Description of Bow-Tie Nanoantennas Excited by Localized Emitters Using Conformal Transformation

The unprecedented advance experienced by nano fabrication techniques and plasmonics research over the past few years has made possible the realization of nanophotonic systems entering into. the so-called strong coupling regime between localized surface plasmon (LSP) modes and quantum emitters. Unfortunately, from a theoretical point of view, the field is hindered by the lack of analytical descriptions of the electrcimagnetic interaction between strongly hybridized LSP modes and nanoemitters even within the Markovian approximation. This gap is tackled here by exploiting a conformal transformation where a bow-tie nanoantenna excited by a dipole is mapped into a periodic slab dipole framework whose analytical solution is available. Solving the problem in the transformed space not only provides a straightforward analytical explanation for the original problem (validated using full-wave simulations) but also grants a deep physical insight and simple design guidelines to maximize the coupling between localized dipoles and the bow-tie LSP modes. The results presented here therefore pave the way for a full analytical description of realistic scenarios where quantum dots or dye molecules (modeled beyond a two-level system) are placed near a metallic bow-tie nanoantenna.