13 th International Congress on Artificial Materials for Novel Wave Phenomena – Metamaterials 2019 Rome, Italy, Sept. 16 th – Sept. 21 st , 2019 Conformal transformation in bowtie nanoantennas and nanocavities: unveiling hidden symmetries V. Pacheco-Peña 1 , Rúben Alves 2 and M. Navarro-Cía 2 1 School of Engineering, Newcastle University, Merz Court, Newcastle Upon Tyne NE17RU, United Kingdom 2 School of Physics and Astronomy, University of Birmingham, Birmingham, Edgbaston B15 2TT, UK victor.pacheco-pena@newcastle.ac.uk, m.navarro-cia@bham.ac.uk Abstract – In this work, bowtie nanoantennas and nanocavities are analyzed using the conformal transformation technique. Their performance is studied in terms of the non-radiative Purcell enhancement and self-induced optical forces experienced by quantum emitters. It is demonstrated how these two geometrically different plasmonic nanoparticles can share the same non-radiative Purcell spectra. This hidden symmetric response is unveiled by properly applying the conformal transformation technique, demonstrating that both nanoparticles share the same transformed geometry. I. INTRODUCTION The unprecedented advance in nanofabrication techniques has enabled the experimental study of nanostructures with different geometries using a wide range of metals and dielectrics [1]–[4]. The comprehensive analysis of the coupling between quantum emitters and localized surface plasmons (LSP) resonances in plasmonic nanoparticles has become an important research field [5], [6]. To understand the performance of these nanoparticles, full-wave simulations have been widely used. However, the dispersion of metals at optical frequencies and sizes of the nanoparticles can increase both the computational burden and complexity of the numerical studies. As it is known, analytical solutions for canonical cases such as a dipole next to a plasmonic nanosphere are accessible. However, to efficiently design plasmonic nanoparticles and gain physical insight on their performance, analytical solutions for more complex scenarios are needed. In this realm, the conformal transformation has become by its own merit as one of the preferred methods to study plasmonic nanoparticles [7], [8]. This technique was first proposed at microwave frequencies [9] and has demonstrated to be a powerful tool to gain physical understanding of plasmonic nanoparticles at optical frequencies, providing a high accuracy. It has been applied to different geometries such as cylinders, crescent-shaped nanoparticles [10], plasmonic gratings [11] and bowtie [12]–[14] and tripod nanoantennas [15]. Inspired by the importance of the conformal transformation technique and the necessity of analytical solutions for plasmonic nanoparticles, in this work, we study the coupling between quantum emitters (analytically treated as a point dipole) near bowtie nanoantennas and nanocavities. The Purcell enhancement and self-induced optical forces experienced by the nanoemitters are studied using bowtie nanoparticles with a length of l’ = 20 nm. As it will be shown, similar Purcell enhancement is achieved with both bowtie nanoantenna and nanocavities. This hidden symmetry is here unveiled and studied using the conformal transformation technique [16]. All the results are compared with numerical simulations using COMSOL Multiphysics ® . II. CONFORMAL TRANSFORMATION TECHNIQUE The schematic representations of the bowtie nanoantenna and nanocavity are shown in Fig. 1a,b, respectively, where it is shown how they are connected and disconnected at their center, respectively. Since both nanoparticles are geometrically different, non-radiative Purcell spectra can be expected (this performance will be studied in the following section and detailed during the conference).The nanoparticles (made of gold, Au) are immersed in vacuum and they are illuminated by a point dipole placed (y’ = 0, x’ = 1 nm) away from the center (0,0). Multiple conformal transformations can be cascaded depending on the nanoparticle to be studied [8]. Here, the single-step conformal transformation  = (′  ⁄ ) is applied to both nanoparticles with z = x + iy and z’ = x’ + iy’ as the