Light Interaction with Photonic and Plasmonic Resonances

Abstract

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...

Nano‐Cavity QED with Tunable Nano‐Tip Interaction

“…We then image the spatial dependence of the coupling strength due to changes in the cavity geometry as the tip is scanned in relation to a single QD along both the lateral and vertical directions. Furthermore, for a deeper understanding of our previous results, we compare these results to theoretical predictions based on both a classical Maxwell's equation solver and recently established techniques for the normalization of leaky resonator modes in a quasinormal‐mode formalism for a rigorous definition of the plasmonic cavity mode volume and its spatial dependence …”

“…It is worth noting, however, that while simulations based on Maxwell's equations confirm that the electric field in common plasmonic cavity designs is confined to a nanoscopic volume, calculation of a specific value of must be handled with care in these highly dissipative, non‐Hermitian systems. In this regime, modes become complex fields and their frequencies also become complex, as described earlier, making a complex number containing information about the local phase shift of the mode compared to that of the cavity which is related to the loss rate κ …”

“…Due to these constraints, a systematic understanding of the interrelation between coupling strength, cavity mode volume, and relative cavity–emitter position on the spatio‐spectral properties of the nano‐cavity emitter coupled system is lacking, and this has limited the systematic development of a broader application space. Furthermore, established theories for the determination of cavity mode volume do not always predict the behavior of non‐Hermitian, or lossy, plasmonic cavities . While theories for modeling plasmonic cavity mode volumes have been proposed, questions remain calling for more precise measurements to inform further theoretical developments.…”

“…Furthermore, established theories for the determination of cavity mode volume do not always predict the behavior of non‐Hermitian, or lossy, plasmonic cavities . While theories for modeling plasmonic cavity mode volumes have been proposed, questions remain calling for more precise measurements to inform further theoretical developments.…”

“…The Purcell factor can be re‐derived in this regime in terms of the relevant parameters for a resonant cavity mode: where is the wavelength corresponding to the cavity resonance, n is the refractive index, is the quality factor of the resonance mode with frequency , linewidth , and complex mode volume . In the limit of very high Q factors, the modal electric fields are real, which leads to real values, and Equation can be reduced to the usual formula defined in common textbooks of Hermitian cavities . Early cQED experiments employed a variety of cavity geometries to optimize , ranging from parallel flat mirrors to spherical mirrors in a Fabry–Perot geometry which reduced diffractive edge effects and significantly increased Q , to more complex microwave cavity designs .…”