Topological soliton metacrystals

Designing metamaterials with the required band structure, topology and chirality using nano-fabrication technology revolutionise modern science. The approach of this work to the metamaterial theme is, however, different. We report that a periodic sequence, i.e., metacrystal, of the dissipative optical solitons rotating in a ring microresonator acts as an effective metamaterial in the radio to terahertz frequency range. The metacrystal unit cell consists of the bound pair of solitons, where the inter-soliton distance is used as a control parameter. We investigate the soliton metacrystal band structure and topological properties. The latter is confirmed by the π steps experienced by the crystal phonons’ geometrical (Zak) phase. Furthermore, we found the phononic edge states in the metacrystals with defects made by removing several solitons. Optical frequency combs corresponding to the soliton metacrystals hide the spectral butterfly pattern serving as a signature of the spatio-temporal chirality and bearing a resemblance to the natural occurrences of chirality. Topological photonics and time crystals push frontiers of modern physics and promise a host of applications. Here, we report the bandgap structure and topological properties of the soliton trains in Kerr microresonators.