Rujiang Li

Optical frequency combs (OFCs) are revolutionary light sources characterized by discrete and equally spaced spectral lines, and they have found widespread applications in metrology, spectroscopy, and communications. In the early stages, OFCs were realized using mode-locked lasers. With advancements in the fabrication of high-quality factor (Q) microresonators and the increasing demand for miniaturized and integrable photonic chips, microresonator-based OFCs, commonly referred to as microcombs, have been developed. Although early studies of microcombs primarily focused on single microresonators or a few resonators, a significant breakthrough occurred in 2021 when it was theoretically predicted that light propagating in the topological edge channel of an array of ring resonators could generate nested frequency combs known as topological OFCs. Since then, the field of topological OFCs has progressed rapidly, with experimental observations made in 2024. This Perspective will introduce the history of OFCs, placing particular emphasis on the emergence and development of topological OFCs, as well as exploring the research challenges and opportunities associated with them.

We propose that the symmetry-breaking bifurcation of coupled topological edge states (CTESs) can be used as a general principle for achieving spontaneous symmetry breaking (SSB) in a nonlinear topological lattice. Using an optical resonator array composed of two Su–Schrieffer–Heeger (SSH) chains as an example, we find that as the nonlinearity strength increases, the symmetric CTESs undergo a supercritical bifurcation. Beyond the critical threshold, the originally stable symmetric state becomes unstable, leading to the formation of a pair of stable asymmetric states. Both sides of the symmetric CTESs exhibit sublattice polarization, while the side of the asymmetric CTESs that is predominantly occupied demonstrates stronger sublattice polarization. We further find that as interchain coupling increases, the frequency range for stable symmetric CTESs expands, while the frequency range for stable asymmetric CTESs decreases. Our work provides a universal mechanism for realizing SSB in nonlinear topological lattices.

Higher-order topological insulators (HOTIs) represent a family of topological phases that go beyond the conventional bulkboundary correspondence. d-dimensional n-th order HOTIs maintain (d - n)-dimensional gapless boundary states (in particular, zero-dimensional corner states in the case of d = n = 2). HOTIs of the Wannier type cam be extended into the nonlinear regime. Another prominent class of HOTIs, in the form of multipole insulators, was investigated only in the linear regime, due to the challenge of simultaneously achieving both negative hopping and strong nonlinearity. Here we propose the concept of nonlinear quadrupole topological insulators (NLQTIs) and report their experimental realization in an electric circuit lattice. Quench-initiated dynamics gives rise to nonlinear topological corner states and topologically trivial corner solitons, in weakly and strongly nonlinear regimes, respectively. Furthermore, we reveal the formation of two distinct types of bulk solitons, one existing in the middle finite gap under the action of weak nonlinearity, and another one found in the semi-infinite gap under strong nonlinearity. This work realizes another member of the nonlinear HOTI family, suggesting directions for exploring novel solitons across a broad range of topological insulators.