Abstract: The different orders of complex variable Hermite-Gaussian beams have different intensity and phase distributions. When the order increases, the number of vortex singularities increases, i.e., the number is equal to the order, and both the beam width and ellipticity also increase. The split-step Fourier method is used to numerically simulate the propagation of complex variable Hermite-Gaussian beams in strong nonlocal medium. When the initial power of the beam is equal to the critical power, the stable soliton can be obtained. The rotation direction of the soliton light intensity depends on the sign in front of the imaginary part in the parameter . However, when the initial power is not equal to the critical power, the breather with oscillating width can be obtained; The critical powers of solitons with different orders are equal, but the orbital angular momentum (OAM) increases as the order increases. After adding noise, the propagations of complex variable Hermite-Gaussian solitons are still stable.

Key words: nonlinear optics, strong nonlocal media, split-step Fourier method, complex variable Hermite-Gaussian beam, orbital angular momentum