利用球差透镜获得超衍射极限聚焦

从ＨｕｙｇｅｎｓＦｒｅｓｎｅｌ衍射积分公式出发，得到了高斯光束经过球差透镜聚焦之后聚焦光场的光强分布的表示式。数值计算结果表明，当透镜存在负球差时，可获得超衍射极限聚焦，即得到的聚焦光斑比高斯光束经过无球差透镜聚焦而得到的聚焦光斑还小。并且，透镜的负球差系数越大，得到的聚焦光斑越小。相反，当高斯光束经过正球差透镜聚焦，得到的聚焦光斑比无球差时大。透镜的球差系数愈大，得到的聚焦光斑愈大。讨论了透镜的球差对轴上光强最大点（最佳聚焦点）的影响。

Lenses with Spherical Aberration for Generating Subdiffraction-limited Focusing

Based on Huygens Fresnel diffraction integral, an expression describing the focused field of Gaussian beams focused by a lens with spherical aberration is derived. The numerical results show that when the coefficient of the spherical aberration is negative, one can get subdiffraction limited focusing, that is, one can achieve a smaller focused beam radius than that of no spherical aberration (SA) cases. The larger the coefficient of negative SA, the smaller the focused beam radius. On the contrary, when a Gaussian beam is focused by lenses with positive SA, the focused beam radius is larger than that of no SA cases. And, the larger coefficient of positive SA, the larger the focused beam radius. The effect of the SA coefficient on the positions where the axial focused intensity is maximum (best focal point) is also discussed.