Phase-locking characteristics and dynamics of the subharmonic entrainment of breathing temporal solitons

Subharmonic entrainment (SHE) of the breathing solitons, an intriguing resonance phenomenon, arises from frequency locking between the breathing frequency and the cavity repetition frequency. This study investigates the phase-locking characteristics and dynamics of the SHE of breathing temporal cavity solitons. We reveal that the breathing solitons arise from the periodic enhancement and depletion of coherence between solitons and pump light, achieving SHE locking across various periods within the stringent parameter ranges of driving intensity, detuning, and cavity finesse. Furthermore, we summarize the excitation condition of SHE within the phase-locking region, enhancing the understanding of the dynamics of SHE. Our research could provide valuable insights into the generation and regulation of SHE.