环状平顶光束的传输特性研究

利用偏心高斯光束相干叠加方法，建立了柱坐标系下环状平顶光束模型.采用广义强度二阶矩定义，推导出环状光束广义M2因子的解析表达式.利用广义衍射积分理论，给出环状光束经过近轴ABCD光学系统的传输公式，并进一步给出了环状平顶光束修正的菲涅耳数定义.分析了环状平顶光束在自由空间的传输规律.研究结果表明，该模型可统一描述基模高斯光束、环状高斯光束以及环状平顶光束.环状平顶光束的广义M2因子和环状平顶光束的传输特性与其阶数及遮拦比有关.

Study on Propagation Properties of Annular Flattened Beams

Using the treatment of the combination of off-axial Gaussian beams,the model of the annular flattened beams under the cylindrical coordinate system was proposed.On the basis of the definition of generalized second-order moments,an analytical expression for the generalized M2-factor of annular beams was derived.Through the theory of generalized diffraction integration,the formula for the annular flattened beams propagating through paraxial ABCD optical systems were developed.Furthermore,the modified Fresnel number of annular flattened beams was defined,and propagation properties of annular flattened beams in free space were analyzed.It can be seen that the model proposed in this paper can describe fundamental Gaussian beams,annular Gaussian beams and annular flattened beams.The generalized M2 factor and propagation properties of annular flattened beams depend on the beam orders and the obscuration ratio.