J. Armstrong, N. Bloembergen, J. Ducuing-&-p, and . Pershan, Interactions between Light Waves in a Nonlinear Dielectric, Physical Review, vol.127, issue.6, pp.1918-1957, 1962.
DOI : 10.1103/PhysRev.127.1918

P. Pershan, Nonlinear Optical Properties of Solids: Energy Considerations, Physical Review, vol.130, issue.3, pp.919-948, 1963.
DOI : 10.1103/PhysRev.130.919

F. Brown, R. E. Parks-&-a, and . Sleeper, Nonlinear Optical Reflection from a Metallic Boundary, Physical Review Letters, vol.14, issue.25, pp.1029-1060, 1965.
DOI : 10.1103/PhysRevLett.14.1029

]. N. Bloembergen, R. Chang, S. Jha-&-c, and . Lee, Optical Second-Harmonic Generation in Reflection from Media with Inversion Symmetry, Physical Review, vol.174, issue.3, pp.813-835, 1968.
DOI : 10.1103/PhysRev.174.813

J. Rudnick-&-e and . Stern, Second-Harmonic Radiation from Metal Surfaces, Physical Review B, vol.4, issue.12, pp.4274-4290, 1971.
DOI : 10.1103/PhysRevB.4.4274

J. Sipe, C. So, M. Fukui-&-g, and . Stegeman, Analysis of second-harmonic generation at metal surfaces, Physical Review B, vol.21, issue.10, pp.4389-402, 1980.
DOI : 10.1103/PhysRevB.21.4389

P. Guyot-sionnest and &. Y. Shen, Local and nonlocal surface nonlinearities for surface optical second-harmonic generation, Physical Review B, vol.35, issue.9, pp.4420-4426, 1987.
DOI : 10.1103/PhysRevB.35.4420

Y. Shen, The principles of nonlinear optics (A Wiley-interscience Publication, 1984.

P. Guyot-sionnest, W. Chen-&-y, and . Shen, General considerations on optical second-harmonic generation from surfaces and interfaces, Physical Review B, vol.33, issue.12, pp.8254-63, 1986.
DOI : 10.1103/PhysRevB.33.8254

]. N. Bloembergen, R. Chang, S. Jha-&-c, and . Lee, Optical Second-Harmonic Generation in Reflection from Media with Inversion Symmetry, Physical Review, vol.174, issue.3, pp.813-835, 1968.
DOI : 10.1103/PhysRev.174.813

J. Sipe, C. So, M. Fukui-&-g, and . Stegeman, Analysis of second-harmonic generation at metal surfaces, Physical Review B, vol.21, issue.10, pp.4389-402, 1980.
DOI : 10.1103/PhysRevB.21.4389

G. Agarwal-&-s and . Jha, Surface-enhanced second-harmonic generation at a metallic grating, Physical Review B, vol.26, issue.2, pp.482-96, 1982.
DOI : 10.1103/PhysRevB.26.482

S. Enoch, Second-harmonic scattered light from one-dimensional rough thin films, Optics Communications, vol.148, issue.1-3, pp.137-180, 1998.
DOI : 10.1016/S0030-4018(97)00572-5

R. Depine-&-m and . Gigli, Diffraction from corrugated gratings made with biaxial crystals: Rayleigh methods, Optics Communications, vol.130, issue.1-3, pp.109-130, 1996.
DOI : 10.1016/0030-4018(96)00273-8

D. Maystre, M. Nevière, R. Reinisch-&-j, and . Coutaz, Integral theory for metallic gratings in nonlinear optics and comparison with experimental results on second-harmonic generation, Journal of the Optical Society of America B, vol.5, issue.2, pp.338-384, 1988.
DOI : 10.1364/JOSAB.5.000338

E. Popov-&-m and . Nevière, Surface-enhanced second-harmonic generation in nonlinear corrugated dielectrics: new theoretical approaches, Journal of the Optical Society of America B, vol.11, issue.9, pp.1555-64, 1994.
DOI : 10.1364/JOSAB.11.001555

M. Nevière, P. Vincent, D. Maystre, R. Reinisch-&-j, and . Coutaz, Differential theory for metallic gratings in nonlinear optics: second-harmonic generation, Journal of the Optical Society of America B, vol.5, issue.2, pp.330-336, 1988.
DOI : 10.1364/JOSAB.5.000330

G. D. Aguanno, M. Centini, C. Sibilia, M. Bertolotti, M. Bloemer-&-c et al., Generalized coupled-mode theory for ??^(2) interactions in finite multilayered structures, Journal of the Optical Society of America B, vol.19, issue.9, pp.2111-2132, 2002.
DOI : 10.1364/JOSAB.19.002111

W. Nakagawa, R. Tyan-&-y, and . Fainman, Analysis of enhanced second-harmonic generation in periodic nanostructures using modified rigorous coupled-wave analysis in the undepleted-pump approximation, Journal of the Optical Society of America A, vol.19, issue.9, pp.1919-1947, 2002.
DOI : 10.1364/JOSAA.19.001919

J. Haus, B. Soon, M. Scalora, C. Sibilia-&-i, and . Mel-'nikov, Coupled-mode equations for Kerr media with periodically modulated linear and nonlinear coefficients, Journal of the Optical Society of America B, vol.19, issue.9, pp.2282-91, 2002.
DOI : 10.1364/JOSAB.19.002282

R. Fikri, D. Barchiesi, F. H. Dhili, R. Bachelot, A. Vial-&-p et al., Modeling recent experiments of apertureless near-field optical microscopy using 2D finite element method, Optics Communications, vol.221, issue.1-3, pp.13-22, 2003.
DOI : 10.1016/S0030-4018(03)01463-9

R. Joseph-&-a and . Taflove, FDTD Maxwell's equations models for nonlinear electrodynamics and optics, IEEE Transactions on Antennas and Propagation, vol.45, issue.3, pp.364-74, 1997.
DOI : 10.1109/8.558652

M. Goorjian, A. J. Taflove-&-m, . C. Ans-s, and . Hagness, Computational modeling of femtosecond optical solitons from Maxwell's equations, IEEE Journal of Quantum Electronics, vol.28, issue.10, pp.2416-2438, 1992.
DOI : 10.1109/3.159548

A. Bourgeade-&-e and . Freysz, Computational modeling of second-harmonic generation by solution of full-wave vector Maxwell equations, Journal of the Optical Society of America B, vol.17, issue.2, pp.226-260, 2000.
DOI : 10.1364/JOSAB.17.000226

T. Lee-&-s and . Hagness, Pseudospectral time-domain methods for modeling optical wave propagation in secondorder nonlinear materials, J. Opt. Soc. Am. B, vol.21, pp.330-342, 2004.

D. V. Labeke-&-d and . Barchiesi, Scanning-tunneling optical microscopy: a theoretical macroscopic approach, Journal of the Optical Society of America A, vol.9, issue.5, pp.732-738, 1992.
DOI : 10.1364/JOSAA.9.000732

D. V. Labeke, A. Vial-&-d, and . Barchiesi, Near-field theoretical study of a magneto-optical grating, Ultramicroscopy, vol.61, issue.1-4, pp.51-56, 1995.
DOI : 10.1016/0304-3991(95)00102-6

D. V. Labeke, A. Vial, V. Novosad, Y. Souche, M. D. Schlenker-&-a et al., Diffraction of light by a corrugated magnetic grating: experimental results and calculation using a perturbation approximation to the Rayleigh method, Optics Communications, vol.124, issue.5-6, pp.519-547, 1996.
DOI : 10.1016/0030-4018(95)00598-6

G. Parent, D. Van-labeke-&-f, and . Baida, Theoretical study of transient phenomena in near-field optics, Journal of Microscopy, vol.202, issue.2, pp.296-306, 2001.
DOI : 10.1046/j.1365-2818.2001.00886.x

F. V. Baida-&-d and . Labeke, Light transmission by subwavelength annular aperture arrays in metallic films, Optics Communications, vol.209, issue.1-3, pp.17-22, 2002.
DOI : 10.1016/S0030-4018(02)01690-5

R. Petit, Electromagnetic Theory of Gratings, 1980.
DOI : 10.1007/978-3-642-81500-3

J. Berenger, A perfectly matched layer for the absorption of electromagnetic waves, Journal of Computational Physics, vol.114, issue.2, pp.185-200, 1994.
DOI : 10.1006/jcph.1994.1159

J. Berenger, A perfectly matched layer for free-space simulation in finite-difference computer codes, Ann. Telecomm, vol.51, pp.39-46, 1996.

J. Berenger, Three-Dimensional Perfectly Matched Layer for the Absorption of Electromagnetic Waves, Journal of Computational Physics, vol.127, issue.2, pp.363-79, 1996.
DOI : 10.1006/jcph.1996.0181

Z. Li, B. Gu-&-g, and . Yang, Strong localization of near-field second-harmonic generation for nonlinear mesoscopic surface structures, Physical Review B, vol.59, issue.19, pp.12622-12628, 1999.
DOI : 10.1103/PhysRevB.59.12622

A. Xie, B. Gu, G. Yang-&-z, and . Zhang, domains, Physical Review B, vol.63, issue.5, pp.54104-54105, 2001.
DOI : 10.1103/PhysRevB.63.054104

S. Bozhevolnyi-&-v and . Lozovski, Second-harmonic scanning optical microscopy of individual nanostructures, Physical Review B, vol.65, issue.23, pp.235420-235421, 2002.
DOI : 10.1103/PhysRevB.65.235420

A. Yariv-&-p and . Yeh, Optical waves in crystals, 1984.

D. V. Labeke-&-d and . Barchiesi, Probes for scanning tunneling optical microscopy: a theoretical comparison, Journal of the Optical Society of America A, vol.10, issue.10, pp.2193-201, 1993.
DOI : 10.1364/JOSAA.10.002193

D. V. Barchiesi-&-d and . Labeke, A perturbative diffraction theory of a multilayer system: applications to near-field optical microscopy SNOM and STOM, Ultramicroscopy, vol.57, issue.2-3, pp.196-203, 1995.
DOI : 10.1016/0304-3991(94)00135-A

T. Grosjean-&-d and . Courjon, Polarization filtering induced by imaging systems: Effect on image structure, Physical Review E, vol.67, issue.4, pp.1-6, 2003.
DOI : 10.1103/PhysRevE.67.046611

J. Greffet-&-r and . Carminati, Image formation in near-field optics, Progress in Surface Science, vol.56, issue.3, pp.133-237, 1997.
DOI : 10.1016/S0079-6816(98)00004-5

J. Porto, R. Carminati-&-j, and . Greffet, Theory of electromagnetic field imaging and spectroscopy in scanning near-field optical microscopy, Journal of Applied Physics, vol.88, issue.8, pp.4845-4850, 2000.
DOI : 10.1063/1.1311811

L. Novotny, E. Sánchez-&-x, and . Xie, Near-field optical imaging using metal tips illuminated by higher-order Hermite???Gaussian beams, Ultramicroscopy, vol.71, issue.1-4, pp.21-30, 1998.
DOI : 10.1016/S0304-3991(97)00077-6

V. Konopsky, Operation of scanning plasmon near-field microscope with gold and silver tips in tapping mode: demonstration of subtip resolution, Optics Communications, vol.185, issue.1-3, pp.83-93, 2000.
DOI : 10.1016/S0030-4018(00)00994-9

D. V. Labeke-&-d and . Barchiesi, Probes for scanning tunneling optical microscopy: a theoretical comparison, Journal of the Optical Society of America A, vol.10, issue.10, pp.2193-201, 1993.
DOI : 10.1364/JOSAA.10.002193

H. Cory, A. Boccara, J. Rivoal-&-a, and . Lahrech, Electric field intensity variation in the vicinity of a perfectly conducting conical probe: Application to near-field microscopy, Microwave and Optical Technology Letters, vol.18, issue.2, pp.120-124, 1998.
DOI : 10.1002/(SICI)1098-2760(19980605)18:2<120::AID-MOP10>3.0.CO;2-B

L. Novotny, M. Berverluis, K. Youngworth-&-t, and . Brown, Longitudinal Field Modes Probed by Single Molecules, Physical Review Letters, vol.86, issue.23, pp.5251-5255, 2001.
DOI : 10.1103/PhysRevLett.86.5251

L. Novotny, R. Bian-&-x, and . Xie, Theory of Nanometric Optical Tweezers, Physical Review Letters, vol.79, issue.4, pp.645-653, 1997.
DOI : 10.1103/PhysRevLett.79.645

R. Fikri, D. Barchiesi, F. H. Dhili, R. Bachelot, A. Vial-&-p et al., Modeling recent experiments of apertureless near-field optical microscopy using 2D finite element method, Optics Communications, vol.221, issue.1-3, pp.13-22, 2003.
DOI : 10.1016/S0030-4018(03)01463-9

A. Bouhelier, M. Beverluis, A. Hartschuh-&-l, and . Novotny, Near-Field Second-Harmonic Generation Induced by Local Field Enhancement, Physical Review Letters, vol.90, issue.1, pp.13903-13904, 2003.
DOI : 10.1103/PhysRevLett.90.013903

E. Sánchez, L. Novotny-&-x, and . Xie, Near-field fluorescencce microscopy based on two-photn excitation with metal tips, Phys. Rev. Let, vol.82, pp.14014-14021, 1999.

Y. Kawata, C. Xu-&-w, and . Denk, Feasibility of molecular-resolution fluorescence near-field microscopy using multi-photon absorption and field enhancement near a sharp tip, Journal of Applied Physics, vol.85, issue.3, pp.1294-301, 1999.
DOI : 10.1063/1.369260

S. Takahashi-&-a and . Zayats, Near-field second-harmonic generation at a metal tip apex, Applied Physics Letters, vol.80, issue.19, pp.3479-81, 2002.
DOI : 10.1063/1.1478780

A. Zayats-&-v and . Sandoghdar, Apertureless near-field optical microscopy via local second-harmonic generation, Journal of Microscopy, vol.202, issue.1, pp.94-103, 2001.
DOI : 10.1046/j.1365-2818.2001.00810.x

F. Brown, R. E. Parks-&-a, and . Sleeper, Nonlinear Optical Reflection from a Metallic Boundary, Physical Review Letters, vol.14, issue.25, pp.1029-1060, 1965.
DOI : 10.1103/PhysRevLett.14.1029

I. Smolyaninov, A. Zayats-&-c, and . Davis, Near-field second harmonic generation from a rough metal surface, Physical Review B, vol.56, issue.15, pp.9290-9293, 1997.
DOI : 10.1103/PhysRevB.56.9290

V. Shalaev-&-a and . Sarychev, Nonlinear optics of random metal-dielectric films, Physical Review B, vol.57, issue.20, pp.13265-88, 1998.
DOI : 10.1103/PhysRevB.57.13265

J. Greffet-&-c and . Baylard, Nonspecular astigmatic reflection of a 3D gaussian beam on an interface, Optics Communications, vol.93, issue.5-6, pp.271-277, 1992.
DOI : 10.1016/0030-4018(92)90184-S

W. Nasalski, Longitudinal and transverse effects of nonspecular reflection, Journal of the Optical Society of America A, vol.13, issue.1, pp.172-81, 1996.
DOI : 10.1364/JOSAA.13.000172

F. Baida, D. V. Labeke-&-j, and . Vigoureux, Theoretical study of near-field surface plasmon excitation, propagation and diffraction, Optics Communications, vol.171, issue.4-6, pp.317-348, 1999.
DOI : 10.1016/S0030-4018(99)00565-9

F. Baida, D. Barchiesi-&-d, and . Vanlabeke, Near-field effects of focused illumination on periodic structures in scanning tunneling optical microscopy, Optics Letters, vol.24, issue.22, pp.1587-1596, 1999.
DOI : 10.1364/OL.24.001587

F. Baida, D. V. Labeke-&-j.-m, and . Vigoureux, Numerical study of the displacement of a three-dimensional Gaussian beam transmitted at total internal reflection Near-field applications, Journal of the Optical Society of America A, vol.17, issue.5, pp.858-66, 2000.
DOI : 10.1364/JOSAA.17.000858

S. Bozhevilnyi-&-k and . Pedersen, Second Harmonic generation due to surface plasmon localization, Surface Science, pp.384-391, 1997.

T. Driscoll-&-d and . Guidotti, Symmetry analysis of second-harmonic generation in silicon, Physical Review B, vol.28, issue.2, pp.1171-1174, 1983.
DOI : 10.1103/PhysRevB.28.1171

A. Bouhelier, M. Beverluis, A. Hartschuh-&-l, and . Novotny, Near-Field Second-Harmonic Generation Induced by Local Field Enhancement, Physical Review Letters, vol.90, issue.1, pp.13903-13904, 2003.
DOI : 10.1103/PhysRevLett.90.013903

I. Smolyaninov, A. Zayats-&-c, and . Davis, Near-field second harmonic generation from a rough metal surface, Physical Review B, vol.56, issue.15, pp.9290-9293, 1997.
DOI : 10.1103/PhysRevB.56.9290

T. Heinz, M. Loy-&-w, and . Thompson, Study of Si(111) Surfaces by Optical Second-Harmonic Generation: Reconstruction and Surface Phase Transformation, Physical Review Letters, vol.54, issue.1, pp.63-69, 1985.
DOI : 10.1103/PhysRevLett.54.63

Y. An-&-s and . Cundiff, Bulk and Surface Contributions to Resonant Second-Harmonic Generation from Si(001) surfaces, Appl. Phys. Lett, vol.81, p.5174, 2002.

Y. Q. Bozhevilnyi-&-k and . Pedersen, AN, thesis, Faculty of the Graduate School of the University of Colorado Second Harmonic generation due to surface plasmon localization, Surface Science, pp.384-391, 1997.

A. Zayats, I. Smolyaninov-&-c, and . Davis, Observation of localized plasmonic excitations in thin metal films with near-field second-harmonic microscopy, Optics Communications, vol.169, issue.1-6, pp.93-96, 1999.
DOI : 10.1016/S0030-4018(99)00420-4

J. Seidel, S. Grafstrm, L. Eng, and &. L. Bischoff, Surface plasmon transmission across narrow grooves in thin silver films, Applied Physics Letters, vol.82, issue.9, p.1368, 2003.
DOI : 10.1063/1.1558219

R. Chang-&-n and . Bloembergen, Experimental Verification of the Laws for the Reflected Intensity of Second-Harmonic Light, Physical Review, vol.144, issue.2, pp.775-80, 1966.
DOI : 10.1103/PhysRev.144.775

D. Courjon, Near-Field Microscopy and Near-Field Optics, 2003.

P. Franken, A. Hil, C. Peters-&-g, and . Weinreich, Generation of Optical Harmonics, Physical Review Letters, vol.7, issue.4, pp.118-120, 1961.
DOI : 10.1103/PhysRevLett.7.118

R. Terhune, P. Maker-&-c, and . Savage, Optical Harmonic Generation in Calcite, Physical Review Letters, vol.8, issue.10, pp.404-410, 1962.
DOI : 10.1103/PhysRevLett.8.404

N. Bloembergen, R. Chang, S. Jha-&-c, and . Lee, Optical Second-Harmonic Generation in Reflection from Media with Inversion Symmetry, Physical Review, vol.174, issue.3, pp.813-835, 1968.
DOI : 10.1103/PhysRev.174.813

P. Guyot-sionnest, W. Chen-&-y, and . Shen, General considerations on optical second-harmonic generation from surfaces and interfaces, Physical Review B, vol.33, issue.12, pp.8254-63, 1986.
DOI : 10.1103/PhysRevB.33.8254

J. Sipe, D. Moss-&-h, and . Van-driel, Phenomenological theory of optical second- and third-harmonic generation from cubic centrosymmetric crystals, Physical Review B, vol.35, issue.3, pp.1129-1170, 1987.
DOI : 10.1103/PhysRevB.35.1129

J. Sipe, C. So, M. Fukui-&-g, and . Stegeman, Analysis of second-harmonic generation at metal surfaces, Physical Review B, vol.21, issue.10, pp.4389-402, 1980.
DOI : 10.1103/PhysRevB.21.4389

I. Smolyaninov, A. Zayats-&-c, and . Davis, Near-field second-harmonic imaging of ferromagnetic and ferroelectric materials, Optics Letters, vol.22, issue.21, pp.1592-1596, 1997.
DOI : 10.1364/OL.22.001592

S. Bozhevolnyi, K. Pedersen-&-b, and . Vohnsen, Near-field optical microscopy of nonlinear susceptibilities, Optics Communications, vol.150, issue.1-6, pp.49-55, 1998.
DOI : 10.1016/S0030-4018(98)00014-5

R. Vollmer, Q. Jin, H. Regensburger-&-j, and . Kirschner, Second harmonic generation from magnetic surfaces and thin films, Journal of Magnetism and Magnetic Materials, vol.198, issue.199, pp.611-616, 1999.
DOI : 10.1016/S0304-8853(98)01216-5

S. Lim, Magnetic second-harmonic generation of an antiferromagnetic film, Journal of the Optical Society of America B, vol.19, issue.6, pp.1401-1411, 2002.
DOI : 10.1364/JOSAB.19.001401

A. Zayats-&-v and . Sandoghdar, Apertureless scanning near-field second-harmonic microscopy, Optics Communications, vol.178, issue.1-3, pp.245-294, 2000.
DOI : 10.1016/S0030-4018(00)00655-6

S. Takahashi-&-a and . Zayats, Near-field second-harmonic generation at a metal tip apex, Applied Physics Letters, vol.80, issue.19, pp.3479-81, 2002.
DOI : 10.1063/1.1478780

A. Bouhelier, M. Beverluis, A. Hartschuh-&-l, and . Novotny, Near-Field Second-Harmonic Generation Induced by Local Field Enhancement, Physical Review Letters, vol.90, issue.1, pp.13903-13904, 2003.
DOI : 10.1103/PhysRevLett.90.013903

S. Bozhevilnyi-&-k and . Pedersen, Second Harmonic generation due to surface plasmon localization, Surface Science, pp.384-391, 1997.

A. Zayats, I. Smolyaninov-&-c, and . Davis, Observation of localized plasmonic excitations in thin metal films with near-field second-harmonic microscopy, Optics Communications, vol.169, issue.1-6, pp.93-96, 1999.
DOI : 10.1016/S0030-4018(99)00420-4

D. Newman, M. Wears-&-r, and . Matelon, Plasmon enhanced magneto-optic behaviour in the linear and nonlinear optical fields, J. of Magnetism and Magnetic Materials International, vol.242, pp.980-983, 2002.

D. V. Labeke-&-d and . Barchiesi, Scanning-tunneling optical microscopy: a theoretical macroscopic approach, Journal of the Optical Society of America A, vol.9, issue.5, pp.732-738, 1992.
DOI : 10.1364/JOSAA.9.000732

P. Van, &. J. Berg, and . Fokkema, The Rayleigh hypothesis in the theory of reflection by a grating, J. Opt. Soc. Am, vol.69, pp.27-31, 1979.

R. Depine-&-m and . Gigli, Diffraction from corrugated gratings made with biaxial crystals: Rayleigh methods, Optics Communications, vol.130, issue.1-3, pp.109-130, 1996.
DOI : 10.1016/0030-4018(96)00273-8

G. Parent, D. Van-labeke-&-f, and . Baida, Theoretical study of transient phenomena in near-field optics, Journal of Microscopy, vol.202, issue.2, pp.296-306, 2001.
DOI : 10.1046/j.1365-2818.2001.00886.x

F. V. Baida-&-d and . Labeke, Light transmission by subwavelength annular aperture arrays in metallic films, Optics Communications, vol.209, issue.1-3, pp.17-22, 2002.
DOI : 10.1016/S0030-4018(02)01690-5

A. Yariv-&-p and . Yeh, Optical waves in crystals, 1984.

N. Bloembergen-&-p and . Pershan, Light Waves at the Boundary of Nonlinear Media, Physical Review, vol.128, issue.2, pp.606-628, 1962.
DOI : 10.1103/PhysRev.128.606

J. Armstrong, N. Bloembergen, J. Ducuing-&-p, and . Pershan, Interactions between Light Waves in a Nonlinear Dielectric, Physical Review, vol.127, issue.6, pp.1918-1957, 1962.
DOI : 10.1103/PhysRev.127.1918

P. Pershan, Nonlinear Optical Properties of Solids: Energy Considerations, Physical Review, vol.130, issue.3, pp.919-948, 1963.
DOI : 10.1103/PhysRev.130.919

F. Brown, R. E. Parks-&-a, and . Sleeper, Nonlinear Optical Reflection from a Metallic Boundary, Physical Review Letters, vol.14, issue.25, pp.1029-1060, 1965.
DOI : 10.1103/PhysRevLett.14.1029

J. Rudnick-&-e and . Stern, Second-Harmonic Radiation from Metal Surfaces, Physical Review B, vol.4, issue.12, pp.4274-4290, 1971.
DOI : 10.1103/PhysRevB.4.4274

P. Guyot-sionnest and &. Y. Shen, Local and nonlocal surface nonlinearities for surface optical second-harmonic generation, Physical Review B, vol.35, issue.9, pp.4420-4426, 1987.
DOI : 10.1103/PhysRevB.35.4420

Y. Shen, The principles of nonlinear optics (A Wiley-interscience Publication, 1984.

R. Weast, Handbook of lasers (Chemical Rubber Co, 1971.

N. Bloembergen, R. Chang-&-c, and . Lee, Second-Harmonic Generation of Light in Reflection from Media with Inversion Symmetry, Physical Review Letters, vol.16, issue.22, pp.986-89, 1966.
DOI : 10.1103/PhysRevLett.16.986

P. Guyot-sionnest and &. Y. Shen, Bulk contribution in surface second-harmonic generation, Physical Review B, vol.38, issue.12, pp.7985-7994, 1988.
DOI : 10.1103/PhysRevB.38.7985

K. Bennemann, Nonlinear optics in metals (Clarendon press, 1998.

H. Tom-&-g and . Aumiller, Observation of rotational anisotropy in the second-harmonic generation from a metal surface, Phys. Rev. B, vol.33, pp.8818-8839, 1986.

P. Fisher-&-a and . Buckingham, Surface second-order nonlinear optical activity, Journal of the Optical Society of America B, vol.15, issue.12, pp.2951-2958, 1998.
DOI : 10.1364/JOSAB.15.002951

G. Agarwal-&-s and . Jha, Surface-enhanced second-harmonic generation at a metallic grating, Physical Review B, vol.26, issue.2, pp.482-96, 1982.
DOI : 10.1103/PhysRevB.26.482

S. Enoch, Second-harmonic scattered light from one-dimensional rough thin films, Optics Communications, vol.148, issue.1-3, pp.137-180, 1998.
DOI : 10.1016/S0030-4018(97)00572-5

D. Maystre, M. Nevière, R. Reinisch-&-j, and . Coutaz, Integral theory for metallic gratings in nonlinear optics and comparison with experimental results on second-harmonic generation, Journal of the Optical Society of America B, vol.5, issue.2, pp.338-384, 1988.
DOI : 10.1364/JOSAB.5.000338

E. Popov-&-m and . Nevière, Surface-enhanced second-harmonic generation in nonlinear corrugated dielectrics: new theoretical approaches, Journal of the Optical Society of America B, vol.11, issue.9, pp.1555-64, 1994.
DOI : 10.1364/JOSAB.11.001555

M. Nevière, P. Vincent, D. Maystre, R. Reinisch-&-j, and . Coutaz, Differential theory for metallic gratings in nonlinear optics: second-harmonic generation, Journal of the Optical Society of America B, vol.5, issue.2, pp.330-336, 1988.
DOI : 10.1364/JOSAB.5.000330

G. D. Aguanno, M. Centini, C. Sibilia, M. Bertolotti, M. Bloemer-&-c et al., Generalized coupled-mode theory for ??^(2) interactions in finite multilayered structures, Journal of the Optical Society of America B, vol.19, issue.9, pp.2111-2132, 2002.
DOI : 10.1364/JOSAB.19.002111

W. Nakagawa, R. Tyan-&-y, and . Fainman, Analysis of enhanced second-harmonic generation in periodic nanostructures using modified rigorous coupled-wave analysis in the undepleted-pump approximation, Journal of the Optical Society of America A, vol.19, issue.9, pp.1919-1947, 2002.
DOI : 10.1364/JOSAA.19.001919

J. Haus, B. Soon, M. Scalora, C. Sibilia-&-i, and . Mel-'nikov, Coupled-mode equations for Kerr media with periodically modulated linear and nonlinear coefficients, Journal of the Optical Society of America B, vol.19, issue.9, pp.2282-91, 2002.
DOI : 10.1364/JOSAB.19.002282

R. Fikri, D. Barchiesi, F. H. Dhili, R. Bachelot, A. Vial-&-p et al., Modeling recent experiments of apertureless near-field optical microscopy using 2D finite element method, Optics Communications, vol.221, issue.1-3, pp.13-22, 2003.
DOI : 10.1016/S0030-4018(03)01463-9

R. Joseph-&-a and . Taflove, FDTD Maxwell's equations models for nonlinear electrodynamics and optics, IEEE Transactions on Antennas and Propagation, vol.45, issue.3, pp.364-74, 1997.
DOI : 10.1109/8.558652

M. Goorjian, A. J. Taflove-&-m, . C. Ans-s, and . Hagness, Computational modeling of femtosecond optical solitons from Maxwell's equations, IEEE Journal of Quantum Electronics, vol.28, issue.10, pp.2416-2438, 1992.
DOI : 10.1109/3.159548

A. Bourgeade-&-e and . Freysz, Computational modeling of second-harmonic generation by solution of full-wave vector Maxwell equations, Journal of the Optical Society of America B, vol.17, issue.2, pp.226-260, 2000.
DOI : 10.1364/JOSAB.17.000226

T. Lee-&-s and . Hagness, Pseudospectral time-domain methods for modeling optical wave propagation in second-order nonlinear materials, J. Opt. Soc. Am. B, vol.21, pp.330-342, 2004.

D. V. Labeke, A. Vial-&-d, and . Barchiesi, Near-field theoretical study of a magneto-optical grating, Ultramicroscopy, vol.61, issue.1-4, pp.51-56, 1995.
DOI : 10.1016/0304-3991(95)00102-6

D. V. Labeke, A. Vial, V. Novosad, Y. Souche, M. D. Schlenker-&-a et al., Diffraction of light by a corrugated magnetic grating: experimental results and calculation using a perturbation approximation to the Rayleigh method, Optics Communications, vol.124, issue.5-6, pp.519-547, 1996.
DOI : 10.1016/0030-4018(95)00598-6

R. Petit, Electromagnetic Theory of Gratings, 1980.
DOI : 10.1007/978-3-642-81500-3

M. Bagieu-&-d and . Maystre, Waterman and Rayleigh methods for diffraction grating problems : extension of the convergence domain, J. Opt. Soc. Am. A pp, pp.1566-76, 1998.

R. Carminati-&-j and . Greffet, Influence of dielectric contrast and topography on the near field scattered by an inhomogeneous surface, Journal of the Optical Society of America A, vol.12, issue.12, pp.2716-2725, 1995.
DOI : 10.1364/JOSAA.12.002716

D. V. Barchiesi-&-d and . Labeke, A perturbative diffraction theory of a multilayer system: applications to near-field optical microscopy SNOM and STOM, Ultramicroscopy, vol.57, issue.2-3, pp.196-203, 1995.
DOI : 10.1016/0304-3991(94)00135-A

P. Yeh, Electromagnetic propagation in birefringent layered media, Journal of the Optical Society of America, vol.69, issue.5, pp.742-755, 1979.
DOI : 10.1364/JOSA.69.000742

F. Abelès, Investigations on the propagation of sinusoidal electromagnetic waves in stratified media. Application to thin films, Ann. Phys. Paris, vol.5, pp.596-706, 1950.

J. Vigoureux, Use of Einstein???s addition law in studies of reflection by stratified planar structures, Journal of the Optical Society of America A, vol.9, issue.8, p.1313, 1992.
DOI : 10.1364/JOSAA.9.001313

K. J. Kunz-&-r and . Luebbers, The finite difference time domain method for electromagnetics, 1993.

A. Taflove-&-s and . Hagness, Computational electrodynamics : The finite difference time domain method, 2000.

K. Yee, Numerical Solution of Initial Boundary Value Problems involving Maxwell's Equations, IEEE Trans. Antennas and Propagation, vol.14, pp.302-309, 1966.

J. Schneider-&-s and . Hudson, A finite-difference time-domain method applied to anisotropic material, IEEE Transactions on Antennas and Propagation, vol.41, issue.7, pp.994-1003, 1993.
DOI : 10.1109/8.237636

J. Ma, J. Xu-&-z, and . Chen, Nonlinear PML for absorption of nonlinear electromagnetic waves, IEEE MTT-S Int. Microwave Symp, vol.3, pp.1381-1385, 1997.

G. Lazzi, Unconditionally stable D-H FDTD formulation with anisotropic PML boundary conditions, IEEE Microwave and Wireless Components Letters, vol.11, issue.4, pp.149-51, 2001.
DOI : 10.1109/7260.916326

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.477.3151

J. Berenger, A perfectly matched layer for the absorption of electromagnetic waves, Journal of Computational Physics, vol.114, issue.2, pp.185-200, 1994.
DOI : 10.1006/jcph.1994.1159

J. Berenger, A perfectly matched layer for free-space simulation in finite-difference computer codes, Ann. Telecomm, vol.51, pp.39-46, 1996.

J. Berenger, Three-Dimensional Perfectly Matched Layer for the Absorption of Electromagnetic Waves, Journal of Computational Physics, vol.127, issue.2, pp.363-79, 1996.
DOI : 10.1006/jcph.1996.0181

S. Haitao, K. Kuroda-&-y, and . Suzuki, Non-uniform grid finite-difference time-domain method for the simulation of electromagnetic distributions, IEEE Antennas and Propagation Society International Symposium, vol.1, pp.124-131, 1996.

S. Bozhevolnyi, K. Pedersen, T. Skettrup, X. Zhang-&-m, and . Belmote, Far- and near-field second-harmonic imaging of ferroelectric domain walls, Optics Communications, vol.152, issue.4-6, pp.221-225, 1998.
DOI : 10.1016/S0030-4018(98)00176-X

I. Smolyaninov, C. Lee-&-c, and . Davis, Near-field second harmonic imaging of lead zirconate titanate piezoceramic, Applied Physics Letters, vol.74, issue.14, pp.1942-1946, 1999.
DOI : 10.1063/1.123735

V. Dmitriev, G. Gurzadyan-&-d, and . Nikogosyan, Handbook of nonlinear optical crystals, 1999.

D. V. Labeke-&-d and . Barchiesi, Probes for scanning tunneling optical microscopy: a theoretical comparison, Journal of the Optical Society of America A, vol.10, issue.10, pp.2193-201, 1993.
DOI : 10.1364/JOSAA.10.002193

V. Bhanthumnavin-&-c and . Lee, Optical second-harmonic generation at total reflection in a potassium dihydrogen phosphate crystal, Physical Review A, vol.50, issue.3, pp.2579-86, 1994.
DOI : 10.1103/PhysRevA.50.2579

Z. Li, B. Gu-&-g, and . Yang, Strong localization of near-field second-harmonic generation for nonlinear mesoscopic surface structures, Physical Review B, vol.59, issue.19, pp.12622-12628, 1999.
DOI : 10.1103/PhysRevB.59.12622

A. Xie, B. Gu, G. Yang-&-z, and . Zhang, domains, Physical Review B, vol.63, issue.5, pp.54104-54105, 2001.
DOI : 10.1103/PhysRevB.63.054104

S. Bozhevolnyi-&-v and . Lozovski, Second-harmonic scanning optical microscopy of individual nanostructures, Physical Review B, vol.65, issue.23, pp.235420-235421, 2002.
DOI : 10.1103/PhysRevB.65.235420

T. Grosjean-&-d and . Courjon, Polarization filtering induced by imaging systems: Effect on image structure, Physical Review E, vol.67, issue.4, pp.1-6, 2003.
DOI : 10.1103/PhysRevE.67.046611

J. Greffet-&-r and . Carminati, Image formation in near-field optics, Progress in Surface Science, vol.56, issue.3, pp.133-237, 1997.
DOI : 10.1016/S0079-6816(98)00004-5

J. Porto, R. Carminati-&-j, and . Greffet, Theory of electromagnetic field imaging and spectroscopy in scanning near-field optical microscopy, Journal of Applied Physics, vol.88, issue.8, pp.4845-4850, 2000.
DOI : 10.1063/1.1311811

L. Novotny, E. Sánchez-&-x, and . Xie, Near-field optical imaging using metal tips illuminated by higher-order Hermite???Gaussian beams, Ultramicroscopy, vol.71, issue.1-4, pp.21-30, 1998.
DOI : 10.1016/S0304-3991(97)00077-6

V. Konopsky, Operation of scanning plasmon near-field microscope with gold and silver tips in tapping mode: demonstration of subtip resolution, Optics Communications, vol.185, issue.1-3, pp.83-93, 2000.
DOI : 10.1016/S0030-4018(00)00994-9

H. Cory, A. Boccara, J. Rivoal-&-a, and . Lahrech, Electric field intensity variation in the vicinity of a perfectly conducting conical probe: Application to near-field microscopy, Microwave and Optical Technology Letters, vol.18, issue.2, pp.120-124, 1998.
DOI : 10.1002/(SICI)1098-2760(19980605)18:2<120::AID-MOP10>3.0.CO;2-B

L. Novotny, M. Berverluis, K. Youngworth-&-t, and . Brown, Longitudinal Field Modes Probed by Single Molecules, Physical Review Letters, vol.86, issue.23, pp.5251-5255, 2001.
DOI : 10.1103/PhysRevLett.86.5251

L. Novotny, R. Bian-&-x, and . Xie, Theory of Nanometric Optical Tweezers, Physical Review Letters, vol.79, issue.4, pp.645-653, 1997.
DOI : 10.1103/PhysRevLett.79.645

E. Sánchez, L. Novotny-&-x, and . Xie, Near-field fluorescencce microscopy based on two-photn excitation with metal tips, Phys. Rev. Let, vol.82, pp.14014-14021, 1999.

Y. Kawata, C. Xu-&-w, and . Denk, Feasibility of molecular-resolution fluorescence near-field microscopy using multi-photon absorption and field enhancement near a sharp tip, Journal of Applied Physics, vol.85, issue.3, pp.1294-301, 1999.
DOI : 10.1063/1.369260

A. Zayats-&-v and . Sandoghdar, Apertureless near-field optical microscopy via local second-harmonic generation, Journal of Microscopy, vol.202, issue.1, pp.94-103, 2001.
DOI : 10.1046/j.1365-2818.2001.00810.x

I. Smolyaninov, A. Zayats-&-c, and . Davis, Near-field second harmonic generation from a rough metal surface, Physical Review B, vol.56, issue.15, pp.9290-9293, 1997.
DOI : 10.1103/PhysRevB.56.9290

V. Shalaev-&-a and . Sarychev, Nonlinear optics of random metal-dielectric films, Physical Review B, vol.57, issue.20, pp.13265-88, 1998.
DOI : 10.1103/PhysRevB.57.13265

J. Greffet-&-c and . Baylard, Nonspecular astigmatic reflection of a 3D gaussian beam on an interface, Optics Communications, vol.93, issue.5-6, pp.271-277, 1992.
DOI : 10.1016/0030-4018(92)90184-S

W. Nasalski, Longitudinal and transverse effects of nonspecular reflection, Journal of the Optical Society of America A, vol.13, issue.1, pp.172-81, 1996.
DOI : 10.1364/JOSAA.13.000172

F. Baida, D. V. Labeke-&-j, and . Vigoureux, Theoretical study of near-field surface plasmon excitation, propagation and diffraction, Optics Communications, vol.171, issue.4-6, pp.317-348, 1999.
DOI : 10.1016/S0030-4018(99)00565-9

F. Baida, D. Barchiesi-&-d, and . Vanlabeke, Near-field effects of focused illumination on periodic structures in scanning tunneling optical microscopy, Optics Letters, vol.24, issue.22, pp.1587-1596, 1999.
DOI : 10.1364/OL.24.001587

F. Baida, D. V. Labeke-&-j.-m, and . Vigoureux, Numerical study of the displacement of a three-dimensional Gaussian beam transmitted at total internal reflection Near-field applications, Journal of the Optical Society of America A, vol.17, issue.5, pp.858-66, 2000.
DOI : 10.1364/JOSAA.17.000858

T. Driscoll-&-d and . Guidotti, Symmetry analysis of second-harmonic generation in silicon, Physical Review B, vol.28, issue.2, pp.1171-1174, 1983.
DOI : 10.1103/PhysRevB.28.1171

T. Grosjean, D. Courjon-&-m, and . Spajer, An all-fiber device for generating radially and other polarized light beams, Optics Communications, vol.203, issue.1-2, pp.1-5, 2002.
DOI : 10.1016/S0030-4018(02)01122-7

URL : https://hal.archives-ouvertes.fr/hal-00093567

E. Palik, Handbook of Optical Constants of Solids, 1997.

T. Heinz, M. Loy-&-w, and . Thompson, Study of Si(111) Surfaces by Optical Second-Harmonic Generation: Reconstruction and Surface Phase Transformation, Physical Review Letters, vol.54, issue.1, pp.63-69, 1985.
DOI : 10.1103/PhysRevLett.54.63

Y. An-&-s and . Cundiff, Bulk and Surface Contributions to Resonant Second-Harmonic Generation from Si(001) surfaces, Appl. Phys. Lett, vol.81, p.5174, 2002.

J. Seidel, S. Grafstrm, L. Eng, and &. L. Bischoff, Surface plasmon transmission across narrow grooves in thin silver films, Applied Physics Letters, vol.82, issue.9, p.1368, 2003.
DOI : 10.1063/1.1558219

A. Zayats, T. Kalkbrenner, V. Sandoghdar-&-j, and . Mlynek, Second-harmonic generation from individual surface defects under local excitation, Physical Review B, vol.61, issue.7, pp.4545-4553, 2000.
DOI : 10.1103/PhysRevB.61.4545

R. Chang-&-n and . Bloembergen, Experimental Verification of the Laws for the Reflected Intensity of Second-Harmonic Light, Physical Review, vol.144, issue.2, pp.775-80, 1966.
DOI : 10.1103/PhysRev.144.775

.. Au-niveau-de-la-surface, La couche métallique est en argent (? c (2?) = ?1, 13 + 0, 45i) Elle se situe en z = 0. L'épaisseur de la couche est e = 60 nm et sa largeur de l = 20 µm. Les unités sont normalisées par rapport au maximum de l'intensité fondamentale avec la couche métallique. (a) Vue d'ensemble. (b) Zoom de la figure (a) sur le milieu de transmission (z > 0), Module carré du champ au second harmonique dans la configuration de Kretschmann, p.134