Position Mapping Relationship for Converting Laguerre-Gaussian Beam Array into Hermite-Gaussian Beam Array Based on a Tilted Lens

A Laguerre-Gaussian beam can be converted into a Hermite-Gaussian beam using a tilted lens. In this work, a position mapping relationship was derived between the incident Laguerre-Gaussian beam array and the Hermite-Gaussian beam array converted by the tilted lens. When the tilted lens is rotated around an arbitrary axis by a certain angle, the positions of the two beam arrays will be symmetrical about that axis. In the experiments, Laguerre-Gaussian beam arrays of 1x1, 2x2, 3x3, 3x1, and 1x3 were generated using a spatial light modulator and converted into Hermite-Gaussian beam arrays via a tilted lens, and the above theoretical analysis was verified through comparison of the distributions of the two beam arrays. The experimental results are in perfect agreement with the theoretical analysis. Based on the theoretical results and the position distribution of the Hermite-Gaussian beam array, the topological charge of the Laguerre-Gaussian beam array can be detected. This work provides clearer theoretical guidance for the orbital angular momentum detection of Laguerre-Gaussian beam arrays.