用二阶矩法研究复宗量正弦高斯光束的焦移

Focal Shift in Elegant sin Gaussian Beams Using Second-Order Moment Method

根据Collins公式,研究了复宗量正弦高斯光束通过薄透镜的聚焦特性,发现聚焦复宗量正弦高斯光束的轴上光强为零.用二阶矩法推导出了复宗量正弦高斯光束的束腰宽度及其位置的解析表达式,用此表达式可计算复宗量正弦高斯光束的焦移.作为特例,给出了聚焦正弦高斯光束和聚焦双曲正弦高斯光束的相对焦移解析表达式.研究表明,相对焦移与光学系统参数、光束参数以及菲涅耳数有关.当光束的入射面与透镜的距离取适当值时,会出现无焦移现象.

The focal shift of elegant sin-Gaussian beams passing through a lens was studied using the Collin＇s formula. It was found that the axial intensity intensity of a focused elegant sin-Gaussian beam was null. The second-order moment method was used to derive the analytical formulas for both beam waist and the position of the waist of the focused elegant sin-Gaussian beam. The focal shifts of elegant sin-Gaussian beams can be obtained using the derived formulas. The analytical formulas for the relative focus shifts of focused elegant sin-Gaussian beams were presented as examples. Numerical calculations demonstrate that focal shifts of focused elegant sin-Gaussian beams depend on optical system parameters, beam parameters and Fressnel number. Proper choice of the distance from the incidence plane to the lens leads to disappearance of focal shift.