Modes and Mode Volumes of Leaky Optical Cavities and Plasmonic Nanoresonators

Electromagnetic cavity modes in photonic and plasmonic resonators offer rich and attractive regimes for tailoring the properties of light-matter interactions. Yet there is a disturbing lack of a precise definition for what constitutes a cavity mode, and as a result their mathematical properties remain largely unspecified. The lack of a definition is evidenced in part by the diverse nomenclature at use - "resonance", "leaky mode", "quasimode", to name but a few - suggesting that the dissipative nature of cavity modes somehow makes them different from other modes, but an explicit distinction is rarely made. This perspective article aims to introduce the reader to some of the subtleties and working definitions that can be rigorously applied when describing the modal properties of leaky optical cavities and plasmonic nanoresonators. We describe some recent development in the field, including {calculation methods for quasinormal modes of both photonic and plasmonic resonators and the concept of a generalized effective mode volume, and we} illustrate the theory with several representative cavity structures from the fields of photonic crystals and nanoplasmonics.