径向洛伦兹阵列光束在自由空间的传输特性

推导出有初始相位分布的径向洛伦兹阵列光束在自由空间传输的解析公式，用以研究相干合成光束在自由空间的传输特性。结果表明:在远场，具有不同相位分布的光束光强剖面成为空心形状，具有相同相位分布的光束光强剖面中心为亮斑。合成光束束宽和桶中功率与子光束束腰宽度、径向阵列的初始相位分布和半径有关。对所得结果用数值计算例做了说明。当阵列半径较大和束腰宽度较小时，具有不同相位分布和相同相位的光束束宽随传输距离的变化曲线和桶中功率都趋于一致。

Propagation properties of radial Lorentz array beam in free space

The analytical expression for the propagation of a radial Lorentz array beam with an initial phase distribution is derived and used to study the propagation properties of the coherently combined beam in free space. For the case of the radial Lorentz array beam with a certain different initial phase distribution, the intensity profile of the resulting beam becomes a dark-hollow one, whereas for the case of the array beam with an equal initial phase distribution, the center of the intensity profile is a bright spot. The beam width and power in the bucket of the resulting beam depend on the waist width of the Lorentz beamlet, and on the initial phase distribution and radius of the radial array. The results are illustrated by numerical examples. When the radius of the radial array is larger an