Khonina Svetlana N, Ustinov Andrey V, Porfirev Alexey P
Appl Opt. 2018 Feb 20;57(6):1410-1416. doi: 10.1364/AO.57.001410.
We investigate theoretically, numerically, and experimentally a novel type of laser beam-an aberration laser beam (ALB). To generate the ALB, a diffractive optical element with a phase transmission function having an arbitrary radial dependence of power q and a periodic angular dependence of sin(mϕ) or cos(mϕ) form can be used. Such a light distribution is more general than classic aberrations including Zernike polynomials. We demonstrate that such radial nonuniformity results in autofocusing properties of ALBs. The autofocusing feature of ALBs is analogous to that of circular Airy beams, but the ALBs' autofocusing feature has more flexibility. The presence of the periodic angular dependence in the phase results in a diffraction pattern with mth-order symmetry. Transformation of ALBs during propagation in free space is analogous to transformation of the three-Airy beams; however, the generated light distributions have an arbitrary integer order of symmetry. The presence of an additional focusing lens leads to formation of an optical field in its focal plane with symmetry that depends on the parity of m: for even m, the generated light distribution has 2mth-order symmetry, and, for odd m, it has mth-order symmetry.
我们从理论、数值和实验方面研究了一种新型激光束——像差激光束（ALB）。为了产生ALB，可以使用一种衍射光学元件，其相位传输函数具有与幂次q的任意径向相关性以及sin(mϕ)或cos(mϕ)形式的周期性角相关性。这种光分布比包括泽尼克多项式在内的经典像差更为普遍。我们证明了这种径向不均匀性会导致ALB具有自聚焦特性。ALB的自聚焦特性类似于圆形艾里光束，但ALB的自聚焦特性具有更大的灵活性。相位中周期性角相关性的存在会导致具有m阶对称性的衍射图案。ALB在自由空间中传播时的变换类似于三艾里光束的变换；然而，所产生的光分布具有任意整数阶对称性。额外聚焦透镜的存在会导致在其焦平面上形成具有取决于m奇偶性的对称性的光场：对于偶数m，所产生的光分布具有2m阶对称性，对于奇数m，它具有m阶对称性。
