为了研究梯度折射率介质中双曲余弦高斯光束的束腰及其位置，推导出了双曲余弦高斯光束在梯度折射率介质中的传输场，并运用空间二阶矩的定义解出了光斑尺寸、束腰宽度及位置的表达式，讨论了梯度折射率介质对双曲余弦高斯光束的光斑尺寸、束腰宽度及位置的影响。研究结果表明：梯度折射率介质中光斑尺寸随传输距离的增加出现了周期性变化，周期由折射率系数决定；随偏心参数的增大，束腰宽度先逐渐减小再逐渐增大后趋于稳定；并且发现偏心参数决定光斑尺寸振荡幅度。

In order to study beam waist width and waist location of cosh-Gaussian beams in a Gradient-index medium, the propagation field of cosh-Gaussian beams in a gradient-index medium is deduced, and expressions of spot size , beam waist width and waist location by using the definitions of second-order moment are presented. Based on the expressions, the influence of the Gradient-index medium on the spot size, beam waist width and waist location are mainly discussed. The results show that spot size cyclical changes in a Gradient-index medium with increasing distance from the propagation, and the cycle is determined by gradientindex parameters. With increasing eccentric parameters, beam waist width first decreases then increases and stabilizes at last, and the spot size oscillation amplitude is determined by eccentric parameters.