Direct observation of energy band attraction effect in non-Hermitian systems

The energy band attraction (EBA) caused by the non-orthogonal eigenvectors is a unique phenomenon in the non-Hermitian (NH) system. However, restricted by the required tight-binding approximation and meticulously engineered complex potentials, such effect has not been experimentally demonstrated. Here, an experimentally verifiable model is proposed based on the photonic counterpart of the all-dielectric Mie-resonator lattice in a parallel-plate transmission line. Through theoretical derivation, we directly connect the transmission spectra with eigenvalues and eigenvectors of the NH Hamiltonians. By precisely tuning the resonance loss of the Mie-resonators, the evolution of the EBA effect in two-level NH systems, from gapped bands, gapless bands to flat bands, is directly observed for the first time. Furthermore, such effect can be extended to a graphene-like two-dimensional NH system. Our works show a metamaterial approach towards NH topological photonics and offer a deeper understanding of band theory in open systems.