The propagation properties of vortex cosine-hyperbolic-Gaussian beams (vChGBs) through a strongly nonlocal nonlinear media (SNNM) are investigated theoretically based on the Snyder-Mitchell model. The propagation formula, the second-order intensity moment beam width and the curvature radius of an on-waist incident vChGB in SNNM are derived. The evolutions of the intensity distribution pattern, the beam width and the curvature radius during propagation in SNNM are illustrated graphically with numerical examples. It is found that the vChGBs pattern evolves periodically upon propagation and its behavior is strongly affected by the initial beam power and the beam parameters; the beam evolution is a breather-like. For a critical initial power and under specific values of the beam parameters, the beam characteristics are invariant during propagation; the vChGBs behavior is a soliton-like.

基于Snyder-Mitchell模型，从理论上研究了旋涡余弦-双曲-高斯光束（vChGBs）通过强非局部非线性介质（SNNM）的传播特性。推导了SNNM中腰部入射vChGB的传播公式，二阶强度矩光束宽度和曲率半径。用数值示例以图形方式说明了SNNM中传播过程中强度分布模式，光束宽度和曲率半径的变化。研究发现，vChGBs方向图在传播时会周期性地演化，其行为受到初始光束功率和光束参数的强烈影响。光束的演变就像呼吸一样。对于临界的初始功率并且在光束参数的特定值下，光束特性在传播过程中是不变的。