  A conventional optical cavity supports modes which are confined because they
are unable to leak out of the cavity. Bound state in continuum (BIC) cavities
are an unconventional alternative, where light can leak out, but is confined by
multimodal destructive interference. BICs are a general wave phenomenon, of
particular interest to optics, but BICs and multimodal interference have never
been demonstrated at the nanoscale. Here, we demonstrate the first nanophotonic
cavities based on BIC-like multimodal interference. This novel confinement
mechanism for deep sub-wavelength light shows orders of magnitude improvement
in several confinement metrics. Specifically, we obtain cavity volumes below
100x100x3nm^3 with quality factors about 100, with extreme cases having
23x23x3nm^3 volumes or quality factors above 400. Key to our approach, is the
use of pristine crystalline hyperbolic dispersion media (HyM) which can support
large momentum excitations with relatively low losses. Making a HyM cavity is
complicated by the additional modes that appear in a HyM. Ordinarily, these
serve as additional channels for leakage, reducing cavity performance. But, in
our experiments, we find a BIC-like cavity confinement enhancement effect,
which is intimately related to the ray-like nature of HyM excitations. In fact,
the quality factors of our cavities exceed the maximum that is possible in the
absence of higher order modes. The alliance of HyM with BICs in our work yields
a radically novel way to confine light and is expected to have far reaching
consequences wherever strong optical confinement is utilized, from ultra-strong
light-matter interactions, to mid-IR nonlinear optics and a range of sensing
applications.
