Embedded scattering eigenstates using resonant metasurfaces

Optical embedded eigenstates (EEs) are localized modes of an open structure that are compatible to radiation, yet they have infinite lifetime and diverging quality factors. Their realization in nanostructures finite in all dimensions is inherently challenging, because they require materials with extreme electromagnetic properties. Here we explore the realization of these bound states in the continuum using ultrathin metasurfaces composed of arrays of nanoparticles. We first show that arrays of lossless nanoparticles can realize the condition for EEs, and then explore the use of Ag nanoparticles coated with gain media shells to compensate material loss and revive the EE despite realistic loss in plasmonic materials. We discuss the possible experimental realization of the proposed structures, and provide useful guidelines for practical implementation in nanophotonics systems with largely enhanced light-matter interactions. These metasurfaces may lead to highly efficient lasers, filters, frequency comb generation and sensors.