Spawning a ring of exceptional points from a metamaterial

Exceptional points(EPs) are degeneracies in non-Hermitian systems and give rise to counter intuitive, yet interesting physical effects. Inspired by the exotic physics of EP in designed metamaterials, we theoretically explore how an EPs-ring can be generated from a non-Hermitian resonant metamaterial bearing both dissipation and radiation losses. When the substrate thickness of this metamaterial is varied, the complex eigenvalues of the scattering matrix show a transition from single EP to a ring of EPs, where each EP is associated with maximally asymmetric reflection. We show that our scattering matrix based fitted coupled mode theory results agree very well with finite-difference time-domain simulations. Our work illustrates that the optical properties of the metamaterials can be dramatically altered by carefully tuning the dissipation and radiation losses.