## Second-harmonic generation in the scattering of light by two-dimensional particles

JOSA B, Vol. 20, Issue 10, pp. 2150-2161 (2003)

http://dx.doi.org/10.1364/JOSAB.20.002150

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### Abstract

A numerical technique for studying the generation of second-harmonic radiation in the interaction of light with two-dimensional particles of arbitrary shape is described. The medium of which the particles are composed is assumed to be homogeneous and isotropic. For the special case of cylindrical particles the numerical results are compared with results obtained with a Mie-type theory. The numerical technique is then illustrated through calculations for particles of various shapes by use of a free-electron model for nonlinear polarization. Among other things, we have found that, when a symmetrical particle is illuminated along its axis of symmetry, there is no second-harmonic radiation along that axis and that *s*-polarized second-harmonic light can be generated only by a mixture of *s*- and *p*-polarized illumination. The effects that the departure from cylindrical shape has on the resonances were also studied.

© 2003 Optical Society of America

**OCIS Codes**

(190.3970) Nonlinear optics : Microparticle nonlinear optics

(190.4350) Nonlinear optics : Nonlinear optics at surfaces

(240.4350) Optics at surfaces : Nonlinear optics at surfaces

(290.5850) Scattering : Scattering, particles

**Citation**

Claudio I. Valencia, Eugenio R. Méndez, and Bernardo S. Mendoza, "Second-harmonic generation in the scattering of light by two-dimensional particles," J. Opt. Soc. Am. B **20**, 2150-2161 (2003)

http://www.opticsinfobase.org/josab/abstract.cfm?URI=josab-20-10-2150

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### References

- J. F. McGilp, “Optical characterization of semiconductor surfaces and interfaces,” Prog. Surf. Sci. 49, 1–106 (1995).
- Y. R. Shen, “Wave mixing spectroscopy for surface studies,” Solid State Commun. 102, 221–229 (1997).
- G. Lüpke, “Characterization of semiconductor interfaces by second-harmonic generation,” Surf. Sci. Rep. 35, 75–161 (1999).
- M. C. Downer, B. S. Mendoza, and V. I. Gavrilenko, “Optical second harmonic spectroscopy of semiconductor surfaces: advances in microscopic understanding,” Surf. Interface Anal. 31, 966–986 (2001).
- F. Brown, R. E. Parks, and A. M. Sleeper, “Nonlinear optical reflection from a metallic boundary,” Phys. Rev. Lett. 14, 1029–1031 (1965).
- F. Brown and R. E. Parks, “Magnetic-dipole contribution to optical harmonics in silver,” Phys. Rev. Lett. 16, 507–509 (1966).
- N. Bloembergen, R. K. Chang, and C. H. Lee, “Second harmonic generation of light in reflection from media with inversion symmetry,” Phys. Rev. Lett. 16, 986–989 (1966).
- N. Bloembergen, R. K. Chang, S. S. Jha, and C. H. Lee, “Optical second-harmonic generation in reflection from media with inversion symmetry,” Phys. Rev. 174, 813–822 (1968).
- J. Rudnick and E. A. Stern, “Second harmonic generation from metal surfaces,” Phys. Rev. B 4, 4274–4290 (1971).
- P. Guyot-Sionnest and Y. R. Shen, “Bulk contribution in surface second-harmonic generation,” Phys. Rev. B 38, 7985–7989 (1988).
- B. S. Mendoza and W. L. Mochán, “Exactly solvable model of surface second-harmonic generation,” Phys. Rev. B 53, 4999–5006 (1996).
- B. S. Mendoza and W. L. Mochán, “Erratum: Exactly solvable model of surface second-harmonic generation,” Phys. Rev. B 53, 4999 (1996).
- G. A. Farias and A. A. Maradudin, “Second harmonic generation in reflection from a metallic grating,” Phys. Rev. B 30, 3002–3012 (1984).
- R. T. Deck and R. K. Grygier, “Surface-plasmon enhanced harmonic generation at a rough metal surface,” Appl. Opt. 23, 3202–3213 (1984).
- J. L. Coutaz, M. Neviere, E. Pic, and R. Reinisch, “Experimental study of surface-enhanced second-harmonic generation on silver gratings,” Phys. Rev. B 32, 2227–2232 (1985).
- A. R. McGurn, V. M. Agranovich, and T. A. Leskova, “Weak-localization effects in the generation of second harmonics of light at a randomly rough vacuum-metal grating,” Phys. Rev. B 44, 11441–11456 (1991).
- K. A. O’Donnell, R. Torre, and C. S. West, “Observations of backscattering effects in second-harmonic generation from a weakly rough metal surface,” Opt. Lett. 21, 1738–1740 (1996).
- K. A. O’Donnell, R. Torre, and C. S. West, “Observations of second-harmonic generation from randomly rough metal surface,” Phys. Rev. B 55, 7985–7992 (1997).
- K. A. O’Donnell and R. Torre, “Second-harmonic generation from strongly rough metal surfaces,” Opt. Commun. 138, 341–344 (1997).
- M. Leyva-Lucero, E. R. Méndez, T. A. Leskova, A. A. Maradudin, and J. Q. Lu, “Multiple scattering effects in the second harmonic generation of light in reflection from a randomly rough metal surface,” Opt. Lett. 21, 1809–1811 (1996).
- M. A. Leyva-Lucero, E. R. Méndez, T. A. Leskova, and A. A. Maradudin, “Destructive interference effects in the second harmonic light generated at randomly rough metal surfaces,” Opt. Commun. 161, 79–94 (1999).
- X. M. Hua and J. I. Gersten, “Theory of second harmonic generation by small metal spheres,” Phys. Rev. B 33, 3756–3764 (1986).
- D. Rogovin and T. P. Shen, “Microparticle surface-enhanced second-harmonic generation,” J. Opt. Soc. Am. B 5, 1886–1889 (1988).
- K. Hayata and M. Koshiba, “Theory of surface-emitting second-harmonic generation from optically trapped microspheres,” Phys. Rev. A 46, 6104–1889 (1992).
- J. Martorell, R. Vilaseca, and R. Crobalán, “Scattering of second-harmonic light from small spherical particles ordered in a crystalline lattice,” Phys. Rev. A 55, 4520–4525 (1997).
- J. I. Dadap, J. Shan, K. B. Eisenthal, and T. F. Heinz, “Second-harmonic Rayleigh scattering from a sphere of centrosymmetric material,” Phys. Rev. Lett. 83, 4045–4048 (1999).
- V. L. Brudny, B. S. Mendoza, and W. L. Mochán, “Second-harmonic generation from spherical particles,” Phys. Rev. B 62, 11152–11162 (2000).
- R. W. Boyd, Nonlinear Optics (Academic, New York, 1992).
- J. E. Sipe and G. I. Stegeman, “Nonlinear optical response of metal surfaces,” in Surface Polaritons, V. M. Agranovich and D. L. Mills, eds. (North-Holland, Amsterdam, 1982), pp. 661–701.
- Y. R. Shen, The Principles of Nonlinear Optics (Wiley, New York, 1984), p. 10.
- D. Maystre, M. Neviere, and R. Reinisch, “Nonlinear polarisation inside metals: a mathematical study of the free electron model,” Appl. Phys. A 39, 115–121 (1986).
- C. I. Valencia, E. R. Méndez, and B. S. Mendoza, “Second-harmonic generation in the scattering of light by an infinite cylinder,” submitted to J. Opt. Soc. Am. B.
- E. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge U. Press, Cambridge, 1999), p. 638.
- A. Mendoza-Suárez and E. R. Méndez, “Light scattering by reentrant fractal surfaces,” Appl. Opt. 36, 3521–3531 (1997).
- C. I. Valencia and R. A. Depine, “Resonant scattering of light by an open cylindrical cavity ruled on a highly conducting flat surface,” Opt. Commun. 159, 254–265 (1999).
- A. A. Maradudin, T. Michel, A. R. McGurn, and E. R. Méndez, “Enhanced backscattering of light from a random grating,” Ann. Phys. (N.Y.) 203, 255–307 (1990).
- M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions (Dover, New York, 1970), p. 364.
- P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6, 4370–4379 (1972).
- S. C. Hill and R. E. Benner, “Morphology-dependent resonances,” in Optical Effects Associated with Small Particles, P. W. Barber and R. K. Chang, eds. (World Scientific, Singapore, 1988), pp. 3–61.
- J. P. Kottmann, O. J. F. Martin, D. R. Smith, and S. Schultz, “Non-regularly shaped plasmon resonant nanoparticle as localized light source for near field microscopy,” J. Microsc. (Oxford) 202, 60–65 (2000).
- J. P. Kottmann, O. J. F. Martin, D. R. Smith, and S. Schultz, “Dramatic localized electromagnetic enhancement in plasmon resonant nanowires,” Chem. Phys. Lett. 341, 1–6 (2001).

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