  Plasmonic hyperbolic metasurfaces have emerged as an effective platform for
manipulating the propagation of light. In this work, we leverage confined modes
on arrays of silver nanoridges, which exhibit a hyperbolic-in-nature refractive
index, to theoretically demonstrate and model a super-resolution imaging
technique based on structured illumination microscopy. We demonstrate a spatial
resolution of ~52 nm at 458 nm, which is 3.44 times better than an equivalent
diffraction limited image. In addition, we demonstrate how the anisotropic
properties of the metasurface dispersion can be leveraged to further improve
the resulting spatial resolution to ~50 nm. This work emphasizes the ability to
engineer the properties of confined optical modes and to leverage those
characteristics for applications in imaging. The results of this work could
lead to improved approaches for super-resolution imaging using designed
sub-wavelength structures.
