Parallelism of multiple nonlinear states in the mode-division-multiplexed resonator

Cavity solitons are localized optical pulses that stably form in coherently driven passive Kerr resonators, supported by a balance among Kerr nonlinearity, dispersion, and cavity gain-loss dynamics. As a foundational mechanism for microcomb generation, they have enabled advances in optical ranging, high-speed communications, spectroscopy, and optical clocking. Beyond solitons, optical cavities can support a variety of nonlinear states, including Turing patterns, chaotic states, and breathers, each offering distinct functionalities in photonic systems. While previous studies have demonstrated bistable coexistence among such states, systematic realization and control of triply coexisting nonlinear states remain largely unexplored. In this work, we design a few-mode fiber (FMF) resonator that enables homogeneous coexistence (each mode exhibits the same state) of Turing patterns, chaotic states, breathers, and stable cavity solitons across the LP01, LP11, and LP21 modes under anomalous dispersion. By finely controlling intermodal detuning, we further demonstrate the dynamic heterogeneous coexistence of nonlinear states (each mode exhibits different states) among the three modes, thereby significantly enriching the dynamical behaviors in few-mode nonlinear photonics and effectively extending the utilization of dimension. Our approach offers a versatile platform for exploring complex dissipative dynamics. It paves the way for mode-division-multiplexed (MDM) photonic systems with enhanced functionality, including multi-wavelength LiDAR, high-capacity optical communication, and on-chip nonlinear signal processing.