Geometric phase topological resonators

Geometrical phases play a central role in numerous phenomena from optical waveguides and metasurfaces to topological photonic materials. Acquired during the adiabatic evolution of the multimodal system, they can add up to the conventional propagation phase and alter interference phenomena and resonance conditions. Here we introduce a new type of resonators whose resonant condition is defined solely by the geometrical phase. In such a geometrical phase resonator, implemented in photonic topological metasurfaces, topological boundary modes are designed to undergo an adiabatic evolution that gives rise to the net geometrical phase of 2π, rendering resonance without any propagation phase. This makes the resonance condition invariant with respect to its shape and length, which we confirmed both using first-principles simulations and in experiments. Specifically, we show that a set of samples with completely different geometries exhibit an extremely stable "geometrical phase resonance" pinned to a specific fixed frequency. We believe that geometrical phase resonators can be of profound importance for applications where such spectral stability of resonances can be required.