High-order exceptional points and novel light transmission spectra in PT symmetric ring resonator array

In this paper we construct PT symmetric 1D multi-mode ring resonator arrays to study the high-order exceptional points and related light transmission spectra. We first focus on arrays with the underling symmetry given by SU(2) group possessing high-order exceptional points (EPs). The Gilmore-Perelomov coherent state approach has been well tested in SU(2) symmetric waveguide array, but how this approach is applied in resonator arrays, and how the divergent peaks change near high-order EPs is still remains to be seen. After the study on SU(2) symmetric arrays, we change the coupling coefficients to a uniformed value, and the high-order EP splits into several lower order EPs, thus the original clear boundary between the PT unbroken and broken regions is replaced by a transition region, wherein we observe some interesting results such as multi-number of non-divergent peaks and the coexistence of divergent and non-divergent peaks.