由轴锥镜折射阴影区产生的泊松衍射斑

Poisson Diffraction Spot Generated in Shadow Area of Axicon

为完善轴锥镜衍射场分布描述与认识,根据积分渐进理论处理了含大数且稳相点不在积分域中的衍射场积分函数,获得了轴锥镜折射阴影区的近轴域衍射场的近似解析解,且发现了该衍射场分布服从泊松散射分布这一新奇的现象。实验结果表明:在其阴影近轴区域的光强分布很好地服从零阶贝塞尔函数,并且中心光斑直径正比于传播距离,但其强度随纵面传播而衰减。由于照射光束与衍射斑的直径都随传播距离线性增大,二者永远不会重叠,所以理论上这个泊松衍射可传播到无穷远。相对于传统的圆屏衍射实现方式,轴锥镜透镜为超远距离空间中泊松衍射斑的产生提供了一种新的、更便捷的方法。

In order to describe and congnize the distribution of the diffraction field of axicon completely, according to the theory of asymptotic expansion, the diffraction integral function with large number and non-stationary end-point in integral domain is processed, the approximate analytical solution of intensity distribution in the shadow paraxial area of axicon is obtained, and a novel phenomenon that the distribution is Poisson diffraction spot is found. The experimental results show that the intensity distribution of diffraction spot follows zeroth-order Bessel function in shadow paraxial region, and the diffraction spot diameter increases linearly with the propagation distance, although its energy in longitudinal section has attenuation along with propagation. The illuminated beam and Poisson diffraction spot never overlap for both of their diameters increase linearly with propagation distance, so in theory this Poisson diffraction spot can be propagated to infinity. Compared with common methods, which through circular screen to generate Poisson diffraction spot, axicon provides a new convenient way for the production of Poisson diffraction spot in large-scale space.