# Electromagnetic-dual metasurfaces for topological states along a one-dimensional interface

## TL;DR

This paper demonstrates a simple method to realize topological states in metasurfaces by coupling surface modes, creating robust edge states at microwave frequencies, with potential for compact topological insulator applications.

## Contribution

It introduces a straightforward approach to achieve topological states in metasurfaces through stacking unit cells, avoiding complex designs and narrow bandwidths of previous methods.

## Key findings

- Stacked metasurfaces produce double Dirac cones and wide non-trivial bandgaps.
- Robust gapless edge states are observed along a one-dimensional interface.
- The approach is effective at microwave frequencies and suitable for compact applications.

## Abstract

The discovery of topological insulators has rapidly been followed by the advent of their photonic analogues, motivated by the prospect of backscattering-immune light propagation. So far, however, implementations have mainly relied on engineering bulk modes in photonic crystals and waveguide arrays in two-dimensional systems, which closely mimic their electronic counterparts. In addition, metamaterials-based implementations subject to electromagnetic duality and bianisotropy conditions suffer from intricate designs and narrow operating bandwidths. Here, it is shown that symmetry-protected topological states akin to the quantum spin-Hall effect can be realized in a straightforward manner by coupling surface modes over metasurfaces of complementary electromagnetic responses. Specifically, stacking unit cells of such metasurfaces directly results in double Dirac cones of degenerate transverse-electric and transverse-magnetic modes, which break into a wide non-trivial bandgap at small inter-layer separation. Consequently, the ultrathin structure supports robust gapless edge states, which are confined along a one-dimensional line rather than a surface interface, as demonstrated at microwave frequencies by near field imaging. The simplicity and versatility of the proposed approach proves attractive as a tabletop platform for the study of classical topological phases, as well as for applications benefiting the compactness of metasurfaces and the potential of topological insulators.

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Source: https://tomesphere.com/paper/1907.06684