Collective resonances in a circular array of gyromagnetic rods

We present a rigorous theoretical investigation on the collective magnetic resonance of a circular array of subwavelength gyromagnetic rods. We derive the closed-form solutions to the eigenmodes within the framework of the dynamic dipole approximation using an eigenresponse theory. Owing to the lack of time-reversal symmetry and Lorentz reciprocity, the eigenpolarizability spectra exhibit significant nonreciprocal characteristics: only a single branch of rotating magnetic dipoles is supported, whereas another one corresponding to inversely rotating magnetic dipoles is totally suppressed. We found that the collective coupled magnetic dipole and coupled electric dipole (CED) modes of the circular arrays display remarkable distinction in both the resonant frequency and the radiative width in comparison with the isolated gyromagnetic rod. We further carry out full-wave numerical simulation to test the accuracy of the analytical results on the CED mode.