有限半径平面波和高斯光束被螺旋轴棱锥和螺旋相位板的衍射

Diffraction of a finite-radius plane wave and a Gaussian beam by a helical axicon and a spiral phase plate.

作者信息

Kotlyar Victor V, Kovalev Alexey A, Skidanov Roman V, Moiseev Oleg Yu, Soifer Victor A

机构信息

Image Processing Systems Institute, Russian Academy of Sciences, Samara State Aerospace University, Russia.

出版信息

J Opt Soc Am A Opt Image Sci Vis. 2007 Jul;24(7):1955-64. doi: 10.1364/josaa.24.001955.

DOI:10.1364/josaa.24.001955

PMID:17728819

Abstract

We derive what we believe to be new analytical relations to describe the Fraunhofer diffraction of the finite-radius plane wave by a helical axicon (HA) and a spiral phase plate (SPP). The solutions are deduced in the form of a series of the Bessel functions for the HA and a finite sum of the Bessel functions for the SPP. The solution for the HA changes to that for the SPP if the axicon parameter is set equal to zero. We also derive what we believe to be new analytical relations to describe the Fresnel and Fraunhofer diffraction of the Gaussian beam by a HA are derived. The solutions are deduced in the form of a series of the hypergeometric functions. We have fabricated by photolithography a binary diffractive optical element (a HA with number n=10) able to produce in the focal plane of a spherical lens an optical vortex, which was then used to perform rotation of several polystyrene beads of diameter 5 microm.

摘要

我们推导出了我们认为是新的解析关系式，用于描述螺旋轴锥镜（HA）和螺旋相位板（SPP）对有限半径平面波的夫琅禾费衍射。对于HA，解是以贝塞尔函数的级数形式推导出来的；对于SPP，解是贝塞尔函数的有限和形式。如果将轴锥镜参数设为零，HA的解就会变为SPP的解。我们还推导出了我们认为是新的解析关系式，用于描述HA对高斯光束的菲涅耳衍射和夫琅禾费衍射。解是以超几何函数的级数形式推导出来的。我们通过光刻技术制造了一个二元衍射光学元件（一个n = 10的HA），它能够在球面透镜的焦平面上产生一个光学涡旋，然后用它来使几个直径为5微米的聚苯乙烯珠子旋转。