Synergetic interaction of dark-modes and Faraday rotation for enhanced non-reciprocity

Dark-mode of a small particle consists of two co-existing equal-intensity and mutually opposing dipolar excitations. Each of these two opposing dipoles may even resonate at or near the dark-mode frequency. Nevertheless, the net dipole moment of the system vanishes due to the destructive interference between the opposing dipoles, hence the dark-mode resonance cannot be observed externally. We show that under external magnetic bias the opposing dark-resonances of a plasmonic particle shift in opposite directions and create a region of extremely sensitive Faraday rotation. We show that the magnetized dark resonance in Ag particle may provide 50 degrees rotation under magnetic fields of the order of 1 Tesla.