A general framework of canonical quasinormal mode analysis for extreme nano-optics

Optical phenomena associated with extremely localized field should be understood with considerations of nonlocal and quantum effects, which pose a hurdle to conceptualize the physics with a picture of eigenmodes. Here we first propose a generalized Lorentz model to describe general nonlocal media under linear mean-field approximation and formulate source-free Maxwell's equations as a linear eigenvalue problem to define the quasinormal modes. Then we introduce an orthonormalization scheme for the modes and establish a canonical quasinormal mode framework for general nonlocal media. Explicit formalisms for metals described by quantum hydrodynamic model and polar dielectrics with nonlocal response are exemplified. The framework enables for the first time direct modal analysis of mode transition in the quantum tunneling regime and provides physical insights beyond usual far-field spectroscopic analysis. Applied to nonlocal polar dielectrics, the framework also unveils the important roles of longitudinal phonon polaritons in optical response.