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.
By placing a quantum emitter in the mouths of nanogaps consisting of two metal nanoparticles nearly into contact, significant increases in emission rate are obtained. This mechanism is central in the design of modern plasmonic nanoantennas. However, due to the lack of general knowledge on the balance between the different decay rates in nanogaps (emission, quenching, and metal absorption), the design of light-emitting devices based on nanogaps is performed in a rather hazardous fashion; general intuitive recipes do not presently exist. With accurate and simple closed-form expressions for the quenching rate and the decay rate into gap plasmons, we provide a comprehensive analysis of nanogap light emitting devices in the limit of small gap thickness. We disclose that the total decay rate in gap plasmons can largely overcome quenching for specifically selected metallic and insulator materials, regardless of the gap size. To confront these theoretical predictions, we provide a comprehensive numerical analysis of nanocube-type antennas in the limit of small gap thickness and further provide upper bounds for the photon-radiation efficiency.
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