  Bound states in the continuum (BIC) are highly confined, nonradiative modes
that can exist in open structures, despite their potential compatibility and
coupling with the radiation spectrum, and may give rise to resonances with
arbitrarily large lifetimes. Here, we study this phenomenon in layered
materials featuring epsilon-near-zero constituents. Specifically, we outline a
systematic procedure to synthesize quasi-BIC resonances at given frequency,
incidence angle and polarization, and investigate the role of certain critical
parameters in establishing the quality factor of the resonances. Moreover, we
also provide an insightful phenomenological interpretation in terms of the
recently introduced concept of "photonic doping", and study the effects of the
unavoidable material loss and dispersion. Our results indicate the possibility
to synthesize sharp resonances, for both transversely magnetic and electric
polarizations, which are of potential interest for a variety of nanophotonics
scenarios, including light trapping, optical sensing and thermal radiation.
