Quantum mechanics

Perturbation theory (quantum mechanics)

Metamaterial

Fano resonance

Photonics

Physics

Mathematics

Optics

Electromagnetic field

Resonator

Geometry

Quantum

Rotation formalisms in three dimensions

Plasmon

Electromagnetism

Laser & Photonics Review

In this Review, the theory and applications of optical micro and nanoresonators are presented from the underlying concept of their natural resonances, the so-called quasi-normal modes (QNMs). The latter are the basic constituents governing the response of resonators. Characterized by complex frequencies, QNMs are initially loaded by a driving field and then decay exponentially in time due to power leakage or absorption. Here, the use of QNM-expansion formalisms to model these basic effects is explored. Such modal expansions that operate at complex frequencies distinguish from the current user habits in electromagnetic modeling, which rely on classical Maxwell equation solvers operating at real frequencies or in the time domain; they also bring much deeper physical insight into the analysis. An extensive overview of the historical background on QNMs in electromagnetism and a detailed discussion of recent relevant theoretical and numerical advances are therefore presented. Additionally, a concise description of the role of QNMs on a number of examples involving electromagnetic resonant fields and matter, including the interaction between quantum emitters and resonators (Purcell effect, weak and strong coupling, superradiance...), Fano interferences, the perturbation of resonance modes, and light transport and localization in disordered media is provided.

Light Interaction with Photonic and Plasmonic Resonances