Rigorous modal analysis of plasmonic nanoresonators

Abstract

The specificity of modal-expansion formalisms is their capabilities to model the physical properties in the natural resonance-state basis of the system in question, leading to a transparent interpretation of the numerical results. In electromagnetism, modal-expansion formalisms are routinely used for optical waveguides. In contrast, they are much less mature for analyzing open non-Hermitian systems, such as micro and nanoresonators. Here, by accounting for material dispersion with auxiliary fields, we considerably extend the capabilities of these formalisms, in terms of computational effectiveness, number of states handled and range of validity. We implement an efficient finite element solver to compute the resonance states, and derive new closed-form expressions of the modal excitation coefficients for reconstructing the scattered fields. Together, these two achievements allow us to perform rigorous modal analysis of complicated plasmonic resonators, being not limited to a few resonance states, with straightforward physical interpretations and remarkable computation speeds. We particularly show that, when the number of states retained in the expansion increases, convergence towards accurate predictions is achieved, offering a solid theoretical foundation for analyzing important issues, e.g. Fano interference, quenching, coupling with the continuum, which are critical in nanophotonic research.

Nano‐Cavity QED with Tunable Nano‐Tip Interaction

“…Although these FEM calculations provide insight into the TESC system, they are computationally demanding, requiring an independent calculation to be performed for each tip position. A more computationally efficient approach, which also provides additional physical insight, is to use a quasinormal mode (QNM) framework . In this approach, FEM simulations are used not to calculate scattering spectra, but to calculate the complex effective mode volumes for the quasinormal modes of the tip‐substrate system.…”

How to calculate the pole expansion of the optical scattering matrix from the resonant states

“…Note added in proof. Recently, the scattered field has been computed more accurately by using a larger number of resonant states and adding an auxiliary group of artificial, so-called perfectly-matched-layer modes [33]. …”

“…The approach of Perrin [32] for the pole expansion of a scattered field is more general and has been validated for two poles. Recently, the scattered field has been computed more accurately by using a larger number of resonant states and adding an auxiliary group of artificial, so-called perfectly-matched-layer modes [33]. In a similar manner, Yang et al show how to derive the outgoing channels for a known electromagnetic near field [34], but both Perrin's and Yang's approaches do not provide the pole expansion of the scattering matrix, which directly relates incoming and outgoing channels.…”

Quasinormal-Mode Non-Hermitian Modeling and Design in Nonlinear Nano-Optics

“…The AlGaAs Drude-Lorentz model parameters are given by ε∞ = 1, ωp = 1.69 · 10 16 rad/s, ω0 = 5.55 · 10 15 rad/s, and γ = 0 in the transparency window of AlGaAs (λ > 760 nm). The COMSOL model used to obtain the figure can be downloaded with the QNMEig software [30].…”

“…where α [30] at FF. Note that the integral is performed of the volume V that defines the resonator in the scattered field formulation.…”