Nanoscale nonlinear optical process: Theoretical modeling of second-harmonic generation for both forbidden and allowed light

Based on a combination of the multiple-multipole method and nonlinear coupled-wave equations, a rigorous three-dimensional numerical simulation of nonlinear optical interactions between an optical near field and a nonlinear medium is performed, allowing us to study the dependence of second-harmonic (SH) near-field intensity on tip-sample distance and the polarization state of the incident fundamental wave. It is demonstrated that allowed and forbidden light make different contributions to the SH near-field intensity.