The vortex cosine-gaussian beam in strongly nonlocal nonlinear media

Different cosine phase factors n can make the vortex cosine-Gaussian beam(VCGB) exhibit a multi-ring structure. When the number of vortex points of the VCGB was 1, the analytical expression of the orbital angular momentum was the Dawson integral function. By the split-step Fourier method, the propagation of a VCGB in nonlocalized medium was numerically simulated. It was found that when the vortex point was asymmetric with respect to the origin, the energy flow distribution of the VCGB was asymmetric. The center of mass is move with the transmission of the beam in nonlocal medium, resulting in oblique transmission. If the sign in front of the imaginary part of the vortex point changes, the rotation direction of the soliton changes. When two VCGBs were transmitted in nonlocalized medium, they can be intertwined or transmitted in serpentine shapes. Therefore, the beam information can be encoded by changing the phase factor and the number of vortex points. The beam transmission path in the nonlocal medium can be controlled by changing the vortex position.