Fundamentals to emerging concepts and applications of metasurfaces for flat optics: a tutorial

Metasurfaces offer unprecedented freedom in the flexible and efficient manipulation of light across multiple dimensions such as amplitude, phase, and polarization, enabling the realization of low-cost, high-performance, ultra-lightweight, and ultra-thin optical elements with novel functionalities to overcome traditional optical limitations in volume, weight, functionality, and efficiency. In recent years, this potential has attracted growing attention from both academic and industrial communities. After more than a decade of development, on the one hand, the design of a wide range of metasurfaces has gradually become mature, encompassing physical principles, design methodologies, and devices for diverse applications; on the other hand, metasurfaces with novel physical concepts and functionalities have emerged through integration with other disciplines, including nonlinearity, chirality, optical resonance, non-Hermitian physics, Fourier optics, and topological photonics. In this tutorial, we propose a unified and forward-looking theoretical framework that connects traditional metasurfaces with these emerging metasurfaces, aiming to clarify their underlying relationships and development trends. We introduce the mainstream design methodologies, highlighting the most recent advancements. We further examine five representative application areas: metalenses, metasurface holograms, quantum photonic metasurfaces, optical computing metasurfaces, and active metasurfaces, in terms of their principles, evaluation criteria, theoretical analyses, and design methods. By bridging fundamentals and emerging concepts under a unified perspective, this tutorial aims to provide a holistic physical understanding and critical insight into the global metasurface landscape, from fundamentals to emerging concepts and applications.