  Passive Kerr cavities driven by coherent laser fields display a rich
landscape of nonlinear physics, including bistability, pattern formation, and
localised dissipative structures (solitons). Their conceptual simplicity has
for several decades offered an unprecedented window into nonlinear cavity
dynamics, providing insights into numerous systems and applications ranging
from all-optical memory devices to microresonator frequency combs. Yet despite
the decades of study, a recent theoretical study has surprisingly alluded to an
entirely new and unexplored paradigm in the regime where nonlinearly tilted
cavity resonances overlap with one another [T. Hansson and S. Wabnitz, J. Opt.
Soc. Am. B 32, 1259 (2015)]. We have used synchronously driven fiber ring
resonators to experimentally access this regime, and observed the rise of new
nonlinear dissipative states. Specifically, we have observed, for the first
time to the best of our knowledge, the stable coexistence of dissipative
(cavity) solitons and extended modulation instability (Turing) patterns, and
performed real time measurements that unveil the dynamics of the ensuing
nonlinear structures. When operating in the regime of continuous wave
tristability, we have further observed the coexistence of two distinct cavity
soliton states, one of which can be identified as a "super" cavity soliton as
predicted by Hansson and Wabnitz. Our experimental findings are in excellent
agreement with theoretical analyses and numerical simulations of the
infinite-dimensional Ikeda map that governs the cavity dynamics. The results
from our work reveal that experimental systems can support complex combinations
of distinct nonlinear states, and they could have practical implications to
future microresonator-based frequency comb sources.
