在傍轴近似条件下，基于广义惠更斯菲涅耳衍射积分公式，推导了双曲正弦平方高斯光束在自由空间、左手平板材料中及通过左手平板材料后的三维光强传输公式，并进行数值计算和分析，探究了双曲正弦平方高斯光束通过左手平板材料的传输特性。研究表明，左手材料对双曲正弦平方高斯光束轴上光强和横向光强分布规律的影响是使光强呈对称分布；材料的负折射率会影响光束轴上光强极大值的位置；轴上光强和横向光强均随传输距离和偏心参数的改变而变化，即双曲正弦平方高斯光束不能保持其传输不变性。实际应用中，可用改变偏心参数的方法在不同位置对光束进行整形。

Under the paraxial approximation and based on the generalized Huygens-Fresnel diffraction integral formula, the propagation expressions of three-dimensional intensity of sinh-squared-Gaussian beams in free space, in a left-handed material slab and after propagation through the left-handed material slab are derived, and the numerical calculation and analysis are performed with the expressions to explore propagation properties of the sinh-squared-Gaussian beams through the left-handed material slab. The results show that the influence of the left-handed materials on the axial and the transversal intensity distribution of sinh-squared-Gaussian beams makes the intensity exhibit symmetrical distribution. The negative refractive index of the left-handed material slab changes the position of the maximum intensity. The axial and the transversal intensity changes with different propagation distances and decentered parameters, which shows that the sinh-squared-Gaussian beams cannot remain the same during propagation. In practical applications, it is feasible to shape beams in the manner of adjusting the decentered parameter at different locations.