Exceptional Points in the Scattering Resonances of a Sphere Dimer

TL;DR

This paper explores the existence and properties of exceptional points in the electromagnetic scattering of a sphere dimer, revealing how material tuning and symmetry breaking influence resonance degeneracies and sensing capabilities.

Contribution

It analytically demonstrates the conditions for exceptional points in sphere dimers across different regimes, including symmetry considerations and the effects of retardation.

Findings

EPDs occur in $ rev$-symmetric configurations with complex susceptibilities.

Retardation breaks symmetry, but EPDs can still be achieved through material dispersion tuning.

Near an EPD, eigenfrequency splitting follows a square-root law, affecting scattering and sensing.

Abstract

We investigate exceptional points of degeneracy (EPDs) in electromagnetic scattering of a sphere dimer from the electroquasistatic limit to the fully retarded regime. In the quasistatic limit, we prove that $\parity\trev$-symmetric configurations, realized by spheres with complex-conjugate susceptibilities, host EPDs. Beyond this limit, retardation breaks $\parity\trev$-symmetry; nevertheless, by jointly tuning the material dispersion of the two spheres, we derive analytic conditions for the existence of EPDs at \textit{real-frequencies}. Near an EPD, we show that single-parameter perturbations yield the characteristic square-root splitting of the eigenfrequencies, and we quantify its impact on scattering, extinction, and absorption, clarifying sensing implications.