Exceptional Rings in Nonlinear Non-Hermitian Planar Optical Microcavities: Implementation, Signal Enhancement, and Topology

Non-Hermitian
systems hosting exceptional points (EPs) exhibit
signal enhancement and unconventional mode dynamics. Going beyond
isolated EPs, here we report on the existence of exceptional rings
(ERs) in planar optical resonators with a specific form of circular
dichroism and TE–TM splitting. Such exceptional rings possess
intriguing topologies as discussed earlier for condensed matter systems,
but they remain virtually unexplored in the presence of nonlinearity,
for which our photonic platform is ideal. We find that when Kerr-type
nonlinearity (or saturable gain) is introduced, the linear ER splits
into two concentric ERs, with the larger-radius ring being a ring
of third-order EPs. Transitioning from linear to nonlinear regime,
we present a rigorous analysis of (spectral and band) topologies and
report an enhanced and adjustable perturbation response in the nonlinear
regime. Whereas certain features are specific to our system, the results
on non-Hermitian topologies and nonlinearity-enhanced perturbation
responses are generic and equally relevant to a broad class of other
nonlinear non-Hermitian systems, providing a universal framework for
engineering ERs and EPs in nonlinear non-Hermitian systems.