  Confining electromagnetic energy is crucial to enhance light-matter
interactions, with important implications for science and technology. Here, we
discuss the opportunities offered by trapping and confining light in open
structures, based on the concept of embedded eigenstates within the radiation
continuum enabled by zero-index metamaterials. Building upon the physical
insights offered by our analysis, we put forward a general platform that allows
realizing extremely high field enhancements in open structures under external
illumination. Structures supporting embedded eigenstates represent a rare
example of physical systems in which extreme - in principle unbounded -
responses can be tamed. Our proposed design recipe to realize bound states in
the continuum also offers a simple model that allows testing important
questions that surround the concept of embedded eigenstates, such as their
effect on the local density of photonic states. Our findings help clarifying
which nano-optical and radio-wave applications may benefit from this unusual
and singular response.
