超短脉冲经过小数值口径透镜的聚焦特性

 从亥姆霍兹方程出发，考虑透镜的色差和球差，得到了超短脉冲经过小数值口径透镜后光场的解析表达式；利用数值模拟得到了旁轴焦平面和边缘焦平面上光场强度的时空分布，以及聚焦区域内轴上点的强度分布图，并分析了色差和球差的大小对它们的影响。由于通过透镜中心和边缘之间的大部分脉冲产生了干涉相消，因此在旁轴焦平面与边缘焦平面上都出现前、后两个峰值相差很大的脉冲，并且随着球差的增大，两峰值差更大了；聚焦区域内轴上点的强度分布基本是对称的，强度最大点不是出现在旁轴和边缘焦平面上，而是在它们之间的某个位置，并且随着球差的增加，该位置将向聚焦区域的边缘靠近。

Focusing of ultrashort pulse by small-aperture lenses

From the Helmholtz equation,the optical field analytical expression of an ultrashort pulse propagating through a small aperture lens was acquired with chromatic and spherical aberration.By numerical modulation of the analytical expression,the spatial and temporal distributions of intensity in the paraxial and marginal focal plane and on the axis were obtained,and the impact of spherical aberration on them was also summarized.Because of the interference among the pulses passing through the lens from center to edge,two pulses with apparently different peak values appeared both in the paraxial and in the marginal focal plane.The intensity distribution was basically symmetrical on the axis in the focal region.The peak value didn't appear in the paraxial or marginal focal plane,but at some point between the paraxial and the marginal focal plane.The peak value moved towards the edge of the focal region with the increase of the spherical aberration.