Near-Zero-Dispersion Kerr Soliton Molecules with Coexisting Dark and Bright States

Temporal cavity solitons, the temporal counterparts of Kerr frequency combs in the spectral domain, have found extensive applications over the past decade, ranging from integrated optical clocks to low-noise microwave generation. These localized waveforms present as ultra-narrow bright pulses in the anomalous dispersion regime and as dip-embedded dark pulses in the normal dispersion regime, which are conventionally considered mutually exclusive within the same cavity. However, recent studies have demonstrated that near-zero-dispersion Kerr resonators can support the coexistence of these contrasting states. While the properties of a single soliton are extensively explored, the interaction between two solitons forming a soliton molecule remains inadequately understood. This study focuses on the coexistence of bright and dark soliton molecules in the presence of third-order dispersion. Beginning with the fundamental element known as the switching wave, the bifurcation structures and eigenvalue distributions of both strong- and weak-binding soliton molecules are systematically investigated. Furthermore, the latter can be viewed as the linear superposition of two independent solitons, where one provides alternating stable and unstable trapping spots for the other. This binding behavior can be theoretically anticipated through internal perturbation analysis.