Placing quantum dots at polarisation singularities is expected to allow for direct control over the directionality of the emitted light. Possibly creating a photon driven quantum bit. Here, we investigate the occurrence of polar- isation singularities on plasmonic nanowires with periodic extrusions. We build a 3D model based on a finite element method in order to calculate the electric fields using Floquet periodicity and the theory of surface plasmons, propagating along the metal-dielectric interface. To validate our model we first show qualitative agreement between results ob- tained with the 3D model and earlier 2D models of a straight wire. Secondly we develop a piece of mathematics that allows for determining polarisation singularities independent of a reference frame and we show that polarisa- tion singularities exist on plasmonic nanowire with periodic extrusions at the surface of the metal
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