基于伴随法的周期与非周期超表面逆向设计方法：具有类随机分布纳米棒的金属透镜
Inverse design method for periodic and aperiodic metasurfaces based on the adjoint-method: metalens with random-like distributed nano-rods
AI总结：
本文提出一种基于伴随法的低参数几何拓扑优化方法，通过调整纳米棒宽度与位置，将计算时间降低约一个数量级，并成功设计周期性超光栅和非周期金属透镜。
摘要：
经典的基于伴随的拓扑优化（TO）方法，以随机连续介电函数作为伴随变量分布，被认为是能够设计出性能卓越的光学器件的最有效优化方法之一。然而，选择最优解的策略要求对优化中的介电常数分布进行非常精细的像素化。通常，在优化一个波长宽的1D超光栅时至少需要28个像素。这使得将TO方法扩展到大规模优化问题变得非常困难。本文提出了一种新的基于伴随的拓扑优化概念，能够对周期性和非周期性超表面进行快速且高效的基于几何的设计。结构由纳米棒构成，其宽度和位置需要调整。我们的新方法所需的设计参数数量非常少，从而使计算时间大幅减少：约一个数量级。因此，这一概念使得在极短时间内完成大规模结构的优化成为可能。作为概念验证，我们将该方法应用于以下设计：（i）一个周期性超光栅，优化为在特定方向上具有特定响应；（ii）一个介电金属透镜（非周期性超表面），能够将高能量聚焦到一个清晰的焦斑上。
英文摘要：
The classical adjoint-based topology optimization (TO) method, based on the use of a random continuous dielectric function as an adjoint variable distribution, is known to be one of the most efficient optimization methods that enable the design of optical devices with outstanding performances. However, the strategy for selecting the optimal solution requires a very fine pixelation of the permittivity function of the profile under optimization. Typically, at least 28 pixels are needed while optimizing a one wavelength wide 1D metagrating. This makes it very difficult to extend TO methods to large-scale optimization problems. In this paper, we introduce a new concept of adjoint-based topology optimization that enables fast and efficient geometry based design of both periodic and aperiodic metasurfaces. The structures are built from nano-rods whose widths and positions are to be adjusted. Our new approach requires a very low number of design parameters, thus leading to a drastic reduction in the computational time: about an order of magnitude. Hence, this concept makes it possible to address the optimization of large-scale structures in record time. As a proof-of-concept we apply this method to the design of (i) a periodic metagrating, optimized to have a specific response into a particular direction, and (ii) a dielectric metalens (aperiodic metasurface), enabling a high energy focusing into a well-defined focal spot.
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