The functional and optimal design of optical metasurfaces poses great challenges, particularly in situations requiring multifunctionalities. The conventional forward design relies on a priori knowledge, which limits the development of metasurfaces with customized functions. Inverse design has achieved major breakthroughs in developing new optical functionalities but has been hindered by inevitably invoking a full-wave electromagnetic solver, subjected to low efficiency, slow convergence, and being hard to implement. Here, we propose a general and computationally efficient inverse-design framework based on multipole decomposition and adjoint optimization. By this method, we demonstrate an achromatic metalens working across the visible and near-infrared band with a bandwidth over 400 nm. We also show the design of the metasurface for multiplexed focusing at the RGB wavelength, and the metasurface for stimulated emission depletion (STED) microscopy, which generates a tightly focusing point at the excitation beam wavelength and doughnut-shaped focus for the STED beam wavelength. Our scheme could be further improved to include more geometrical degrees of freedom and show great applications in free-space diffractive optics and deep diffractive neural network.

中文翻译：

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基于多极分解和伴随法的多功能超曲面逆向设计

光学超表面的功能和优化设计提出了巨大的挑战，特别是在需要多功能的情况下。传统的正向设计依赖于先验知识，这限制了具有定制功能的超表面的发展。逆向设计在开发新的光学功能方面取得了重大突破，但不可避免地需要调用全波电磁求解器，效率低，收敛速度慢，难以实现。在这里，我们提出了一个基于多极分解和伴随优化的通用且计算高效的逆向设计框架。通过这种方法，我们展示了一种在可见光和近红外波段工作且带宽超过 400 nm 的消色差超透镜。我们还展示了用于在 RGB 波长下进行多路复用聚焦的超表面设计，以及用于受激发射耗尽 (STED) 显微镜的超表面设计，它在激发光束波长处产生紧密聚焦点，在 STED 光束波长处产生环形焦点。我们的方案可以进一步改进，以包含更多的几何自由度，并在自由空间衍射光学和深度衍射神经网络中显示出巨大的应用。