Optical Theory Group

Abstract : Spectral degeneracies, including diabolic (DP) and exceptional (EP) points, exhibit unique sensitivity to external perturbations, enabling powerful control and engineering of wave phenomena. We present a residue-based perturbation theory that quantifies complex resonance splitting of DP and EP type spectral degeneracies using generalized Wigner–Smith operators. We validate our theory using both analytic Hamiltonian models and numerical electromagnetic simulations, demonstrating excellent agreement across a range of cases. Our approach accurately predicts degenerate resonance splitting using only scattering data, offering a powerful framework for precision tuning, inverse design, and practical exploitation of non-Hermitian phenomena.

Abstract : 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.

Abstract : Perturbing resonant systems causes shifts in their associated scattering poles in the complex plane. In a previous study [arXiv: 2408.11360], we demonstrated that these shifts can be calculated numerically by analyzing the residue of a generalized Wigner-Smith operator associated with the perturbation parameter. In this work, we extend this approach by connecting the Wigner-Smith formalism with results from standard electromagnetic perturbation theory applicable to open systems with resonances of arbitrary quality factors. We further demonstrate the utility of the method through several numerical examples, including the inverse design of a multi-layered nanoresonator sensor and an analysis of the enhanced sensitivity of scattering zeros to perturbations.