Conditions for enhanced scattering and field confinement in single-mode metasurface cavities

Closed-form conditions for bound states in the continuum are derived for planar, cylindrical, and spherical cavities enclosed by metasurfaces with electric and magnetic response. While the combined response in lossless systems enables field confinement in arbitrarily small cavities, the gain-enabled bound states in the continuum are found to coalesce with a laser mode, leading to intriguing single-mode spectral singularities characterized by divergent scattered fields with simultaneously vanishing internal fields of the respective cavities. In support of the analytical characterizations, a full-wave numerical demonstration of the spectral singularities is presented in cylindrical metasurface cavities made of dielectric particles situated in a host gain medium. Beyond unveiling the fundamental physics governing metasurface cavities, our results offer a compact and broadly applicable tool for designing next-generation devices across the electromagnetic spectrum.