Second-harmonic generation in a KTP crystal driven by vortex beams with integer topological charges

Second-harmonic generation (SHG) is a nonlinear, perturbative optical process governed by the second-order nonlinear susceptibility of birefringent materials that lack a center of inversion. We theoretically investigate SHG in a potassium titanyl phosphate (KTP) crystal using scalar Laguerre-Gaussian (LG) vortex beams carrying integer topological charges (TCs). A detailed theoretical model is developed to validate the experimental results presented in [1]. Our analysis predicts that, for a given beam waist and power of the fundamental laser beam, the SHG efficiency decreases as the TC of the fundamental beam increases. The law of orbital angular momentum (OAM) upscaling is strictly followed during the perturbative interaction between the laser and the crystal. Additionally, we propose two simple and direct methods to measure the TCs of the fundamental and second-harmonic (SH) beams using (i) a tilted spherical bi-convex lens and (ii) an interference technique involving LG vortices and their corresponding mirror images. The beam divergence of both the fundamental and SH beams is found to be directly proportional to their respective TCs.