Photonics of Topological Transition from Dielectric Ring to Split Ring

In this work, we theoretically and experimentally study the topological transition from a flat dielectric ring with a rectangular cross-section to a split ring by introducing a gap and gradually increasing its size from zero, as well as the process of further unbending the split ring into a cuboid, while leaving the length of the structure constant. We observe impressive photonic effects due to the change in resonant conditions from a closed ring to a Fabry-Pérot resonator. We observe a splitting of the doubly degenerate CW-CCW modes of the ring into two families: topological modes that acquire an additional phase in the range from 0 to π depending on the gap width, and ordinary modes that do not acquire an additional phase. Finally, we present a new type of topological resonator in which an arbitrary non-integer number of waves fit along the length of a dielectric split ring, opening new possibilities in in a variety of photonic applications.