  In this paper, we describe the manifestation of localized states through
coherent and incoherent analyses of a diffuse elastic wavefield inside a
two-dimensional metamaterial made of a collection of vertical long beams glued
to a thin plate. We demonstrate that localized states arise due to multi-wave
interactions at the beam-plate attachment when the beams acts as coupled
resonators for both compressional and flexural resonances on the metasurface.
Due to the low-quality factor compressional resonance of the beams, inside the
main bandgap the modal density of the systel drops to near a high-quality
factor flexural resonance of the beams, and blocks the diffusion process of the
wavefield intensity. This experiment physically highlights the
tight-binding-like coupling in the localized regime for this two-dimensional
metamaterial.
