In this Review, the theory and applications of optical micro-and nano-resonators are presented from the underlying concept of their natural resonances, the so-called quasi-normal modes (QNMs). QNMs 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's 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.
(3 of 38)www.advancedsciencenews.com www.lpr-journal.org Figure 2. Examples of applications whose analysis benefit from QNM-expansion approaches. a) Nonlocal plasmonics. QNMs can be used to predict the nonlocal response of free electron gas on the Purcell factor of an emitter placed in the near-field of a gold nanorod. Predictions from two different nonlocal models-the hydrodynamic Drude model (HDM) and the generalized nonlocal optical response (GNOR) Model-are shown and compared to classical predictions obtained with a Drude model. The inset shows the electric field intensity of the nonlocal GNOR QNM. Adapted with permission. [53] Copyright 2017, Optical Society of America. b) QNM expansion of the scattering matrix. (Upper panel) Absorption cross section of a multi-layered metallic-dielectric sphere in air, demonstrating the good agreement between the results obtained with Mie's scattering theory (dashed black curve) and a QNM-expansion formalism for the scattering matrix (solid red curve) computed with the QNM eigenfrequencies shown in the Lower panel. Reproduced with permission. [40] Copyright 2017, American Physical Society. c) Quantum hybrids. Supperradiant and subradiant decay rates m and energies m of a quantum hybrid formed by 100 molecules that are randomly distributed and oriented around a silver nanorod (diameter 30 nm, length 100 nm), predicted with the QNM formalism. γ 0 denotes the decay rate of every individual molecule in the vacuum. The left inset shows the superradiant state of the hybrid, with a large cooperativity involving more than one half of the molecules. Reproduced with permission. [28] Copyright 2017, American Physical Society. d) Quant...