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 <i>s</i>-polarized second-harmonic light can be generated only by a mixture of <i>s</i>- and <i>p</i>-polarized illumination. The effects that the departure from cylindrical shape has on the resonances were also studied.
© 2003 Optical Society of America
(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
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)