球差透镜对余弦高斯光束聚焦特性的影响

Effect of the spherically aberrated lens on the property of cosine-Gaussian

本文基于余弦高斯光束通过球差透镜聚焦的轴上光强分布表达式,讨论了球差系数kS1及高斯光束菲涅耳数Nw对轴上光强的影响。数值计算结果表明负球差可作为获得轴向光强平顶分布的一种方法。当无球差时,最佳聚焦点位于几何焦点的左侧。当透镜具有正球差时,通过改变菲涅耳数Nw可以实现最佳聚焦点由几何焦点左侧zf1快速跃变到右侧zf2,此时出现焦开关现象。球差系数越大,对应的相对跃迁量Δzf=|zf1-zf2|也越大,而临界菲涅耳数(Nw)c则越小,如当kS1=0.5和0.3时,发生跃变的临界点分别为(Nw)0.5=7.03和(Nw)0.3=8.68,其相对跃迁量Δzf分别为0.246及0.146。

Based on the expression for the axial light intensity of cosine - Gaussian beam by a lens with spherical aberration, the influence of the coefficient of the spherical aberration and Fresnal number of Gaussian beams on the axial intensity distribution is discussed. The numerical results show that the lens with negative spherical aberration may be an approach for achieving flattened laser intensity distribution alone propagation axis. For the lens without spherical aberration, the maximum light intensity, or the best focal point is on the left side of the geometrical focus. For the lens with positive spherical aberration, the best focal position can leap to the right side of geometrical focus, ze from the left of it, zf1 when the value of Fresnel number of Gaussian beams Nw changes, and the focal switch occurs at this point. With the increasing of the coefficient of the spherical aberration kS1 relative transition height△zf=｜zf1-zf2｜ increases, but the value of critical Fresnel number （Nw）c decreases. For example, when the coefficient of the spherical aberration equals 0.5 and 0.3,the critical Fresnel number equals 7.03 and 8.68 （ when the tmnssition occurs）, and the relative transition height △zf equals 0. 246 and 0.146 respectively.