Second-harmonic wave induced by vortex beams with radial and azimuthal polarizations

The author investigated second-harmonic (SH) wave patterns generated by focused vortex beams with radial and azimuthal polarizations. Expressions for electric field components near the focus through a dielectric interface were obtained based on vector diffraction theory. Furthermore, the (110) and (001) planes of a crystal classified in the symmetry group 4?3m were considered as second order nonlinear optical medium to analyze nonlinear polarization and the intensity distributions of the SH wave in the far-field were simulated for topological charge m = 1 and 2. Numerical simulations indicated that the intensity and emission pattern of the SH wave depended principally on the electric field component and distribution near the focus. In particular, for the (001) plane, the intensity of the SH wave was strongly correlated with the existence of a longitudinal electric field.