Self-Hybridization within non-Hermitian Localized Plasmonic Systems

Localized surface plasmons resonances occur when a metallic nano-particle is excited by an external electric field. Within the quasi-static limit, Ouyang and Isaacson have shown that the plasmon modes are the solutions of an eigenvalue problem. Depending on the geometry of the particle, this eigenproblem can be non-Hermitian. Apart from bringing additional mathematical difficulties, this particularity of the plasmonic eigenproblem has always been considered as a mere computation detail.
In the present work, we demonstrate that, actually, plasmonic non-Hermiticity has dramatic physical consequences. We show that the bi-orthogonality can trigger the interaction between different plasmon modes within a single particle. Moreover, we relate the splitting energy of this self-hybridization phenomenon to the overlap matrix of the system. This way, we demonstrate that the measurement of the coupling energy enable us to directly measure the degree of bi-orthogonality of the plasmonic system. We unambiguously determine the role of the particle symmetries in the apparition of non-Hermiticity. Using electron energy loss spectroscopy and e-beam lithography, we experimentally realize a self-hybridization in a dagger-like system with a strong experimental coupling energy.