## Three-dimensional finite-difference time-domain study of enhanced second-harmonic generation at the end of a apertureless scanning near-field optical microscope metal tip

JOSA B, Vol. 22, Issue 5, pp. 1045-1051 (2005)

http://dx.doi.org/10.1364/JOSAB.22.001045

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### 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

**OCIS Codes**

(190.4350) Nonlinear optics : Nonlinear optics at surfaces

(240.4350) Optics at surfaces : Nonlinear optics at surfaces

(260.2110) Physical optics : Electromagnetic optics

(260.5430) Physical optics : Polarization

**Citation**

Thierry Laroche, Fadi Issam Baida, and Daniel Van Labeke, "Three-dimensional finite-difference time-domain study of enhanced second-harmonic generation at the end of a apertureless scanning near-field optical microscope metal tip," J. Opt. Soc. Am. B **22**, 1045-1051 (2005)

http://www.opticsinfobase.org/josab/abstract.cfm?URI=josab-22-5-1045

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### References

- 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).
- 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).
- 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).
- S. Takahashi and A. V. Zayats, "Near-field second-harmonic generation at a metal tip apex," Appl. Phys. Lett. 80, 3479-3481 (2002).
- 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).
- 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).
- A. V. Zayats and V. Sandoghdar, "Apertureless scanning near-field second-harmonic microscopy." Opt. Commun. 178, 245-249 (2000).
- D. Maystre, M. Nevière, R. Reinisch, and J. L. Coutaz, "Integral theory for metallic gratings in nonlinear optics and comparison with experimental results on second-harmonic generation," J. Opt. Soc. Am. B 5, 338-346 (1988).
- M. Nevière, P. Vincent, D. Maystre, R. Reinisch, and J. L. Coutaz, "Differential theory for metallic gratings in nonlinear optics: second harmonic generation," J. Opt. Soc. Am. B 5, 330-336 (1988).
- 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).
- S. Enoch, "Second-harmonic scattered light from one-dimensional rough thin films," Opt. Commun. 148, 137-143 (1998).
- 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).
- 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).
- V. M. Shalaev and A. K. Sarychev, "Non-linear optics of random metal-dielectric film," Phys. Rev. B 57, 13265-13288 (1998).
- 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).
- 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).
- 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).
- E. Vasilyeva and A. Taflove, "Three-dimensional modeling of amplitude-object imaging in scanning near-field optical microscopy," Opt. Lett. 23, 1155-1157 (1998).
- J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, "Interactions between light waves in nonlinear dielectric," Phys. Rev. 127, 1918-1939 (1962).
- D. A. Kleinman, "Nonlinear dielectric polarization in optical media," Phys. Rev. 126, 1977-1979 (1962).
- P. S. Pershan, "Nonlinear optical properties of solids: energy considerations," Phys. Rev. 130, 919-929 (1963).
- 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).
- Y.R.Shen, ed., The Principles of Nonlinear Optics (Wiley, New York, 1984).
- 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).
- K.H.Bennemann, ed., Nonlinear Optics in Metals (Clarendon, Oxford, UK, 1998).
- 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).
- B. S. Mendoza and W. L. Mochán, "Exactly solvable model of surface second harmonic generation," Phys. Rev. B 53, 4999-5006 (1996).
- A.Taflove and S.C.Hagness, eds., Computational Electrodynamics: The Finite Difference Time Domain Method (Artech House, Norwood, Mass., 2000).
- K. S. Yee, "Numerical solution of initial boundary value problems involving Maxwell's equations," IEEE Trans. Antennas Propag. 14, 302-307 (1966).
- R. M. Joseph, S. C. Hagness, and A. Taflove, "Direct time integration of Maxwell's equations in linear dispersive media with absorption for scattering and propagation of femtosecond electromagnetic pulses," Opt. Lett. 16, 1412-1414 (1991).
- G. Parent, D. Van-Labeke, and F. I. Baida, "Theoretical study of transient phenomena in near-field optics," J. Microsc. 202, 296-306 (2001).
- J. P. Berenger, "A perfectly matched layer for the absorption of electromagnetic waves," J. Comput. Phys. 114, 185-200 (1994).
- J. J. Greffet and C. Baylard, "Nonspecular astigmatic reflection of a 3D Gaussian beam on an interface," Opt. Commun. 93, 271-276 (1992).
- W. Nasalski, "Longitudinal and transverse effects of nonspecular reflection," J. Opt. Soc. Am. A 13, 172-181 (1996).
- 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).
- 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).
- 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).
- L. Novotny, R. X. Bian, and X. S. Xie, "Theory of nanometric optical tweezers," Phys. Rev. Lett. 79, 645-648 (1997).
- 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).
- F. I. Baida and D. Van Labeke, "Light transmission by subwavelength annular aperture arrays in metallic films," Opt. Commun. 209, 17-22 (2002).
- 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).
- 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).

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