Clusters of Loci of Innumerable Exceptional Points in Purely Real-Parameter Passive Systems: I. Fixed-Free 2DOF Model

Abstract: Research on exceptional points (EPs) as singularities, where eigenvalues and eigenvectors coalesce, has sparked a revolution in non-Hermitian physics [1–7], offering unprecedented sensitivity and wave manipulation. Previous studies have predominantly focused on isolated points in the complex plane [8–12], often relying on nonphysical complex parameters or active gain–loss modulation. However, such approaches introduce significant system complexity and hinder scalability, leaving the realization of continuous EP structures in purely passive, real-world systems an open challenge [13–18]. To address this challenge, this study reports the discovery of an EP surface within a purely passive, real-parameter, two-degree-of-freedom (2DOF) damped system. A hidden physical landscape was unveiled, termed the L-surface, representing clusters of loci of innumerable EPs. Leveraging the L-surface derived from exact analytical solutions, this study identified and validated fundamental topological phenomena, including topological jump, imprint, and nucleation, all of which were previously obscured by numerical noise [19–23]. The comprehensive analysis and precise identification of this manifold required a physical parameter precision of 100 decimal places. This regime has been conventionally dismissed as mere numerical noise in standard 64-bit double-precision floating-point formats. The unveiled L-surface provides a robust foundation for next-generation ultrasensitive sensing and perfect energy absorption across frontiers, ranging from quantum computing [24–26] to advanced biosensing [27, 28], extending its transformative impact to the broader realms of electronics [29, 30] and optics [31–33].