Topological Metasurfaces for Robust One-dimensional Waves

Abstract

The discovery of topological condensed matter systems has rapidly been followed by the advent of their photonic analogues, motivated by the prospect of backscattering-immune light propagation. So far, however, photonic topological phases have mainly relied on engineering bulk modes in photonic crystals and waveguide arrays in two-dimensional systems. Here, we present symmetry protected topological states akin to quantum spin/valley Hall effect by engineering surface modes over metasurfaces of infinitesimal thickness. As a result, the proposed structures support robust gapless edge states, which are highly confined and guided virtually along a one-dimensional line rather than a surface interface. In order to generate the modal degeneracies required for emulating the spin degree of freedom, we exploit the internal symmetry of the electromagnetic field by overlapping hexagonal unit cells of complementary metasurfaces. Conversely, we emulate the valley degree of freedom by reducing the C6υ lattice symmetry of a hexagonal cell-based metasurface of either inductive or capacitive electromagnetic response into C3 point symmetry. The simplicity of the proposed structures makes them attractive as a tabletop platform for the study of photonic topological phases, as well as for applications benefiting the compactness of metasurfaces and the potential of topological insulators.