Kotlyar Victor V, Almazov Anton A, Khonina Svetlana N, Soifer Victor A, Elfstrom Henna, Turunen Jari
Image Processing Systems Institute, Russian Academy of Sciences, Samara State Aerospace University, Samara 443001, Russia.
J Opt Soc Am A Opt Image Sci Vis. 2005 May;22(5):849-61. doi: 10.1364/josaa.22.000849.
We deduce and study an analytical expression for Fresnel diffraction of a plane wave by a spiral phase plate (SPP) that imparts an arbitrary-order phase singularity on the light field. Estimates for the optical vortex radius that depends on the singularity's integer order n (also termed topological charge, or order of the dislocation) have been derived. The near-zero vortex intensity is shown to be proportional to rho2n, where p is the radial coordinate. Also, an analytical expression for Fresnel diffraction of the Gaussian beam by a SPP with nth-order singularity is analyzed. The far-field intensity distribution is derived. The radius of maximal intensity is shown to depend on the singularity number. The behavior of the Gaussian beam intensity after a SPP with second-order singularity (n = 2) is studied in more detail. The parameters of the light beams generated numerically with the Fresnel transform and via analytical formulas are in good agreement. In addition, the light fields with first- and second-order singularities were generated by a 32-level SPP fabricated on the resist by use of the electron-beam lithography technique.
我们推导并研究了平面波通过螺旋相位板（SPP）的菲涅耳衍射的解析表达式，该螺旋相位板在光场上赋予任意阶相位奇点。已经得出了取决于奇点整数阶数n（也称为拓扑电荷或位错阶数）的光学涡旋半径的估计值。结果表明，近零涡旋强度与ρ²ⁿ成正比，其中ρ是径向坐标。此外，还分析了具有n阶奇点的SPP对高斯光束的菲涅耳衍射的解析表达式，得出了远场强度分布，最大强度半径显示取决于奇点数量。更详细地研究了具有二阶奇点（n = 2）的SPP之后高斯光束强度的行为。通过菲涅耳变换和解析公式数值生成的光束参数吻合良好。此外，利用电子束光刻技术在抗蚀剂上制作的32级SPP产生了具有一阶和二阶奇点的光场。
