Evolution of the second-harmonic beam based on a high-order Laguerre–Gaussian laser

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We systematically investigated the second-harmonic generation and propagation based on a high-order Laguerre–Gaussian laser. The Laguerre–Gaussian modes, second-harmonic generation, and propagation processes with opposite topological charges have been theoretically analyzed step by step. Using a side-pumped Nd:YAG module and optimizing the cavity parameters with spherical aberration, the high-order Laguerre–Gaussian laser has been experimentally realized in a solid-state laser. Subsequently, the evolution of the second-harmonic beam for the Laguerre–Gaussian laser has been measured in detail under different cases. The theory and experiment confirm that the transmission properties of the second-harmonic beam for 2 m and −2 m topological charges are different from those of the 0 topological charge. Furthermore, we can separate out the second-harmonic beam with 0 topological charge. Such an interesting characteristic will facilitate potential applications in intracavity second-harmonic generation and spontaneous parametric down-conversion of structural optics.