The spectral shift between near- and far-field resonances of optical nano-antennas

Within the past several years a tremendous progress regarding optical nano-antennas could be witnessed. It is one purpose of optical nano-antennas to resonantly enhance light-matter interactions at the nanoscale, e.g. the interaction of an external illumination with molecules. In this specific, but in almost all schemes that take advantage of resonantly enhanced electromagnetic fields in the vicinity of nano-antennas, the precise knowledge of the spectral position of resonances is of paramount importance to fully exploit their beneficial effects. Thus far, however, many nano-antennas were only optimized with respect to their far-field characteristics, i.e. in terms of their scattering or extinction cross sections. Although being an emerging feature in many numerical simulations, it was only recently fully appreciated that there exists a subtle but very important difference in the spectral position of resonances in the near-and the far-field. With the purpose to quantify this shift, Zuloaga et al. suggested a Lorentzian model to estimate the resonance shift. Here, we devise on fully analytical grounds a strategy to predict the resonance in the near-field directly from that in the far-field and disclose that the issue is involved and multifaceted, in general. We outline the limitations of our theory if more sophisticated optical nano-antennas are considered where higher order multipolar contributions and higher order antenna resonances become increasingly important. Both aspects are highlighted by numerically studying relevant nano-antennas.