, R. Bachelot, A. Vial, and P. Royer, "Modeling recent experiments of apertureless near-field optical microscopy using 2d finite element method," Opt. Commun. 221, 13-22 (2003).
[CrossRef]

A. Bouhelier, M. Beverluis, A. Hartschuh, and L. Novotny, "Near-field second-harmonic generation induced by local field enhancement," Phys. Rev. Lett. 90, 013903/1-4 (2003).
[CrossRef]

2002 (5)

S. Takahashi and A. V. Zayats, "Near-field second-harmonic generation at a metal tip apex," Appl. Phys. Lett. 80, 3479-3481 (2002).
[CrossRef]

F. Raineri, Y. Dumeige, A. Levenson, and X. Letartre, "Nonlinear decoupled FDTD code: phase-matching in 2D defective photonic crystal," Electron. Lett. 38, 1704-1706 (2002).
[CrossRef]

F. I. Baida and D. Van Labeke, "Light transmission by subwavelength annular aperture arrays in metallic films," Opt. Commun. 209, 17-22 (2002).
[CrossRef]

W. Nakagawa, R. C. Tyan, and Y. Fainman, "Analysis of enhanced second-harmonic generation in periodic nanostructures using modified rigorous coupled-wave analysis in the undepleted-pump approximation," J. Opt. Soc. Am. A 19, 1919-1928 (2002).
[CrossRef]

G. D'Aguanno, M. Centini, C. Sibilia, M. Bertolotti, M. J. Bloemer, and C. M. Bowden, "Generalized coupled-mode theory for chi(2) interactions in finite multilayered structures." J. Opt. Soc. Am. B 19, 2111-2121 (2002).
[CrossRef]

2001 (2)

G. Parent, D. Van-Labeke, and F. I. Baida, "Theoretical study of transient phenomena in near-field optics," J. Microsc. 202, 296-306 (2001).
[CrossRef] [PubMed]

I. Smolyaninov, H. Y. Liang, C. H. Lee, C. C. Davis, V. Nagarajan, and R. Ramesh, "Near-field second harmonic imaging of c/a/c/a polydomain structure of epitaxial PbZrxTi1-xO3 thin films," J. Microsc. 202, 250-254 (2001).
[CrossRef] [PubMed]

2000 (5)

A. V. Zayats, T. Kalkbrenner, V. Sandoghdar, and J. Mlynek, "Second harmonic generation from individual surface defects under local excitation," Phys. Rev. B 61, 4545-4548 (2000).
[CrossRef]

A. V. Zayats and V. Sandoghdar, "Apertureless scanning near-field second-harmonic microscopy." Opt. Commun. 178, 245-249 (2000).
[CrossRef]

M. A. Alsunaidi, H. M. Masoudi, and M. Arnold, "A time-domain algorithm for the analysis of second-harmonic generation in nonlinear optical structures," IEEE Photonics Technol. Lett. 12, 395-397 (2000).
[CrossRef]

F. I. Baida, D. Van Labeke, and J.-M. Vigoureux, "Numerical study of the displacement of a three-dimensional Gaussian beam transmitted at total internal reflection. Near-field applications," J. Opt. Soc. Am. A 17, 858-866 (2000).

A. Bourgeade and E. Freysz, "Computational modeling of second-harmonic generation by solution of full-wave vector Maxwell equations," J. Opt. Soc. Am. B 17, 226-234 (2000).
[CrossRef]

1999 (3)

F. I. Baida, D. Barchiesi, and D. Vanlabeke, "Near-field effects of focused illumination on periodic structures in scanning tunneling optical microscopy," Opt. Lett. 24, 1587-1589 (1999).
[CrossRef]

F. I. Baida, D. Van Labeke, and J. M. Vigoureux, "Theoretical study of near-field surface plasmon excitation, propagation and diffraction," Opt. Commun. 171, 317-331 (1999).
[CrossRef]

Z. Y. Li, B. Y. Gu, and G. Z. Yang, "Strong localization of near field second harmonic generation for nonlinear mesoscopic surface structures," Phys. Rev. B 59, 12622-12626 (1999).
[CrossRef]

1998 (5)

S. Enoch, "Second-harmonic scattered light from one-dimensional rough thin films," Opt. Commun. 148, 137-143 (1998).
[CrossRef]

V. M. Shalaev and A. K. Sarychev, "Non-linear optics of random metal-dielectric film," Phys. Rev. B 57, 13265-13288 (1998).
[CrossRef]

S. I. Bozhevolnyi, K. Pedersen, T. Skettrup, X. Zhang, and M. Belmote, "Far- and near-field second-harmonic imaging of ferroelectric domain walls," Opt. Commun. 152, 221-224 (1998).
[CrossRef]

E. Vasilyeva and A. Taflove, "Three-dimensional modeling of amplitude-object imaging in scanning near-field optical microscopy," Opt. Lett. 23, 1155-1157 (1998).
[CrossRef]

A. Madrazo, R. Carminati, M. Nieto-Vesperinas, and J. J. Greffet, "Polarization effects in the optical interaction between a nanoparticle and a corrugated surface: implications for apertureless near-field microscopy," J. Opt. Soc. Am. A 15, 109-119 (1998).
[CrossRef]

1997 (1)

L. Novotny, R. X. Bian, and X. S. Xie, "Theory of nanometric optical tweezers," Phys. Rev. Lett. 79, 645-648 (1997).
[CrossRef]

1996 (2)

B. S. Mendoza and W. L. Mochán, "Exactly solvable model of surface second harmonic generation," Phys. Rev. B 53, 4999-5006 (1996).
[CrossRef]

W. Nasalski, "Longitudinal and transverse effects of nonspecular reflection," J. Opt. Soc. Am. A 13, 172-181 (1996).
[CrossRef]

1994 (1)

J. P. Berenger, "A perfectly matched layer for the absorption of electromagnetic waves," J. Comput. Phys. 114, 185-200 (1994).
[CrossRef]

1992 (1)

J. J. Greffet and C. Baylard, "Nonspecular astigmatic reflection of a 3D Gaussian beam on an interface," Opt. Commun. 93, 271-276 (1992).
[CrossRef]

1991 (1)

1988 (2)

1987 (1)

J. E. Sipe, D. J. Moss, and H. M. van Driel, "Phenomenological theory of optical second- and third-harmonic generation from cubic and centrosymmetric crystals," Phys. Rev. B 35, 1129-1141 (1987).
[CrossRef]

1968 (1)

N. Bloembergen, R. K. Chang, S. S. Jha, and C. H. Lee, "Optical second harmonic generation in reflexion from media with inversion symmetry," Phys. Rev. 174, 813-822 (1968).
[CrossRef]

1966 (2)

N. Bloembergen, R. K. Chang, and C. H. Lee, "Second harmonic generation of light in reflexion from media with inversion symmetry," Phys. Rev. Lett. 16, 986-989 (1966).
[CrossRef]

K. S. Yee, "Numerical solution of initial boundary value problems involving Maxwell's equations," IEEE Trans. Antennas Propag. 14, 302-307 (1966).
[CrossRef]

1963 (1)

P. S. Pershan, "Nonlinear optical properties of solids: energy considerations," Phys. Rev. 130, 919-929 (1963).
[CrossRef]

1962 (2)

J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, "Interactions between light waves in nonlinear dielectric," Phys. Rev. 127, 1918-1939 (1962).
[CrossRef]

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

Alsunaidi, M. A.

M. A. Alsunaidi, H. M. Masoudi, and M. Arnold, "A time-domain algorithm for the analysis of second-harmonic generation in nonlinear optical structures," IEEE Photonics Technol. Lett. 12, 395-397 (2000).
[CrossRef]

Armstrong, J. A.

J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, "Interactions between light waves in nonlinear dielectric," Phys. Rev. 127, 1918-1939 (1962).
[CrossRef]

Arnold, M.

M. A. Alsunaidi, H. M. Masoudi, and M. Arnold, "A time-domain algorithm for the analysis of second-harmonic generation in nonlinear optical structures," IEEE Photonics Technol. Lett. 12, 395-397 (2000).
[CrossRef]

Bachelot, R.

R. Fikri, D. Barchiesi, F. H'Dhili, R. Bachelot, A. Vial, and P. Royer, "Modeling recent experiments of apertureless near-field optical microscopy using 2d finite element method," Opt. Commun. 221, 13-22 (2003).
[CrossRef]

Baida, F. I.

F. I. Baida, D. Van Labeke, and G. Granet, "Origin of the super-enhanced light transmission through a 2-D metallic annular aperture array: a study of photonic bands," Appl. Phys. B: Lasers Opt. 79, 1-8 (2004).
[CrossRef]

F. I. Baida and D. Van Labeke, "Three-dimensional structures for enhanced transmission through a metallic film: annular aperture arrays," Phys. Rev. B 67, 155314/1-7 (2003).
[CrossRef]

F. I. Baida and D. Van Labeke, "Light transmission by subwavelength annular aperture arrays in metallic films," Opt. Commun. 209, 17-22 (2002).
[CrossRef]

G. Parent, D. Van-Labeke, and F. I. Baida, "Theoretical study of transient phenomena in near-field optics," J. Microsc. 202, 296-306 (2001).
[CrossRef] [PubMed]

F. I. Baida, D. Van Labeke, and J.-M. Vigoureux, "Numerical study of the displacement of a three-dimensional Gaussian beam transmitted at total internal reflection. Near-field applications," J. Opt. Soc. Am. A 17, 858-866 (2000).

F. I. Baida, D. Van Labeke, and J. M. Vigoureux, "Theoretical study of near-field surface plasmon excitation, propagation and diffraction," Opt. Commun. 171, 317-331 (1999).
[CrossRef]

F. I. Baida, D. Barchiesi, and D. Vanlabeke, "Near-field effects of focused illumination on periodic structures in scanning tunneling optical microscopy," Opt. Lett. 24, 1587-1589 (1999).
[CrossRef]

Barchiesi, D.

R. Fikri, D. Barchiesi, F. H'Dhili, R. Bachelot, A. Vial, and P. Royer, "Modeling recent experiments of apertureless near-field optical microscopy using 2d finite element method," Opt. Commun. 221, 13-22 (2003).
[CrossRef]

F. I. Baida, D. Barchiesi, and D. Vanlabeke, "Near-field effects of focused illumination on periodic structures in scanning tunneling optical microscopy," Opt. Lett. 24, 1587-1589 (1999).
[CrossRef]

Baylard, C.

J. J. Greffet and C. Baylard, "Nonspecular astigmatic reflection of a 3D Gaussian beam on an interface," Opt. Commun. 93, 271-276 (1992).
[CrossRef]

Belmote, M.

S. I. Bozhevolnyi, K. Pedersen, T. Skettrup, X. Zhang, and M. Belmote, "Far- and near-field second-harmonic imaging of ferroelectric domain walls," Opt. Commun. 152, 221-224 (1998).
[CrossRef]

Berenger, J. P.

J. P. Berenger, "A perfectly matched layer for the absorption of electromagnetic waves," J. Comput. Phys. 114, 185-200 (1994).
[CrossRef]

Bertolotti, M.

Beverluis, M.

A. Bouhelier, M. Beverluis, A. Hartschuh, and L. Novotny, "Near-field second-harmonic generation induced by local field enhancement," Phys. Rev. Lett. 90, 013903/1-4 (2003).
[CrossRef]

Bian, R. X.

L. Novotny, R. X. Bian, and X. S. Xie, "Theory of nanometric optical tweezers," Phys. Rev. Lett. 79, 645-648 (1997).
[CrossRef]

Bloembergen, N.

N. Bloembergen, R. K. Chang, S. S. Jha, and C. H. Lee, "Optical second harmonic generation in reflexion from media with inversion symmetry," Phys. Rev. 174, 813-822 (1968).
[CrossRef]

N. Bloembergen, R. K. Chang, and C. H. Lee, "Second harmonic generation of light in reflexion from media with inversion symmetry," Phys. Rev. Lett. 16, 986-989 (1966).
[CrossRef]

J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, "Interactions between light waves in nonlinear dielectric," Phys. Rev. 127, 1918-1939 (1962).
[CrossRef]

Bloemer, M. J.

Bouhelier, A.

A. Bouhelier, M. Beverluis, A. Hartschuh, and L. Novotny, "Near-field second-harmonic generation induced by local field enhancement," Phys. Rev. Lett. 90, 013903/1-4 (2003).
[CrossRef]

Bourgeade, A.

Bowden, C. M.

Bozhevolnyi, S. I.

S. I. Bozhevolnyi, K. Pedersen, T. Skettrup, X. Zhang, and M. Belmote, "Far- and near-field second-harmonic imaging of ferroelectric domain walls," Opt. Commun. 152, 221-224 (1998).
[CrossRef]

Carminati, R.

Centini, M.

Chang, R. K.

N. Bloembergen, R. K. Chang, S. S. Jha, and C. H. Lee, "Optical second harmonic generation in reflexion from media with inversion symmetry," Phys. Rev. 174, 813-822 (1968).
[CrossRef]

N. Bloembergen, R. K. Chang, and C. H. Lee, "Second harmonic generation of light in reflexion from media with inversion symmetry," Phys. Rev. Lett. 16, 986-989 (1966).
[CrossRef]

Coutaz, J. L.

D'Aguanno, G.

Davis, C. C.

I. Smolyaninov, H. Y. Liang, C. H. Lee, C. C. Davis, V. Nagarajan, and R. Ramesh, "Near-field second harmonic imaging of c/a/c/a polydomain structure of epitaxial PbZrxTi1-xO3 thin films," J. Microsc. 202, 250-254 (2001).
[CrossRef] [PubMed]

Ducuing, J.

J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, "Interactions between light waves in nonlinear dielectric," Phys. Rev. 127, 1918-1939 (1962).
[CrossRef]

Dumeige, Y.

F. Raineri, Y. Dumeige, A. Levenson, and X. Letartre, "Nonlinear decoupled FDTD code: phase-matching in 2D defective photonic crystal," Electron. Lett. 38, 1704-1706 (2002).
[CrossRef]

Enoch, S.

S. Enoch, "Second-harmonic scattered light from one-dimensional rough thin films," Opt. Commun. 148, 137-143 (1998).
[CrossRef]

Fainman, Y.

Fikri, R.

R. Fikri, D. Barchiesi, F. H'Dhili, R. Bachelot, A. Vial, and P. Royer, "Modeling recent experiments of apertureless near-field optical microscopy using 2d finite element method," Opt. Commun. 221, 13-22 (2003).
[CrossRef]

Freysz, E.

Granet, G.

F. I. Baida, D. Van Labeke, and G. Granet, "Origin of the super-enhanced light transmission through a 2-D metallic annular aperture array: a study of photonic bands," Appl. Phys. B: Lasers Opt. 79, 1-8 (2004).
[CrossRef]

Greffet, J. J.

Gu, B. Y.

Z. Y. Li, B. Y. Gu, and G. Z. Yang, "Strong localization of near field second harmonic generation for nonlinear mesoscopic surface structures," Phys. Rev. B 59, 12622-12626 (1999).
[CrossRef]

Hagness, S. C.

Hartschuh, A.

A. Bouhelier, M. Beverluis, A. Hartschuh, and L. Novotny, "Near-field second-harmonic generation induced by local field enhancement," Phys. Rev. Lett. 90, 013903/1-4 (2003).
[CrossRef]

H'Dhili, F.

R. Fikri, D. Barchiesi, F. H'Dhili, R. Bachelot, A. Vial, and P. Royer, "Modeling recent experiments of apertureless near-field optical microscopy using 2d finite element method," Opt. Commun. 221, 13-22 (2003).
[CrossRef]

Jha, S. S.

N. Bloembergen, R. K. Chang, S. S. Jha, and C. H. Lee, "Optical second harmonic generation in reflexion from media with inversion symmetry," Phys. Rev. 174, 813-822 (1968).
[CrossRef]

Joseph, R. M.

Kalkbrenner, T.

A. V. Zayats, T. Kalkbrenner, V. Sandoghdar, and J. Mlynek, "Second harmonic generation from individual surface defects under local excitation," Phys. Rev. B 61, 4545-4548 (2000).
[CrossRef]

Kleinman, D. A.

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

Lee, C. H.

I. Smolyaninov, H. Y. Liang, C. H. Lee, C. C. Davis, V. Nagarajan, and R. Ramesh, "Near-field second harmonic imaging of c/a/c/a polydomain structure of epitaxial PbZrxTi1-xO3 thin films," J. Microsc. 202, 250-254 (2001).
[CrossRef] [PubMed]

N. Bloembergen, R. K. Chang, S. S. Jha, and C. H. Lee, "Optical second harmonic generation in reflexion from media with inversion symmetry," Phys. Rev. 174, 813-822 (1968).
[CrossRef]

N. Bloembergen, R. K. Chang, and C. H. Lee, "Second harmonic generation of light in reflexion from media with inversion symmetry," Phys. Rev. Lett. 16, 986-989 (1966).
[CrossRef]

Letartre, X.

F. Raineri, Y. Dumeige, A. Levenson, and X. Letartre, "Nonlinear decoupled FDTD code: phase-matching in 2D defective photonic crystal," Electron. Lett. 38, 1704-1706 (2002).
[CrossRef]

Levenson, A.

F. Raineri, Y. Dumeige, A. Levenson, and X. Letartre, "Nonlinear decoupled FDTD code: phase-matching in 2D defective photonic crystal," Electron. Lett. 38, 1704-1706 (2002).
[CrossRef]

Li, Z. Y.

Z. Y. Li, B. Y. Gu, and G. Z. Yang, "Strong localization of near field second harmonic generation for nonlinear mesoscopic surface structures," Phys. Rev. B 59, 12622-12626 (1999).
[CrossRef]

Liang, H. Y.

I. Smolyaninov, H. Y. Liang, C. H. Lee, C. C. Davis, V. Nagarajan, and R. Ramesh, "Near-field second harmonic imaging of c/a/c/a polydomain structure of epitaxial PbZrxTi1-xO3 thin films," J. Microsc. 202, 250-254 (2001).
[CrossRef] [PubMed]

Madrazo, A.

Masoudi, H. M.

M. A. Alsunaidi, H. M. Masoudi, and M. Arnold, "A time-domain algorithm for the analysis of second-harmonic generation in nonlinear optical structures," IEEE Photonics Technol. Lett. 12, 395-397 (2000).
[CrossRef]

Maystre, D.

Mendoza, B. S.

B. S. Mendoza and W. L. Mochán, "Exactly solvable model of surface second harmonic generation," Phys. Rev. B 53, 4999-5006 (1996).
[CrossRef]

Mlynek, J.

A. V. Zayats, T. Kalkbrenner, V. Sandoghdar, and J. Mlynek, "Second harmonic generation from individual surface defects under local excitation," Phys. Rev. B 61, 4545-4548 (2000).
[CrossRef]

Mochán, W. L.

B. S. Mendoza and W. L. Mochán, "Exactly solvable model of surface second harmonic generation," Phys. Rev. B 53, 4999-5006 (1996).
[CrossRef]

Moss, D. J.

J. E. Sipe, D. J. Moss, and H. M. van Driel, "Phenomenological theory of optical second- and third-harmonic generation from cubic and centrosymmetric crystals," Phys. Rev. B 35, 1129-1141 (1987).
[CrossRef]

Nagarajan, V.

I. Smolyaninov, H. Y. Liang, C. H. Lee, C. C. Davis, V. Nagarajan, and R. Ramesh, "Near-field second harmonic imaging of c/a/c/a polydomain structure of epitaxial PbZrxTi1-xO3 thin films," J. Microsc. 202, 250-254 (2001).
[CrossRef] [PubMed]

Nakagawa, W.

Nasalski, W.

Nevière, M.

Nieto-Vesperinas, M.

Novotny, L.

A. Bouhelier, M. Beverluis, A. Hartschuh, and L. Novotny, "Near-field second-harmonic generation induced by local field enhancement," Phys. Rev. Lett. 90, 013903/1-4 (2003).
[CrossRef]

L. Novotny, R. X. Bian, and X. S. Xie, "Theory of nanometric optical tweezers," Phys. Rev. Lett. 79, 645-648 (1997).
[CrossRef]

Parent, G.

G. Parent, D. Van-Labeke, and F. I. Baida, "Theoretical study of transient phenomena in near-field optics," J. Microsc. 202, 296-306 (2001).
[CrossRef] [PubMed]

Pedersen, K.

S. I. Bozhevolnyi, K. Pedersen, T. Skettrup, X. Zhang, and M. Belmote, "Far- and near-field second-harmonic imaging of ferroelectric domain walls," Opt. Commun. 152, 221-224 (1998).
[CrossRef]

Pershan, P. S.

P. S. Pershan, "Nonlinear optical properties of solids: energy considerations," Phys. Rev. 130, 919-929 (1963).
[CrossRef]

J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, "Interactions between light waves in nonlinear dielectric," Phys. Rev. 127, 1918-1939 (1962).
[CrossRef]

Raineri, F.

F. Raineri, Y. Dumeige, A. Levenson, and X. Letartre, "Nonlinear decoupled FDTD code: phase-matching in 2D defective photonic crystal," Electron. Lett. 38, 1704-1706 (2002).
[CrossRef]

Ramesh, R.

I. Smolyaninov, H. Y. Liang, C. H. Lee, C. C. Davis, V. Nagarajan, and R. Ramesh, "Near-field second harmonic imaging of c/a/c/a polydomain structure of epitaxial PbZrxTi1-xO3 thin films," J. Microsc. 202, 250-254 (2001).
[CrossRef] [PubMed]

Reinisch, R.

Royer, P.

R. Fikri, D. Barchiesi, F. H'Dhili, R. Bachelot, A. Vial, and P. Royer, "Modeling recent experiments of apertureless near-field optical microscopy using 2d finite element method," Opt. Commun. 221, 13-22 (2003).
[CrossRef]

Sandoghdar, V.

A. V. Zayats, T. Kalkbrenner, V. Sandoghdar, and J. Mlynek, "Second harmonic generation from individual surface defects under local excitation," Phys. Rev. B 61, 4545-4548 (2000).
[CrossRef]

A. V. Zayats and V. Sandoghdar, "Apertureless scanning near-field second-harmonic microscopy." Opt. Commun. 178, 245-249 (2000).
[CrossRef]

Sarychev, A. K.

V. M. Shalaev and A. K. Sarychev, "Non-linear optics of random metal-dielectric film," Phys. Rev. B 57, 13265-13288 (1998).
[CrossRef]

Shalaev, V. M.

V. M. Shalaev and A. K. Sarychev, "Non-linear optics of random metal-dielectric film," Phys. Rev. B 57, 13265-13288 (1998).
[CrossRef]

Sibilia, C.

Sipe, J. E.

J. E. Sipe, D. J. Moss, and H. M. van Driel, "Phenomenological theory of optical second- and third-harmonic generation from cubic and centrosymmetric crystals," Phys. Rev. B 35, 1129-1141 (1987).
[CrossRef]

Skettrup, T.

S. I. Bozhevolnyi, K. Pedersen, T. Skettrup, X. Zhang, and M. Belmote, "Far- and near-field second-harmonic imaging of ferroelectric domain walls," Opt. Commun. 152, 221-224 (1998).
[CrossRef]

Smolyaninov, I.

I. Smolyaninov, H. Y. Liang, C. H. Lee, C. C. Davis, V. Nagarajan, and R. Ramesh, "Near-field second harmonic imaging of c/a/c/a polydomain structure of epitaxial PbZrxTi1-xO3 thin films," J. Microsc. 202, 250-254 (2001).
[CrossRef] [PubMed]

Taflove, A.

Takahashi, S.

S. Takahashi and A. V. Zayats, "Near-field second-harmonic generation at a metal tip apex," Appl. Phys. Lett. 80, 3479-3481 (2002).
[CrossRef]

Tyan, R. C.

van Driel, H. M.

J. E. Sipe, D. J. Moss, and H. M. van Driel, "Phenomenological theory of optical second- and third-harmonic generation from cubic and centrosymmetric crystals," Phys. Rev. B 35, 1129-1141 (1987).
[CrossRef]

Van Labeke, D.

F. I. Baida, D. Van Labeke, and G. Granet, "Origin of the super-enhanced light transmission through a 2-D metallic annular aperture array: a study of photonic bands," Appl. Phys. B: Lasers Opt. 79, 1-8 (2004).
[CrossRef]

F. I. Baida and D. Van Labeke, "Three-dimensional structures for enhanced transmission through a metallic film: annular aperture arrays," Phys. Rev. B 67, 155314/1-7 (2003).
[CrossRef]

F. I. Baida and D. Van Labeke, "Light transmission by subwavelength annular aperture arrays in metallic films," Opt. Commun. 209, 17-22 (2002).
[CrossRef]

F. I. Baida, D. Van Labeke, and J.-M. Vigoureux, "Numerical study of the displacement of a three-dimensional Gaussian beam transmitted at total internal reflection. Near-field applications," J. Opt. Soc. Am. A 17, 858-866 (2000).

F. I. Baida, D. Van Labeke, and J. M. Vigoureux, "Theoretical study of near-field surface plasmon excitation, propagation and diffraction," Opt. Commun. 171, 317-331 (1999).
[CrossRef]

Vanlabeke, D.

Van-Labeke, D.

G. Parent, D. Van-Labeke, and F. I. Baida, "Theoretical study of transient phenomena in near-field optics," J. Microsc. 202, 296-306 (2001).
[CrossRef] [PubMed]

Vasilyeva, E.

Vial, A.

R. Fikri, D. Barchiesi, F. H'Dhili, R. Bachelot, A. Vial, and P. Royer, "Modeling recent experiments of apertureless near-field optical microscopy using 2d finite element method," Opt. Commun. 221, 13-22 (2003).
[CrossRef]

Vigoureux, J. M.

F. I. Baida, D. Van Labeke, and J. M. Vigoureux, "Theoretical study of near-field surface plasmon excitation, propagation and diffraction," Opt. Commun. 171, 317-331 (1999).
[CrossRef]

Vigoureux, J.-M.

Vincent, P.

Xie, X. S.

L. Novotny, R. X. Bian, and X. S. Xie, "Theory of nanometric optical tweezers," Phys. Rev. Lett. 79, 645-648 (1997).
[CrossRef]

Yang, G. Z.

Z. Y. Li, B. Y. Gu, and G. Z. Yang, "Strong localization of near field second harmonic generation for nonlinear mesoscopic surface structures," Phys. Rev. B 59, 12622-12626 (1999).
[CrossRef]

Yee, K. S.

K. S. Yee, "Numerical solution of initial boundary value problems involving Maxwell's equations," IEEE Trans. Antennas Propag. 14, 302-307 (1966).
[CrossRef]

Zayats, A. V.

S. Takahashi and A. V. Zayats, "Near-field second-harmonic generation at a metal tip apex," Appl. Phys. Lett. 80, 3479-3481 (2002).
[CrossRef]

A. V. Zayats and V. Sandoghdar, "Apertureless scanning near-field second-harmonic microscopy." Opt. Commun. 178, 245-249 (2000).
[CrossRef]

A. V. Zayats, T. Kalkbrenner, V. Sandoghdar, and J. Mlynek, "Second harmonic generation from individual surface defects under local excitation," Phys. Rev. B 61, 4545-4548 (2000).
[CrossRef]

Zhang, X.

S. I. Bozhevolnyi, K. Pedersen, T. Skettrup, X. Zhang, and M. Belmote, "Far- and near-field second-harmonic imaging of ferroelectric domain walls," Opt. Commun. 152, 221-224 (1998).
[CrossRef]

Appl. Phys. B: Lasers Opt. (1)

F. I. Baida, D. Van Labeke, and G. Granet, "Origin of the super-enhanced light transmission through a 2-D metallic annular aperture array: a study of photonic bands," Appl. Phys. B: Lasers Opt. 79, 1-8 (2004).
[CrossRef]

Appl. Phys. Lett. (1)

S. Takahashi and A. V. Zayats, "Near-field second-harmonic generation at a metal tip apex," Appl. Phys. Lett. 80, 3479-3481 (2002).
[CrossRef]

Electron. Lett. (1)

F. Raineri, Y. Dumeige, A. Levenson, and X. Letartre, "Nonlinear decoupled FDTD code: phase-matching in 2D defective photonic crystal," Electron. Lett. 38, 1704-1706 (2002).
[CrossRef]

IEEE Photonics Technol. Lett. (1)

M. A. Alsunaidi, H. M. Masoudi, and M. Arnold, "A time-domain algorithm for the analysis of second-harmonic generation in nonlinear optical structures," IEEE Photonics Technol. Lett. 12, 395-397 (2000).
[CrossRef]

IEEE Trans. Antennas Propag. (1)

K. S. Yee, "Numerical solution of initial boundary value problems involving Maxwell's equations," IEEE Trans. Antennas Propag. 14, 302-307 (1966).
[CrossRef]

J. Comput. Phys. (1)

J. P. Berenger, "A perfectly matched layer for the absorption of electromagnetic waves," J. Comput. Phys. 114, 185-200 (1994).
[CrossRef]

J. Microsc. (2)

G. Parent, D. Van-Labeke, and F. I. Baida, "Theoretical study of transient phenomena in near-field optics," J. Microsc. 202, 296-306 (2001).
[CrossRef] [PubMed]

I. Smolyaninov, H. Y. Liang, C. H. Lee, C. C. Davis, V. Nagarajan, and R. Ramesh, "Near-field second harmonic imaging of c/a/c/a polydomain structure of epitaxial PbZrxTi1-xO3 thin films," J. Microsc. 202, 250-254 (2001).
[CrossRef] [PubMed]

J. Opt. Soc. Am. A (4)

J. Opt. Soc. Am. B (4)

Opt. Commun. (7)

S. Enoch, "Second-harmonic scattered light from one-dimensional rough thin films," Opt. Commun. 148, 137-143 (1998).
[CrossRef]

R. Fikri, D. Barchiesi, F. H'Dhili, R. Bachelot, A. Vial, and P. Royer, "Modeling recent experiments of apertureless near-field optical microscopy using 2d finite element method," Opt. Commun. 221, 13-22 (2003).
[CrossRef]

S. I. Bozhevolnyi, K. Pedersen, T. Skettrup, X. Zhang, and M. Belmote, "Far- and near-field second-harmonic imaging of ferroelectric domain walls," Opt. Commun. 152, 221-224 (1998).
[CrossRef]

A. V. Zayats and V. Sandoghdar, "Apertureless scanning near-field second-harmonic microscopy." Opt. Commun. 178, 245-249 (2000).
[CrossRef]

J. J. Greffet and C. Baylard, "Nonspecular astigmatic reflection of a 3D Gaussian beam on an interface," Opt. Commun. 93, 271-276 (1992).
[CrossRef]

F. I. Baida, D. Van Labeke, and J. M. Vigoureux, "Theoretical study of near-field surface plasmon excitation, propagation and diffraction," Opt. Commun. 171, 317-331 (1999).
[CrossRef]

F. I. Baida and D. Van Labeke, "Light transmission by subwavelength annular aperture arrays in metallic films," Opt. Commun. 209, 17-22 (2002).
[CrossRef]

Opt. Lett. (3)

Phys. Rev. (4)

J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, "Interactions between light waves in nonlinear dielectric," Phys. Rev. 127, 1918-1939 (1962).
[CrossRef]

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

P. S. Pershan, "Nonlinear optical properties of solids: energy considerations," Phys. Rev. 130, 919-929 (1963).
[CrossRef]

N. Bloembergen, R. K. Chang, S. S. Jha, and C. H. Lee, "Optical second harmonic generation in reflexion from media with inversion symmetry," Phys. Rev. 174, 813-822 (1968).
[CrossRef]

Phys. Rev. B (6)

B. S. Mendoza and W. L. Mochán, "Exactly solvable model of surface second harmonic generation," Phys. Rev. B 53, 4999-5006 (1996).
[CrossRef]

Z. Y. Li, B. Y. Gu, and G. Z. Yang, "Strong localization of near field second harmonic generation for nonlinear mesoscopic surface structures," Phys. Rev. B 59, 12622-12626 (1999).
[CrossRef]

J. E. Sipe, D. J. Moss, and H. M. van Driel, "Phenomenological theory of optical second- and third-harmonic generation from cubic and centrosymmetric crystals," Phys. Rev. B 35, 1129-1141 (1987).
[CrossRef]

V. M. Shalaev and A. K. Sarychev, "Non-linear optics of random metal-dielectric film," Phys. Rev. B 57, 13265-13288 (1998).
[CrossRef]

A. V. Zayats, T. Kalkbrenner, V. Sandoghdar, and J. Mlynek, "Second harmonic generation from individual surface defects under local excitation," Phys. Rev. B 61, 4545-4548 (2000).
[CrossRef]

F. I. Baida and D. Van Labeke, "Three-dimensional structures for enhanced transmission through a metallic film: annular aperture arrays," Phys. Rev. B 67, 155314/1-7 (2003).
[CrossRef]

Phys. Rev. Lett. (3)

A. Bouhelier, M. Beverluis, A. Hartschuh, and L. Novotny, "Near-field second-harmonic generation induced by local field enhancement," Phys. Rev. Lett. 90, 013903/1-4 (2003).
[CrossRef]

N. Bloembergen, R. K. Chang, and C. H. Lee, "Second harmonic generation of light in reflexion from media with inversion symmetry," Phys. Rev. Lett. 16, 986-989 (1966).
[CrossRef]

L. Novotny, R. X. Bian, and X. S. Xie, "Theory of nanometric optical tweezers," Phys. Rev. Lett. 79, 645-648 (1997).
[CrossRef]

Other (3)

K.H.Bennemann, ed., Nonlinear Optics in Metals (Clarendon, Oxford, UK, 1998).

A.Taflove and S.C.Hagness, eds., Computational Electrodynamics: The Finite Difference Time Domain Method (Artech House, Norwood, Mass., 2000).

Y.R.Shen, ed., The Principles of Nonlinear Optics (Wiley, New York, 1984).

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Figures (6)

Fig. 1
Fig. 1

Schematic of the modeled SHG experiment: A metallic tip with an end radius of 5 nm scans a glass surface ( ϵ r = 2.13 ) illuminated by an on-z-axis Gaussian laser beam ( HG 00 mode) with frequency ω. The SHG ( 2 ω ) generated by the tip is studied for a tip–surface gap of d = 10 nm . The cone half-angle is θ = 14 ° . h is the beam-waist surface distance. w 0 is the beam waist.

Fig. 2
Fig. 2

Intensity maps of the components of the transmitted electric field. (a) x component E trans x 4 , (b) z component E trans z 4 . The fields are calculated for z = 10 nm from a glass surface. The two images are calculated with the same scale.

Fig. 3
Fig. 3

Map of the FF and SH intensity distributions: (a) and (c) FF intensity in the ( x z ) plane for y = 0 and ( x y ) plane for z = 0 . (b) and (d) SH intensity in the ( x z ) plane for y = 0 and ( x y ) plane for z = 0 . The tip–surface distance is z = 10 nm . The tip is placed in the maximum of intensity of the z component of the transmitted field [ x = 280 nm , y = 0 nm in Fig. 2b]. The color bars in (c) and (d) are valid for, respectively, (a) and (b). For FF intensity, the units are normalized compared with the intensity without the tip. As for SH intensity, the units are proportional to ( χ s ) 2 . The axis origins are zero for the tip apex position. The lattice space increments are Δ x = Δ y = Δ z = 1 nm at the tip apex and Δ x = Δ y = Δ z = 25 nm far from it.

Fig. 4
Fig. 4

Origin of SHG. The solid curve corresponds to the variations of the z component of the transmitted field E trans z 4 without a tip for z = 10 nm from the glass. The stars are related to SH intensity at the tip apex for the same scan ( x = y = 0 , z = 10 nm ) .

Fig. 5
Fig. 5

Comparison of field confinement for the FF and SH. The solid curve corresponds to intensity variations of the FF along the negative direction of the z axis below the tip in Fig. 3. The dashed curve is the same for the SH. The intensities are normalized to 1 at the tip apex.

Fig. 6
Fig. 6

(a) FF far-field intensity spectrum. (b) SH far-field spectrum. In both (a) and (b) the solid curves show the results with a surface–tip distance d = 200 nm . The dashed curves are for d = 10 nm .

Equations (8)

Equations on this page are rendered with MathJax. Learn more.

P ( nl ) ( 2 ω ) = P d ( nl ) ( 2 ω ) + P Q ( nl ) ( 2 ω ) + P M ( nl ) ( 2 ω ) ,
[ P d s ( nl ) ( 2 ω ) ] i = j , k χ i j k s E j ( ω ) E k ( ω ) .
P n ( nl ) ( 2 ω ) = χ n n n s E n ( ω ) E n ( ω ) .
rot [ E ( 2 ω ) ] = B ( 2 ω ) t ,
div [ B ( 2 ω ) ] = 0 .
rot [ H ( 2 ω ) ] = P ( nl ) ( 2 ω ) t + [ D ( 2 ω ) ] t ,
div [ D ( 2 ω ) ] = div [ P ( nl ) ( 2 ω ) ] .
D ( 2 ω ) = ϵ 0 ϵ ( 2 ω ) E ( 2 ω ) , B ( 2 ω ) = μ 0 H ( 2 ω ) ,

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