The Neumann Poincaré operator is an integral operator that allows the representation of the solutions to elliptic PDE's with piecewise constant coefficients using layer potentials. Its spectral properties are of interest in particular in the study of plasmonic resonances of metallic particles. We study the case of bowtie-shaped micro antennas, and particularly how the spectrum of the operator may degenerate because of the presence of corners and in terms of the distance between the two wings of the bowtie.