部分相干平顶高斯光束通过透镜的聚焦特性

Focusing properties of Partially Coherent Flattened Gaussian Beam passing through lens

利用惠更斯-菲涅尔衍射积分公式导出了部分相干平顶高斯光束(PCFGB)经过ABCD光学系统的传输公式。进一步导出了PCFGB经透镜聚焦后的任意z处、焦面处、聚焦场轴上的光强分布公式和等效束宽传输公式,并进行数值计算及分析。研究结果表明,PCFGB经透镜聚焦后的传输过程中,光强分布的平顶部分不会消退,并随着阶数N增加和菲涅耳数N_w减小,等效束宽增大,平顶化程度越好;任意z截平面处的光强和焦移量与阶数N无关,但随N_w的增加,其光强成倍增大、焦移量却减小。

The propagation formula of the cross- spectral density of partially coherent flattened Gaussian beam （PCFGB） through ABCD optical system was derived by using the Huygens - Fresnel diffraction integral formula. The expressions of the equivalent beam widths and the intensity of PCFGB through lens were also derived. Simulation result Mows that, the fiat - topped part of the intensity was not died as the PCFGB propagation through the lens. It is shown that when the order N of PCFGB increases and the Fresnel number Nw of the lens decreases, the equivalent beam widths increase and the fiat - topped degree became good. The light intensity of arbitrary z plane and the focal shift were not depended on the order N. However, the intensity of PCFGB increase and the focal shift decrease with the Fresnel number Nw of the lens increasing.