建立了空心锥状双高斯光束的模型。在空心高斯光束模型的基础上,由初始光场的光强分布,利用柱坐标下的柯林斯公式,导出了空心锥状双高斯光束经过傍轴光学系统的解析传输变换式由传输变换式计算分析了空心锥状双高斯光束在自由空间的可控传输特性,及在1,10和60 m的截面光环的光强分布。用KNbO3双轴晶体进行实验,获得了空心锥状双高斯光束,外锥折射的锥角等于入射光会聚角。实验表明,当空心光束处于锥状发射状态时,空心光束的光环内黑斑面积随传输距离的增加而增加,实验结果与模型吻合较好。该研究为进一步设计制备基于空心锥状双高斯光束的新型激光元件提供了理论依据和设计参量。

A new mathematical model named hollow cone double Gaussian beams is set up. Based on mathematical model of hollow double-Gaussian beams and the initial light field intensity distribution,the analytical propagation formula for hollow cone double Gaussian beams through paraxial system was derived by use of Collins formula under the cylindrical coordinates. Using the derived propagation formula,the controllable evolution properties of the intensity distribution of hollow cone double Gaussian beams in free space propagation were illustrated graphically at 1,10 and 60 m. After experenting with the biaxial crystal KNbO3,the hollow cone double Gaussian beams was obtained and the result,that the outer conic refraction angle of was equal to the convergence angle of the beams,was found. The experiment showed that the black spot areas in hollow beams increased with the transmission distance and the mathematical model of hollow cone double Gaussian beams was agreed to the experiment results basically. This research is significant for design of new laser hollow beams to generate the laser device based on hollow cone double Gaussian beams.