Modeling the interaction between light and a plasmonic nanoantenna, whose critical dimension is of a few nanometers, is complex owing to the "hydrodynamic" motion of free electrons in a metal. Such a hydrodynamic effect inevitably leads to a nonlocal material response, which enables the propagation of longitudinal electromagnetic waves in the material. In this paper, within the framework of a boundary integral equation and a method of moments algorithm, a computational scheme is developed for predicting the interaction of light with 3-D nonlocal hydrodynamic metallic nanoparticles of arbitrary shape. The numerical implementation is first demonstrated for the test example of a canonical spherical structure. The calculated results are shown to be in the excellent agreement with the theoretical results obtained with the generalized Mie theory. In addition, the capability of treating 3-D structures of general shapes is demonstrated by ellipsoids and dimers.

Since deep nanoscale systems are increasingly studied, accurate macroscopic theories dealing with quantum mechanical effects are in high demand. Concerning the electromagnetic response of nanoplasmonic systems, several hydrodynamic models have been proposed, each introducing an additional boundary condition (ABC) to describe the behavior of the plasmonic electron cloud. Four hydrodynamic approaches with four different boundary conditions are compared: the hard wall hydrodynamic model with the Sauter ABC, the curl-free hydrodynamic model with the Pekar ABC, the shear forces hydrodynamic model with the specular reflection ABC, and the quantum hydrodynamic model with the corresponding ABC. This is done by investigating near-and far-field features of a metallic nanosphere. It is shown that different hydrodynamic models may result in an entirely different prediction of the nanoparticle's response. These models are validated by using other local and nonlocal response models and experimental results.

In this work, we propose a general boundary integral e quation (BIE) approach for solving both the exterior (e.g., scattering) and interior (e.g., guided wave propagation) problems involving general plasmonic waveguiding structures with arbitrary cross-sectional geometries and with a continuous translational symmetry in the direction of wave propagation. In contrast to the field-based approach which deals with the electric and magnetic fields, we employ a potential -based formalism instead, involving vector and scalar potentials, and match them at the media interfaces. The proposed approach can not only handle conventional plasmonic waveguides on the order of a few hundred nanometers, but also those whose critical sizes are a few nanometers and in which the nonlocal hydrodynamic effects need to be accounted for. The BIEs describing the interaction of light with the plasmonic waveguide are solved by the Method of Moments (MoM) algorithm. Two illustrative examples, the first one of which deals with the scattering problem while the second computes the dispersion diagram of a plasmonic cylinder, are considered for both local and nonlocal cases. An excellent agreement is observed between the numerical and theoretical re sults, with the latter being derived from the generalized Mie the ory.

The interaction between light and plasmonic systems with deep‐nanometer characteristics, which is essentially governed by quantum mechanical effects, has been extensively studied by the nonlocal hydrodynamic approach. Several hydrodynamic models, supplemented by additional boundary conditions, have been introduced in order to describe the collective motion of the free electron gas in metals. Four hydrodynamic models, namely the hard wall hydrodynamic model (HW‐HDM), the curl‐free hydrodynamic model, the shear forces hydrodynamic model, and the quantum hydrodynamic model (Q‐HDM), are thoroughly investigated. The investigation studies the mode structure (the natural modes or, in quantum optics, the quasi‐normal modes) of the spherical core–shell topology, which is complemented by the plane wave response from the system. The results of the above hydrodynamic models are also compared with those of the specular reflection method. It is demonstrated that the choice of a particular hydrodynamic model strongly affects the natural frequencies and modes in the mode structure of the topology and thus drastically modifies the simulated fields in the near and far regions. Contrary to HW‐HDM and Q‐HDM, the other two hydrodynamic models fail to predict the particles’ response accurately, showing artifactual mode hybridization.

Although many commercially available electromagnetic tools are conveniently used in RF and microwave applications, only a few of them provide the capability to analyze the optical response of nanometric radiators and scatterers. The assessment of their performance in the visible to near ultraviolet part of the electromagnetic (EM) spectrum becomes more and more important, considering the exponential rise of nanoscale systems. Since the accuracy of these numerical tools has not been fully investigated in literature, in this paper we essentially demonstrate a comparative study of the most widely used EM field solvers in the area of nano-plasmonics: COMSOL, CST and Lumerical. This is done through the investigation of the near and far field characteristics of basic canonical nanoparticles such as spheres, shells, cubes and cuboids, varying their sizes and constituting materials. The benchmarking results clearly show that at this moment not all EM field solvers offer the same accuracy.