Qiu Xiaodong, Zhang Jingcheng, Fan Yubin, Zhou Junxiao, Chen Lixiang, Tsai Din Ping
Department of Electrical Engineering, City University of Hong Kong, Kowloon, Hong Kong SAR, China.
Department of Physics, Xiamen University, Xiamen, China.
Nat Commun. 2025 Mar 11;16(1):2437. doi: 10.1038/s41467-025-57715-8.
Metasurface-enabled optical analog differentiation has garnered significant attention due to its inherent capacity of parallel operation, compactness, and low power consumption. Most previous works focused on the first- and second-order operations, while several significant works have also achieved higher-order differentiation in both real space and k-space. However, how to construct the desired optical transfer function in a practical system to realize scalable and multi-order-parallel high-order differentiation of images in real space, and particularly how to leverage it to tackle practical problems, have not been fully explored. Here, drawing on the basic mathematical feature of the Fourier transform, we theoretically propose universal phase-gradient functions of the Pancharatnam-Berry-phase-based meta-device for performing arbitrary order differentiation. The fifth-order optical differentiations for both intensity and phase images are realized in the experiment. More importantly, by exploring this elaborately designed spatial differentiator, we construct another scheme for optical super-resolution and achieve the estimation of the distance between two incoherent point sources within 0.015 of the Rayleigh distance, which thereby provides a potential toolkit for optical alignment in high-precision semiconductor nano-fabrication. Our findings hold promise for image processing, microscopy imaging, and optical super-resolution imaging.
基于超表面的光学模拟微分因其固有的并行操作能力、紧凑性和低功耗而备受关注。以往的大多数工作都集中在一阶和二阶操作上，而一些重要的工作也在实空间和k空间中实现了高阶微分。然而，如何在实际系统中构建所需的光学传递函数，以实现实空间中图像的可扩展和多阶并行高阶微分，特别是如何利用它来解决实际问题，尚未得到充分探索。在此，基于傅里叶变换的基本数学特征，我们从理论上提出了基于潘查拉特纳姆-贝里相位的超表面器件的通用相位梯度函数，用于执行任意阶微分。实验中实现了强度图像和相位图像的五阶光学微分。更重要的是，通过探索这种精心设计的空间微分器，我们构建了另一种光学超分辨率方案，并在瑞利距离的0.015范围内实现了两个非相干点源之间距离的估计，从而为高精度半导体纳米制造中的光学对准提供了一个潜在的工具包。我们的研究结果有望应用于图像处理、显微镜成像和光学超分辨率成像。
