Optical vortex copier and regenerator in the Fourier domain

The generation and manipulation of optical vortices are of fundamental importance in a variety of promising applications. Here, we develop a nonlinear optical paradigm to implement self- and cross-convolution of optical vortex arrays, demonstrating the features of a vortex copier and regenerator. We use a phase-only spatial light modulator to prepare the 1064 nm invisible fundamental light to carry special optical vortex arrays and use a potassium titanyl phosphate crystal to perform type II second-harmonic generation in the Fourier domain to achieve 532 nm visible structured vortices. Based on pure cross-convolution, we succeed in copying arbitrary-order single vortices as well as their superposition states onto a prearranged array of fundamental Gaussian spots. Also, based on the simultaneous effect of self- and cross-convolutions, we can expand the initial vortex lattices to regenerate more vortices carrying various higher topological charges. Our presented method of realizing an optical vortex copier and regenerator could find direct applications in optical manipulation, optical imaging, optical communication, and quantum information processing with structured vortex arrays.