  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.
