  Optical metasurfaces have been widely used for manipulating electromagnetic
waves due to their low intrinsic loss and easy fabrication. The metasurfaces
employing the Pancharatnam-Berry (PB) geometric phase, called PB metasurfaces,
have been extensively applied to realize spin-dependent functionalities, such
as beam steering, focusing, holography, etc. The demand for PB metasurfaces in
complex environments has brought about one challenging problem, i.e., the
interference of multiple wave channels that limits the performance of PB
metasurfaces. A promising solution is developing nonreciprocal PB metasurfaces
that can isolate undesired wave channels and exhibit unidirectional
functionalities. Here, we propose a mechanism to realize nonreciprocal PB
metasurfaces of subwavelength thickness by using the magneto-optical effect of
YIG material in synergy with the PB geometric phase of spatially rotating
meta-atoms. Using full-wave numerical simulations, we show that the metasurface
composed of dielectric cylinders and a thin YIG layer can achieve nearly 92%
and 81% isolation of circularly polarized lights at 5.5 GHz and 6.5 GHz,
respectively, attributed to the enhancement of the magneto-optical effect by
the resonant Mie modes and Fabry-P\'erot cavity mode. In addition, the
metasurface can enable efficient unidirectional wavefront manipulations of
circularly polarized lights, including nonreciprocal beam steering and
nonreciprocal beam focusing. The proposed metasurface can find highly useful
applications in optical communications, optical sensing, and quantum
information processing.
