Modelling the Quantum Hydrodynamic Response from an Arbitrarily Shaped Nanoantenna: A Volume Integral Equation Approach

Antennas, as transmitters and receivers of radio waves/microwaves, play an indispensable role in any modern communication system. With the advancement of nanotechnology, antennas are made smaller and smaller and nowadays down to the nanoscale. These nanoscopic antennas, aliased as “nanoantennas”, are nanoscopic replica of their radio/microwave counterparts. They interact with high frequency electromagnetic (EM) waves, e.g., optical frequencies, and radiate visible light. Nanoantennas have found a wide range of applications from nanoscopic communications, via chemistry, to biosensing, just to name a few, and themselves represent a great conceptual expansion than the conventional radio/microwave antennas. Notably, the critical feature of a nanoantenna can be made as small as a few nanometers. This very small size inevitably triggers the consideration of quantum mechanical (QM) effects. At this regime, in contrast to the “bulk material” picture where the EM response of a medium is described by macroscopic parameters, e.g., permittivity and permeability, finer “mesoscopic” material models, which can depict nonclassical effects originating from granularities in metals, must be used. Many semi-classical models (see a recent review for the models [2]) have been proposed. Among them, one category that enjoys much popularity is the hydrodynamic approach. This approach offers a set of models in a hierarchical structure. Starting from the lowest level, the inclusion of the finite compressibility of electron gas results in the nonlocal hydrodynamic Drude model (HDM) [3]. Furthermore, by considering surface scattering, the generalized nonlocal optical response (GNOR) model can be derived [4]. Last, by adding higher order terms, e.g., the von Weizsäcker term, the exchange-correlation term, the quantum hydrodynamic (QHD) model is proposed to account for quantum effects, e.g., electron spill-out, tunneling [5], [6].