2025/10/01 by Takata, Kenta, Mock, Adam, Notomi, Masaya +1
#FOS: Physical sciences #Optics (physics.optics)
paper · doi:10.48550/arxiv.2510.00623
Non-Hermitian systems can have peculiar degeneracies of eigenstates called exceptional points (EPs). An EP of n degenerate states is said to have order n, and higher-order EPs (HEPs) with n ≥ 3 exhibit intrinsic order-scaling responses potentially applied to superior sensing and state control. However, traditional eigenvalue-based searches for HEPs are facing fundamental limitations in terms of complexity and implementation. Here, we propose a design paradigm for HEPs based on a simple property for matrices termed nilpotence and concise inductive procedure. The nilpotence guarantees a HEP with desired order and helps divide the problem. Our inductive scheme repeatedly extends a system and doubles its EP order, starting with a known design. Based on the nilpotence, we systematically design photonic cavity arrays operating at chiral, passive, and active HEPs with n = 3, 6, 7 and show their peculiar directional radiation, induced transparency, and enhanced transmittance and spontaneous emission, respectively. We inductively find lattice systems with diverging EP order originating from a well-known 2 × 2 parity-time-symmetric Hamiltonian. We also extend the active HEP system with n = 7 to another with n = 14 and have further magnified responses. Our work pushes the investigation and application of HEPs to previously unexplored regimes in various physical systems.