The periodic extension of phase difference is commonly applied in device design to obtain phase compensation beyond the system’s original phase modulation capabilities. Based on this extension approach, we propose the application of quasiphase delay matching to extend the range of dispersion compensation for meta-atoms with limited height. Our theory expands the limit of frequency bandwidth coverage and relaxes the constraints of aperture, NA, and bandwidth for metalenses. By applying the uncertainty principle, we explain the fundamental limit of this achromatic bandwidth and obtain the achromatic spectrum using perturbation analysis. To demonstrate the effectiveness of this extended limit, we simulate a quasiachromatic metalens with a diameter of 2 mm and a NA of 0.55 in the range of 400–1500 nm. Our findings provide a novel theory for correcting chromatic aberration in large-diameter ultrawide bandwidth devices.

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.

Mid-infrared spectroscopy is critical for applications like environmental monitoring and medical diagnostics, as it includes the fundamental vibrational frequencies of many molecular bonds, enabling detailed chemical analysis. We developed a miniature mid-infrared spectrometer using a fully dielectric metasurface operating in the 3–5 µm range. By combining simple structural units, design flexibility was enhanced, resulting in rich spectral data. The spectrometer was evaluated using narrowband, broadband, and transmission spectra of real materials. We detected the spectral responses of metasurface arrays and determined the unknown spectrum using an algorithm based on Tikhonov regularization with generalized cross-validation. By reconstructing multiple narrow spectra obtained through rotating the filters, spectral resolution intervals of approximately 10 nm were achieved.

The lidar ratio of seawater is an essential quantity related to both lidar retrieval and water constituent. However, few studies discuss its spatial–temporal characteristics and ecological significance, which limits its applications in lidar remote sensing and marine science. This paper investigates the spatial–temporal characteristics and ecological significance of the lidar ratio of seawater using satellite passive remote sensing, which is validated by in situ measurements. Spatially, nearshore lidar ratio values are higher than offshore, mainly owing to the high concentration of colored dissolved organic matter in nearshore water. Temporally, the lidar ratio in each hemisphere exhibits lower values in summer than in winter due to the annual boom–bust cycle of phytoplankton. Furthermore, the variability patterns of the lidar ratio are nearly consistent with those of the chlorophyll-to-carbon ratio, implying the high ecological significance of phytoplankton physiology. These findings will provide the foundation for the application of lidar ratio in marine science and lidar remote sensing.

Geometric phase phenomena play a foundational role in modern wave physics. In optics, they provide the basis for geometric phase metasurfaces (GPMs), a powerful platform for versatile wavefront shaping. However, conventional GPMs remain fundamentally restricted to circularly polarized light because their operation relies on the symmetry of orthogonal linear eigenstates, preventing their direct use in the linearly polarized platforms widely employed in mainstream optics. Here, we address this longstanding challenge by harnessing the non-Hermitian physics of exceptional points (EPs). We introduce and experimentally realize quasi-EP GPMs, in which engineered singularities drive the coalescence of eigen-polarizations and allow a geometric phase to be directly imparted to linearly polarized light. Proof-of-principle metagratings and holograms demonstrate high-fidelity wavefront shaping under arbitrary linearly polarized illumination over a broad spectral range. Our results reveal an intrinsic connection between geometric phase and EPs, extend GPMs beyond their conventional circular-polarization regime, and provide a practical framework for scalable polarization manipulation, advanced imaging, holography, integrated photonics, and quantum optics.