Second-harmonic wave patterns induced by the tightly focused radially polarized beam loaded with off-axis vortices

We investigated second-harmonic wave patterns induced by the tightly focused radially polarized beam loaded with off-axis vortices. The expression of the electric field of tightly focused radially polarized beam loaded with off-axis vortices through ZnSe crystal was derived, based on which the expression of the polarization distributions of near-field second-harmonic and the intensity distributions of far-field second-harmonic at different incident crystal planes were obtained. Numerical simulations indicated the distinctive polarization distributions of near-field second-harmonic and the intensity distributions of far-field second-harmonic when the incident crystal planes were (110) and (001). The results showed that second-harmonic wave patterns could be regulated flexibly by changing the distance and number of off-axis vortices.