Mode transformation of Laguerre-Gaussian solitons in nonlocal media with linear anisotropic diffraction

We investigate the mode transformation of Laguerre-Gaussian (LG) solitons in nonlocal media when the linear diffraction is anisotropic. We derive analytical solutions of LG solitons using a variational approach and simulate their dynamics numerically. Under the condition of isotropic diffraction and strong nonlocality, LG solitons propagate stably. Conversely, solitons exhibit mode conversion between LG and Hermite-Gaussian (HG) solitons when the diffraction is anisotropic. The physical mechanism of the mode transformations lies in symmetric breaking, modal coupling, and restructuring of the intensity distribution induced by linear anisotropy.