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Plasmonics has attracted much attention not only because it has usefulproperties such as strong field enhancement, but also because it reveals thequantum nature of matter. To handle quantum plasmonics effects, ab initiopackages or empirical Feibelman d-parameters have been used to explore thequantum correction of plasmonic resonances. However, most of these methods areformulated within the quasi-static framework. The self-consistent hydrodynamicsmodel offers a reliable approach to study quantum plasmonics because it canincorporate the quantum effect of the electron gas into classicalelectrodynamics in a consistent manner. Instead of the standard scatteringmethod, we formulate the self-consistent hydrodynamics method as an eigenvalueproblem to study quantum plasmonics with electrons and photons treated on thesame footing. We find that the eigenvalue approach must involve a globaloperator, which originates from the energy functional of the electron gas. Thismanifests the intrinsic nonlocality of the response of quantum plasmonicresonances. Our model gives the analytical forms of quantum corrections toplasmonic modes, incorporating quantum electron spill-out effects andelectrodynamical retardation. We apply our method to study the quantum surfaceplasmon polariton for a single flat interface.

An eigenvalue approach to quantum plasmonics based on a self-consistent hydrodynamics method