Hyperbolic\nTopological Frequency Combs

On-chip generation of optical frequency combs (OFCs)\nholds fundamental\nsignificance for a wide range of applications, such as precision metrology,\noptical communications, and so on. Recent investigations have shown\nthat OFCs can be generated in a topologically coupled array of ring\nresonators, providing a novel avenue to engineer nested temporal solitons\nand robust comb spectra. However, limited by the bulk-edge correspondence,\nthe implementation of topological frequency combs always requires\na substantial number of auxiliary bulk ring resonators, diminishing\nthe ratio of edge ring resonators for OFC generation. Here, we propose\na new approach to generate OFCs and nested temporal solitons using\nhyperbolic photonic topological insulators. Our designed hyperbolic\ntopological OFCs exhibit a significantly reduced frequency spacing\ncompared to that of conventional topological OFCs with the same number\nof optical rings. Thus, for achieving the same frequency spacing,\nhyperbolic topological OFCs require much fewer ring resonators than\nconventional topological OFCs in Euclidean space, giving an extremely\nimproved utilization efficiency of ring resonators. Furthermore, the\nrobustness of hyperbolic topological OFCs is also demonstrated. Our\nresults open up a promising avenue for establishing highly efficient\nnonlinear topological devices.