Optical singularities play a major role in modern optics and are frequently deployed in structured light, super-resolution microscopy, and holography. While phase singularities are uniquely defined as locations of undefined phase, polarization singularities studied thus far are either partial, i.e., bright points of well-defined polarization, or are unstable for small field perturbations. We demonstrate a complete, topologically protected polarization singularity; it is located in the four-dimensional space spanned by the three spatial dimensions and the wavelength and is created in the focus of a cascaded metasurface-lens system. The field Jacobian plays a key role in the design of such higher-dimensional singularities, which can be extended to multidimensional wave phenomena, and pave the way for unconventional applications in topological photonics and precision sensing. Metasurfaces enable topologically protected polarization singularities, paving the way to fault-tolerant precision sensing.

Extreme ultraviolet (EUV) radiation is a key technology for material science, attosecond metrology, and lithography. Here, we experimentally demonstrate metasurfaces as a superior way to focus EUV light. These devices exploit the fact that holes in a silicon membrane have a considerably larger refractive index than the surrounding material and efficiently vacuum-guide light with a wavelength of  50 nanometers. This allows the transmission phase at the nanoscale to be controlled by the hole diameter. We fabricated an EUV metalens with a 10-millimeter focal length that supports numerical apertures of up to 0.05 and used it to focus ultrashort EUV light bursts generated by high-harmonic generation down to a 0.7-micrometer waist. Our approach introduces the vast light-shaping possibilities provided by dielectric metasurfaces to a spectral regime that lacks materials for transmissive optics. The fields of ultrafast spectroscopy and semiconductor photolithography rely on very short wavelengths, typically in the extreme ultraviolet (EUV) realm. However, most optical materials strongly absorb light in this wavelength regime, resulting in a lack of generally available transmissive components. Ossiander et al. designed and fabricated a metalens in which a carefully engineered array of holes in a thin silicon membrane focuses ultrafast EUV pulses close to the diffraction limit by “vacuum guiding.” The results open up transmissive optics to the EUV regime. —ISO Metalens technology can be pushed into the extreme ultraviolet wavelength regime.

We present a path to truly `flat', all-oxide metalenses working at visible wavelength comprising high-aspect ratio TiO2 nanopillars infused into fused silica substrate. We show both a proof-of-concept infused metalens using electron-beam lithography, and an example of mass-manufacturing using deep-ultraviolet projection lithography.

We show that the approximate optical response of a periodic nanostructure with respect to normally incident partially coherent illumination can be reconstructed by a single electromagnetic simulation.

We experimentally demonstrate a dielectric metalens operating at 50 nm wavelength by leveraging that holes in a Silicon membrane guide extreme ultraviolet light. A knife edge measurement shows focusing down to 1.7 times the diffraction limit.

We simulated a free-standing metasurface-based Faraday rotator design. The device gives a high transmittance, large Faraday rotation angle, and figure of merit  24 times higher than a conventional device at the wavelength of 755nm.

We design and experimentally demonstrate a new type of topologically protected polarization singularity using metasurfaces. The singularity is placed in the four-dimensional space formed by the three Cartesian spatial dimensions and the wavelength of light.