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We report a self-consistent quasinormal mode theory for nanometer scaleelectromagnetism where the possible nonlocal and quantum effects are treatedthrough quantum surface responses. With Feibelman's frequency-dependent\textit{d} parameters to describe the quantum surface responses, we formulatethe source-free Maxwell's equations into a generalized linear eigenvalueproblem to define the quasinormal modes. We then construct an orthonormalrelation for the modes and consequently unlock the powerful toolbox of modalanalysis. The orthonormal relation is validated by the reconstruction of thefull numerical results through modal contributions. Significant changes in thelandscape of the modes are observed due to the incorporation of the quantumsurface responses for a number of nanostructures. Our semi-analytical modalanalysis enables transparent physical interpretation of the spontaneousemission enhancement of a dipolar emitter as well as the near-field andfar-field responses of planewave excitations in the nanostructures.

Quasinormal mode theory for nanoscale electromagnetism with quantum surface responses