Regulation of the Second Harmonic Generation of High-Order Poincaré Sphere Beams Using Different Phase Matching

High-order Poincaré sphere (HOPS) beams have attracted tremendous interest due to their complex polarization and phase characteristics. However, manipulating the second harmonics generation (SHG) of HOPS beams is still challenging. Here, we developed a vector-coupled wave model to predict petal-shaped intensity patterns and reveal a linear correlation between petal number and topological order (n = 2 → 4). Moreover, we experimentally investigated the multidimensional regulation of SHG in HOPS beams through tailored phase-matching strategies. By employing three distinct configurations—(i) type-I phase matching, (ii) type-II phase matching, and (iii) orthogonally arranged BBO crystals based on Type-I phase matching—we establish a comprehensive framework for controlling the spatial and polarization properties of SHG in n = 2 HOPS beams. These results advance the manipulation of structured light in nonlinear optics, providing insights for optimizing applications in optical communication and polarization imaging.