Topological Engineering of High-Order Exceptional Points through Transformation Optics

Exceptional points (EPs) in non-Hermitian photonic systems have attracted considerable research interest due to their singular eigenvalue topology and associated anomalous physical phenomena. These properties enable diverse applications ranging from enhanced quantum metrology to chiral light-matter interactions. Practical implementation of high order EPs in optical platforms however remains fundamentally challenging, requiring precise multi-parameter control that often exceeds conventional design capabilities. This work presents a novel framework for engineering high order EPs through transformation optics (TO) principles, establishing a direct correspondence between mathematical singularities and physically controllable parameters. Our TO-based paradigm addresses critical limitations in conventional Hamiltonian approaches, where abstract parameter spaces lack explicit connections to experimentally accessible degrees of freedom, while simultaneously providing full-field mode solutions. In contrast to prevailing parity-time-symmetric architectures, our methodology eliminates symmetry constraints in EP design, significantly expanding the possibilities in non-Hermitian photonic engineering. The proposed technique enables unprecedented control over EP formation and evolution in nanophotonic systems, offering new pathways for developing topological optical devices with enhanced functionality and robustness.