Quasinormal mode theory for nanoscale electromagnetism with quantum surface responses.

We report a self-consistent quasinormal mode theory for nanometer scale electromagnetism where the possible nonlocal and quantum effects are treated through quantum surface responses. With Feibelman's frequency-dependent \textit{d} parameters to describe the quantum surface responses, we formulate the source-free Maxwell's equations into a generalized linear eigenvalue problem to define the quasinormal modes. We then construct an orthonormal relation for the modes and consequently unlock the powerful toolbox of modal analysis. The orthonormal relation is validated by the reconstruction of the full numerical results through modal contributions. Significant changes in the landscape of the modes are observed due to the incorporation of the quantum surface responses for a number of nanostructures. Our semi-analytical modal analysis enables transparent physical interpretation of the spontaneous emission enhancement of a dipolar emitter as well as the near-field and far-field responses of planewave excitations in the nanostructures.