Gyrotropy and permittivity sensing driven by toroidal response

Using a quasi-static model of a toroidal metamaterial we demonstrate analytically that simultaneous excitation of the magnetic and toroidal dipoles in an array of subwavelength toroidal solenoids results in gyrotropic behaviour resembling conventional optical activity. We derive the polarization eigenstates of this uniaxial chiral toroidal metamaterial and show that such a medium is reciprocal, while the eigenstates are represented by two counter-rotating ellipses, one of which can be used for probing changes of the host permittivity in a manner exclusive to the toroidal metamaterial. We also show that the mechanism of permittivity sensing involving resonant toroidal response is fundamentally different from that, which has been exploited so far under the term ‘toroidal’.