Lines of bound states in the continuum in a phononic crystal slab

Bound states in the continuum (BICs) are radiation-free states whose energy is embedded in the continuum spectrum of the radiating modes. In general, BICs in periodic structures appear at isolated points in momentum space, whereas BICs forming a line require radiative continuum designs. Here, we demonstrate theoretically and experimentally that BICs can form continuous lines in a simple phononic crystal slab without special radiative continuums. Contrary to common sense, these BICs are symmetry-protected BICs not only at the center of the Brillouin zone ($\mathrm{\ensuremath{\Gamma}}$ point) but also along high-symmetry directions of momentum space. We utilize numerical simulations, a group theory method, and a mode expansion method to comprehensively understand the formation of the BICs. The BICs lines are observed experimentally by measuring the transmittance of the phononic crystal slab. Moreover, it is revealed that the BICs lines correspond to phase singularity lines of far-field radiation, and the phase winding number can be defined as a topological index. Our findings have the potential to improve multifrequency and multiwave-vector performance for applications such as high-intensity sound sources, filters, and sensors.