像散对聚焦正弦-高斯光束参数的影响

Influence of astigmatism on the beam parameters of focusing sin-Gaussian beams

应用二阶矩法推导出了正弦-高斯光束通过像散透镜后束宽的解析表达式。通过数值计算对正弦-高斯光束通过像散透镜后的光束参数,例如束宽和远场发散角的相对误差进行了研究。结果表明:像散使x方向与y方向的束宽一般不相等,束宽的相对误差在传输距离z上存在零点,但x方向与y方向零点的位值不相同;几何焦面上x方向与y方向束宽的相对误差随像散系数和偏心参量的变化相同,而在像方束腰面上两方向束宽的相对误差变化迥异,适当选择像散系数可消除x方向束腰面上束宽的相对误差。受像散系数的影响远场发散角在x方向与y方向的相对误差不相等,并且与偏心参量有关。

The analytical fommla for the beam width of sin - Ganssian beams passing through an astigmatic lens is derived by using the second - order moment method. By numerical calculation the relative errors of the beam parameters, such as the beam width and far- field divergence angle of sin - Ganssian beams after passing through an astigmatic lens are studied. It is shown that the beam widths in the x and y directions are not equal due tothe astigmatism, the relative errors of the beam widths equal to zero at some points of the propagation distance z, but the points are different in the two directions; with the changes of astigmatic coefficient and decentered parameter the relative errors of the beam widths in the x and y directions at the geometrical focal plane are equal, while at the waist plane in the image space they are different, by choosing the proper astigmatic confiqcient the relative errors of the beam width in the x direction at the waist plane can be eliminated; the relative errors of the far - field divergence angles in the x and y directions are not equal due to the astigmatism and dependant on the decentered parameter.