We study the nonlocal response of a confined electron gas within the hydrodynamical Drude model. We address the question whether plasmonic nanostructures exhibit nonlocal resonances that have no counterpart in the local-response Drude model. Avoiding the usual quasi-static approximation, we find that such resonances do indeed occur, but only above the plasma frequency. Thus the recently found nonlocal resonances at optical frequencies for very small structures, obtained within quasi-static approximation, are unphysical. As a specific example we consider nanosized metallic cylinders, for which extinction cross sections and field distributions can be calculated analytically.

The standard hydrodynamic Drude model with hard-wall boundary conditions can give accurate quantitative predictions for the optical response of noble-metal nanoparticles. However, it is less accurate for other metallic nanosystems, where surface effects due to electron density spill-out in free space cannot be neglected. Here we address the fundamental question whether the description of surface effects in plasmonics necessarily requires a fully quantum-mechanical ab initio approach. We present a self-consistent hydrodynamic model (SC-HDM), where both the ground state and the excited state properties of an inhomogeneous electron gas can be determined. With this method we are able to explain the size-dependent surface resonance shifts of Na and Ag nanowires and nanospheres. The results we obtain are in good agreement with experiments and more advanced quantum methods. The SC-HDM gives accurate results with modest computational effort, and can be applied to arbitrary nanoplasmonic systems of much larger sizes than accessible with ab initio methods.

We study the effect of nonlocal optical response on the optical properties of metallic nanowires, by numerically implementing the hydrodynamical Drude model for arbitrary nanowire geometries. We first demonstrate the accuracy of our frequency-domain finite-element implementation by benchmarking it in a wide frequency range against analytical results for the extinction cross section of a cylindrical plasmonic nanowire. Our main results concern more complex geometries, namely cylindrical and bow-tie nanowire dimers that can strongly enhance optical fields. For both types of dimers we find that nonlocal response can strongly affect both the field enhancement in between the dimers and their respective extinction cross sections. In particular, we give examples of blueshifted maximal field enhancements near hybridized plasmonic dimer resonances that are still large but nearly two times smaller than in the usual local-response description. For the same geometry at a fixed frequency, the field enhancement and cross section can also be significantly more enhanced in the nonlocal-response model.

We present a novel wave equation for linearized plasmonic response, obtained by combining the coupled real-space differential equations for the electric field and current density. Nonlocal dynamics are fully accounted for, and the formulation is very well suited for numerical implementation, allowing us to study waveguides with subnanometer cross-sections exhibiting extreme light confinement. We show that groove and wedge waveguides have a fundamental lower limit in their mode confinement, only captured by the nonlocal theory. The limitation translates into an upper limit for the corresponding Purcell factors, and thus has important implications for quantum plasmonics.

Giant field enhancement and field singularities are a natural consequence of the commonly employed local-response framework. We show that a more general nonlocal treatment of the plasmonic response leads to new and possibly fundamental limitations on field enhancement with important consequences for our understanding of SERS. The intrinsic length scale of the electron gas serves to smear out assumed field singularities, leaving the SERS enhancement factor finite even for geometries with infinitely sharp features. For silver nano-groove structures, mimicked by periodic arrays of half-cylinders (up to 120 nm in radius), we find no enhancement factors exceeding ten orders of magnitude (10 10 ).

We study the refractive-index sensing properties of plasmonic nanotubes with a dielectric core and ultra-thin metal shell. The few-nm thin metal shell is described by both the usual Drude model and the nonlocal hydrodynamic model to investigate the effects of nonlocality. We derive an analytical expression for the extinction cross section and show how sensing of the refractive index of the surrounding medium and the figure-of-merit are affected by the shape and size of the nanotubes. Comparison with other localized surface plasmon resonance sensors reveals that the nanotube exhibits superior sensitivity and comparable figure-of-merit.Keywords Refractive-index sensing · Nanoplasmonics · Hydrodynamic Drude model 1 IntroductionIt is well known that metallic nanoparticles can sustain localized surface plasmon (LSP) oscillations, whose resonance frequencies in the quasi-static limit depend solely on the geometry of the nanoparticle, the permittivity of the metal and the surrounding permittivity. The dependency of the LSP resonance (LSPR) on the surrounding medium makes metallic particles extremely good sensors, progressing

The spontaneous emission rate of dipole emitters close to plasmonic dimers are theoretically studied within a nonlocal hydrodynamic model. A nonlocal model has to be used since quantum emitters in the immediate environment of a metallic nanoparticle probe its electronic structure. Compared to local calculations, the emission rate is significantly reduced. The influence is mostly pronounced if the emitter is located close to sharp edges. We suggest to use quantum emitters to test nonlocal effects in experimentally feasible configurations.

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