We demonstrate the full vectorial feature of second-harmonic generation (SHG), i.e., from infrared full Poincaré beams to visible full Poincaré beams, based on two cascading type I phase-matching beta barium borate crystals of orthogonal optical axes. We visualize the structured features of the vectorial SHG wave by using Stokes polarimetry and show the interesting doubling effect of the polarization topological index, i.e., a low-order full Poincaré beam is converted to a high-order one. However, the polarization singularities of both C points and L lines are found to keep invariant during the SHG process. Our scheme could offer a deeper understanding on the interaction of vectorial light fields with media and can be generalized to other nonlinear optical effects.

In the process of high-harmonic generation with a Laguerre-Gaussian (LG) mode, it was well established that the topological charge could be of an N-fold increase due to angular momentum conservation. Here, by mimicking the effect of high-harmonic generation, we devise a simple algorithm to generate optical vortex arrays carrying arbitrary topological charges with a single phase-only spatial light modulator. By initially preparing a coaxial superposition of suitable low-order LG modes, we demonstrate experimentally that the topological charges of the embedded vortices can be multiplied and transformed into arbitrarily high orders on demand, while the array structure remains unchanged. Our algorithm offers a concise way to efficiently manipulate the structured light beams and holds promise in optical micromanipulation and remote sensing.

We present both numerical and experimental results to study the diffraction of twisted light beams based on orbital angular momentum (OAM) eigenmode decomposition, where the total initial field, including light and aperture, is represented by a two-dimensional spectrum of Laguerre–Gaussian modes. We use a phase-only spatial light modulator to display a holographic grating for both generating the twisted light and mimicking the finite aperture. We take a triangular aperture as an example to describe the diffraction behavior of a twisted light beam carrying an OAM number of =3 from the near-field to far-field regions, where the interesting gradual formation of triangular bright lattices are observed. An excellent agreement between the numerical simulations and experimental observations is clearly seen. It is noted that this method is particularly useful for the study of the diffraction of twisted light fields incident on any apertures of rotational symmetry.