Bound States to Bands in the Continuum in Cylindrical Granular Crystals

We theoretically investigate and experimentally demonstrate that genuine bound states in the continuum (BICs) - polarization-protected BICs - can be completely localized within compact solid resonators. This bound mode is realized in a highly tunable mechanical system made of cylindrical granular crystals, where tuning the contact boundaries enables the in situ transition from the BICs to quasi-BICs in a controllable manner. Since a single-particle resonator can itself support BICs, these bound states can extend to form bound bands within periodic structures composed of such resonators. We experimentally demonstrate the emergence of a quasibound (flat) band in a finite chain with broken resonator symmetry, using a laser Doppler vibrometer. Remarkably, we show that all cylindrical resonators within the entire chain exhibit high-Q and dispersionless resonance.