  The optical activity of achiral nonmagnetic uniaxial metasurfaces caused by
the extrinsic chirality arising from the mutual orientation of their anisotropy
axis and the light plane of incidence is studied. The hyperbolic regime of the
metasurfaces manifests in the amplification of the polarization rotation in the
transmitted light and in the giant enhancement of the effect in the reflected
light. The transition to this regime is frequency dependent and has the
topological nature. The key role in the optical activity enhancement belongs to
the $\sigma$-near-pole and hyperbolic $\sigma$-near-zero regimes of the
metasurfaces. The hyperbolic metasurfaces based on graphene strips or metal
disks, and a black phosphorus thin film as a natural hyperbolic layer are
considered. The efficiency of the predicted effects depends on the metasurfaces
implementation and the role of a substrate. By varying the metasurface
parameters and choosing the physical realizations it is possible to design such
a hyperbolic metasurface polarizer for the THz, infrared, and visible working
ranges. Our findings may help to improve metasurface polarizers by using them
in the hyperbolic regime.
