在傍轴近似下，推导出了左手材料平板聚焦系统的传输矩阵，并利用ABCD定律得到了高斯光束在左手材料中和经过平板透镜聚焦后的传输公式。高斯光束在左手材料内部和像空间的传输公式的研究表明：像高斯光束和物高斯光束束腰大小一致，即左手材料平板透镜实际上对高斯光束没有聚焦作用。研究同时表明左手材料平板对高斯光束的聚焦与几何光学成像规律完全一致，而不存在一般透镜聚焦时的焦移效应。

Under paraxial approximation, the transfer matrix of left-handed slab focusing system is derived. Using ABCD law, the propagation expressions for Gaussian beam focused by a left-handed material slab are obtained. On the basis of propagation formula, the focusing properties of Gaussian beam are analyzed. The beam waist of image Gaussian beam is equal to the beam waist of object Gaussian beam under paraxial approximation, that is to say, the left-handed material slab can not focus Gaussian beam. The focusing for Gaussian beam with a left-handed material coincides with imaging rules of geometrical optics and does not have focal shift.