Nonlinear beam shaping in periodical χ (2) fork gratings with structural defects

Abstract

Nonlinear beam shaping provides an efficient way to control the phase and amplitude of optical waves while shifting their frequency. Periodical topological structures with a modulated second-order nonlinear optical coefficient (χ (2)) are commonly used to generate special optical beams at new frequencies, e.g. the second harmonic vortices. In this paper, we theoretically study the influence of structural imperfection on nonlinear beam shaping and demonstrate how to utilize these imperfections for second harmonic generation with controlled orbital angular momentums. The results indicate that the studied nonlinear beam-shaping process has excellent tolerance to structural defects, and introducing designed defects of different scales and shapes constitutes a flexible approach for controlling the orbital angular momentum of light at new frequencies. As a proof of concept example, the nested χ (2) structures are designed for generating optical vortices with predesigned topological charges along different directions. In addition, the performance of the nonlinear generation of vortex beams with a fundamental beam shifted from the center of the fork grating is also discussed. The study opens up new prospects for the optimization of nonlinear χ (2) structures for special beam generation at new frequencies.