从Collins公式出发研究了无光阑双曲正弦高斯光束的聚焦特性.研究发现聚焦双曲正弦高斯光束的轴上光强为零,因此Li和Wolf二人研究焦移的方法不再适用.使用环围功率法定义束宽和实际焦面,由此可以决定聚焦双曲正弦高斯光束的焦移.数值计算表明,聚焦双曲正弦高斯光束的焦移与偏心参数和菲涅耳数有关,焦移随偏心参数和菲涅耳数的减小而增大.此外,还分析了双曲正弦高斯光束的最佳聚焦问题.

Starting from the Collins formula, focusing properties of un-apertured sinh-Gaussian beam are studied by using the encircled-power method. It is found that the axial intensity of focused sinh-Gaussian beams vanishes, so that Li-Wolf's approach to the focal shift fails. The encircled-power method is introduced to define the beam width and real focal plane of focused sinh-Gaussian beams, thus their focal shift can be determined. Numerical calculations are performed and show that the focal shift in focused sinh-Gaussian beams depends on the Fresnel number and decentered parameter, and increases by decreasing them. The optimal focusing of sinh-Gaussian beams is also analyzed.