Abstract

Concepts of topology arise in condensed matter physics when considering states at the boundary of a periodic structure. Recently, there has been interest in exploring topology in optical contexts. Optics is an excellent platform to study these effects, due to the high degree of control over the geometry and material. The simplest example of a model exhibiting topological properties is the Su-Schrieffer-Heeger (SSH) chain, where an extra periodicity (also known as dimerization) is added to a photonic crystal waveguide. By creating sites where the dimerization changes abruptly, it is possible to create topological edge states, which confines resonant modes that are protected from imperfections.
Here, we study the SSH model in a ring resonator, where a dimerized photonic crystal waveguide loops in on itself. The dispersion relations of various waveguides are first calculated using a frequency domain approach. By using those waveguide unit cells as the elements to construct phase transitions, the properties of those resonant modes and the extent of topological protection will be studied by adding random variations to the holes of the unit cells. Simulations show that topological protection of the quality factors hold for 7.8% variation in the hole radii. The loss mechanisms of these optical cavities will also be analyzed to confirm topological protection of the lattice. At last, we then discuss how these ring resonators can be fabricated and experimentally studied on a silicon chip.