Characterizing the propagation evolution of optical vortex lattices in astigmatic transformations of frequency-doubled laser modes

We develop a wave representation to characterize the propagation evolution of vortex lattice beams, which are produced through a frequency-doubling process of various high-order laser modes, followed by mode conversion. Their phase fields and phase gradients are further analyzed to verify the topological charge for each isolated vortex, as well as the symmetry and net charges of the vortex lattices. In the experiment, we demonstrate the generation of frequency-doubled high-order modes by utilizing an off-center pumped solid-state laser combined with intracavity second-harmonic generation. Subsequently, we employ an astigmatic mode converter to transform the generated frequency-doubled laser modes, obtaining vortex arrays. The strong agreement between theoretical analysis and experimental data not only validates the derived formula but also confirms the creation and characteristics of the vortex lattice beams.