Description of bow-tie nanoantennas excited by localized emitters using conformal transformation

Abstract

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 electro- magnetic 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.