Topological Metasurfaces

Abstract

Research on topological photonics has considerably grown, transferring condensed matter concepts of topological insulators with the discovery of the integer Quantum-Hall effect into the realm of photonics. Today, nanophotonics, which is related to light manipulation with subwavelength objects, offers new opportunities to address light properties. New degrees of freedom in the design of optical components are attained by considering the response of topological nanostructures. So far, optical metasurfaces, made of subwavelength arrangements of nanostructures, have relied on resonant phase scattering occurring in Mie resonators or ultrathin pillars. Full wavefront control requires finding sets of nanostructures that can provide 2π optical phase retardation on the incoming beam. Ultimately, and despite all the efforts in understanding the physical mechanisms leading to optimal designs, including powerful optimization methods, metasurface designs often require witless numerical parameter searches. Relying on symmetry-breaking arguments and topological properties of the associated non-Hermitian matrices representing the metasurfaces, we provide new guidelines for achieving 2π phase coverage in transmission and reflection. This framework allows us to unravel the physical principles underlying Huygens metasurfaces, showing that it exploits degeneracies of transmission- or reflection-matrices Zeros, so-called exceptional points, corresponding to transmissionless and reflectionless states. Overall, symmetry-breaking leading to a displacement of a Zero-Pole pair with its branch cut crossing the real axis, provides a very intuitive design approach for achieving full resonant phase scattering. Encircling EPs and/or zeros in the nanostructure parameter space to provide full 2π-phase are considered, entrusting metasurfaces and flat optics with additional light modulation schemes. Our results explain the importance of topological defects and how they can be manipulated for achieving realistic and insightful metasurface designs.