Optical leaky-wave nanoantenna: Complex modes along linear arrays of plasmonic nanoparticles

We discuss the fundamental leaky-wave properties of linear arrays of plasmonic nanoparticles, in order to realize sub-diffraction optical leaky-wave nanoantennas, with particular attention to the mathematical and analytical aspects of the associated boundary value problem. We focus on the longitudinal polarization regime, which may provide efficient and directive radiation, despite the inherent presence of material absorption in plasmonic materials. Using closed-form dispersion relations derived in the complex domain, we discuss the dispersion properties of leaky and complex modes, and we highlight under which conditions a sub-diffractive nanoparticle array may support directive conical radiation with frequency scanning properties. This may be of great interest for a variety of potential applications in optical communications and radiation.