Abstract In an optical Pancharatnam-Berry (PB) phase metasurface, each sub-wavelength dielectric structure of varied spatial orientation can be treated as a point source with the same amplitude yet varied relative phase. In this work, we introduce an optimized genetic algorithm (GA) method for the synthesis of one-dimensional (1D) PB phase-controlled dielectric metasurfaces by seeking for optimized phase profile solutions, which differs from previously reported amplitude-controlled GA method only applicable to generate transverse optical modes with plasmonic metasurfaces. The GA–optimized phase profiles can be readily used to construct dielectric metasurfaces with improved functionalities. The loop of phase-controlled GA consists of initialization, random mutation, screened evolution, and duplication. Here random mutation is realized by changing the phase of each unit cell, and this process should be efficient to obtain enough mutations to drive the whole GA process under supervision of appropriate mutation boundary. A well-chosen fitness function ensures the right direction of screened evolution, and the duplication process guarantees an equilibrated number of generated light patterns. Importantly, we optimize the GA loop by introducing a multi-step hierarchical mutation process to break local optimum limits. We demonstrate the validity of our optimized GA method by generating longitudinal optical modes (i. e., non-diffractive light sheets) with 1D PB phase dielectric metasurfaces having non-analytical counter-intuitive phase profiles. The produced large-area, long-distance light sheets could be used for realizing high-speed, low-noise light-sheet microscopy. Additionally, a simplified 3D light pattern generated by a 2D PB phase metasurface further reveals the potential of our optimized GA method for manipulating truly 3D light fields.

中文翻译：

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通过优化遗传算法的相控超表面设计

摘要 在光学 Pancharatnam-Berry (PB) 相位超表面中，每个不同空间取向的亚波长介电结构都可以被视为具有相同幅度但相对相位不同的点源。在这项工作中，我们引入了一种优化的遗传算法 (GA) 方法，通过寻求优化的相位轮廓解决方案来合成一维 (1D) PB 相控介电超表面，这不同于之前报道的仅适用于幅度控制的 GA 方法产生具有等离子体超表面的横向光学模式。GA 优化的相位分布可以很容易地用于构建具有改进功能的介电超表面。相控遗传算法的循环包括初始化、随机变异、筛选进化和复制。这里的随机变异是通过改变每个单元的相位来实现的，这个过程应该是有效的，以获得足够的变异来驱动整个 GA 过程，在适当的变异边界的监督下。精心选择的适应度函数确保筛选进化的正确方向，复制过程保证生成的光模式数量平衡。重要的是，我们通过引入多步分层突变过程来打破局部最优限制来优化 GA 循环。我们通过使用具有非解析反直觉相位分布的 1D PB 相介电超表面生成纵向光学模式（即非衍射光片）来证明我们优化的 GA 方法的有效性。生产的大面积、长距离光片可用于实现高速、低噪声光片显微镜。此外，由 2D PB 相位超表面生成的简化 3D 光图案进一步揭示了我们优化的 GA 方法在操纵真正 3D 光场方面的潜力。