Conformal transformation applied to plasmonics beyond the quasistatic limit

A general strategy has been proposed recently to design and study analytically plasmonic devices, such as kissing nanowires, which show unprecedented broadband and nanofocusing properties. These nanostructures result from a conformal transformation applied to infinite plasmonic systems. The conformal transformation tool is powerful since the whole problem is solved in the original frame under the quasistatic approximation. However, this strategy is quite restrictive in perspective of applications since it can only apply to nanostructures of a few tens of nanometers (typically 20 nm). In this study, we extend the range of validity of this approach by taking into account radiation damping. The radiative losses are shown to map directly onto the power dissipated by a fictive absorbing particle in the original frame. Whereas only the surface plasmon mode was considered in previous studies, here lossy surface waves are also taken into account. Their counterpart in the transformed frame is shown to contribute predominantly to the radiative losses. The radiative reaction is then taken into account to predict the optical response of the nanostructure beyond the quasistatic limit. Radiative losses are shown to limit the light harvesting process but improve its broadband feature. The field enhancement induced by the nanostructure decreases with the structure dimension but remains significant (∼10³) over a major part of the near-infrared and visible spectra. Our analytical model is compared to numerical simulations and a quantitative agreement is found for dimension up to 200 nm.