Optical bound states in the continuum in a single slab with zero refractive index

We have investigated theoretically the reflectivity, quality factor, and eigenfrequency for a single slab with zero refractive index. We demonstrate that optical bound states in the continuum can be achieved by the various zero-refractive-index slabs made of epsilon-near-zero, impedance-machted zero-index, or mu-near-zero materials. Moreover, by analytically investigating the frequency of the resonant reflection and resonant transmission, when the quality factor becomes infinity, these two frequencies are precisely equal. For the mu-near-zero slab, the bound states in the continuum are observed at arbitrary incident angles by analyzing the behaviors of complex eigenfrequencies. Our findings may lead to unprecedented high-quality resonators in metamaterials.