Electromagnetic energy conservation theorem and surface energy transfer under nonclassical electromagnetic boundary condition for mesoscale metallic nanostructures

For mesoscale metallic nanostructures (MMNSs) with feature sizes ranging from 1 to 20 nm, the optical response is significantly influenced by nonclassical effects, which can be comprehensively described by the nonclassical electromagnetic boundary condition (NEBC) formulated with the Feibelman d-parameters. In classical electromagnetism, the classical electromagnetic energy conservation theorem (CEECT) is a fundamental law with broad applications. In this paper, a general form of nonclassical electromagnetic energy conservation theorem (NEECT) under the NEBC with a rigorous incorporation of both non-perturbative d-parameters is established. The NEECT reveals that the NEBC will induce electromagnetic energy flow along the metal-dielectric interface and the associated losses, which can be quantified by our proposed concepts of surface Poynting vector and surface electric-energy density. The validity of the NEECT and its important applications are demonstrated by several numerical examples. The proposed NEECT paves the way for extending the wide applications of the CEECT from classical electromagnetism to nonclassical regimes.