Nonlinear beam shaping provides an efficient way to control the phase and amplitude of optical waves while shifting their frequency. Periodical topological structures with a modulated second-order nonlinear optical coefficient (χ ⁽²⁾) are commonly used to generate special optical beams at new frequencies, e.g. the second harmonic vortices. In this paper, we theoretically study the influence of structural imperfection on nonlinear beam shaping and demonstrate how to utilize these imperfections for second harmonic generation with controlled orbital angular momentums. The results indicate that the studied nonlinear beam-shaping process has excellent tolerance to structural defects, and introducing designed defects of different scales and shapes constitutes a flexible approach for controlling the orbital angular momentum of light at new frequencies. As a proof of concept example, the nested χ ⁽²⁾ structures are designed for generating optical vortices with predesigned topological charges along different directions. In addition, the performance of the nonlinear generation of vortex beams with a fundamental beam shifted from the center of the fork grating is also discussed. The study opens up new prospects for the optimization of nonlinear χ ⁽²⁾ structures for special beam generation at new frequencies.

非线性光束整形提供了一种有效的方式来控制光波的相位和幅度，同时改变其频率。具有调制的二阶非线性光学系数（χ ^（2））通常用于产生新频率的特殊光束，例如二次谐波涡旋。在本文中，我们从理论上研究了结构缺陷对非线性波束成形的影响，并演示了如何利用这些缺陷来产生具有受控轨道角动量的二次谐波。结果表明，所研究的非线性光束整形过程对结构缺陷具有很好的耐受性，引入不同比例和形状的设计缺陷构成了一种灵活的方法来控制新频率的光的轨道角动量。作为概念证明的例子，嵌套χ ^（2）这些结构设计用于产生沿不同方向具有预先设计的拓扑电荷的光学涡旋。此外，还讨论了非线性光束在基波从叉形光栅中心偏移的情况下非线性产生的性能。该研究为优化在新频率下产生特殊光束的非线性χ ^（2）结构开辟了新的前景。