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Traditionally in plasmonics, the most common approach in analyzing the resonant behavior of light interaction with plasmonic nanostructures has been to apply the local-response approximation (LRA), using – depending on the structure complexity and relation between a characteristic dimension and the interacting wavelength – either (quasi)analytic or numerical approaches. Recently, however, as the characteristic dimensions of such structures have scaled down, it has turned out that more complex models based on the nonlocal response (NOR), or even quantum interaction) of free electrons are desirable, in order to explain novel effects (new resonances, blue spectral shifts). Newly emerging approaches describing the complexity of interactions at nanoscale, connected with emerging new physics, are shown and discussed in this contribution, in comparison with the standard LRA. This reasoning has lately started a rapid increase of interest in developing appropriate nonlocal models. This new field is by no means completed; there are, actually, several nonlocal models existing, based on different starting conditions, and predicting phenomena. These are, however, not always consistent and equivalent. In particular, in our studies, we have concentrated on understanding the interaction and developing a simple model capable of predicting the longitudinal nonlocal response based on the linearized hydrodynamic model, applied to simple structures, such as a spherical nanoparticle. Within our model, we have also shown and compared several alternatives within the approach, with respect to inclusion of the current “damping”, (1) standard model (with a possible increased damping constant), (2) with damping in acceleration, and (3) with liquid-viscosity damping. Also, the extension to generalized nonlocal response model is considered. In parallel, as an alternative (and more general) approach, based on our previous rich experience with Fourier modal methods, we have considered and developed the extension of the rigorous coupled wave analysis technique capable of treating nonlocal response numerically, for more general structures.
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