Exploring anomalous light dynamics around higher-order conjugate exceptional points with local nonlinearity

Dynamical encirclement around higher-order exceptional point (EP) singularities can provide control over higher-order modal transport, which holds promise for on-chip device applications. For future photonic technologies, controlled light steering is in demand for communication, data processing, and computing. Nonlinearity-driven dynamical encirclement of second-order EPs (EP2s) and corresponding chirality or nonchirality driven nonadiabatic modal dynamics have attracted attention in the topological study of various non-Hermitian photonic systems. Here, we propose the concept of nonlinearity-induced higher-order conjugate EPs, which are analytically associated with multiple pairs of conjugate EP2s. Moreover, in the presence of saturable nonlinearity, dynamical encirclement around higher-order conjugate EPs in two T-symmetric systems are yet to be explored. Here, we report the hosting of higher-order conjugate EPs in two complementary photonic systems in the presence of nonlinearity connected with T-symmetry by using the framework of a multilayer gain-loss assisted planar optical waveguide. We establish that, in the absence of chirality, the same amount of focusing and defocusing types of saturable nonlinearity leads to different dominating higher-order output modes, irrespective of the choice of the inputs, in two T-symmetric devices. An analytical model to describe this anomalous higher-order mode collapsing phenomenon in two T-symmetry systems owing to the interplay between nonlinearity and the topology of the higher-order conjugate EPs has been developed. Our findings provide a promising opportunity to switch higher-order modes and open up a credible platform to study the physics of nonlinearity-induced higher-order conjugate EPs in T-symmetry systems.