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Non-Hermitian systems are known to possess unique singularities in the scattering spectra such as exceptional points, bound states in the continuum, Diabolic points, and anapole states, which are usually considered to be independent. Here, we demonstrate the fundamental relationships between non-Hermitian singularities and observe them experimentally in the scattering spectra. We reveal that exceptional points appear in the anapole regime, and diabolic points are associated with superscattering. We confirm our findings with microwave experiments by measuring the scattering spectra of subwavelength Mie-resonant ceramic rings. Our study underpins the generic behavior of non-Hermitian singularities in the scattering spectra of subwavelength resonators, uncovering their novel applications in non-Hermitian nonlinear optics and topological photonics., Comment: 19 pages, 5 figures

The problem of losses in resonators is a key issue in the design and use of modern plasmonic and photonic meta-devices. We propose a spectroscopic method for determining material and radiation losses in structures with bound states in the continuum using as example the phase-change chalcogenide Ge2Sb2Te5. The complex refractive index for the amorphous and crystalline Ge2Sb2Te5 phases was measured experimentally, and the resonance optical properties were calculated for a telecommunication wavelength of 1500 nm. To demonstrate the validity of the method, two types of resonators were considered - a cylinder and a ring which support bound states in the continuum according to the Friedrich - Wintgen mechanism. We have determined the value of the material quality-factor for the amorphous Ge2Sb2Te5 as Qmat = 46 and the values of the radiation quality-factors Qrad = 608 for the cylinder and Qrad = 332 for the ring of a pair of TE0,1,2 and TE0,2,0 modes in the regime of bound states in the continuum. We also demonstrated two mechanisms for efficient switching of the scattering spectra between the amorphous and crystalline phases of Ge2Sb2Te5., Comment: 21 pages, 7 figures. Submitted to Advanced Optical Materials