  We show that spin wave acquires a polarization-dependent geometric phase
along a cyclic trajectory of non-coplanar magnetizations in antiferromagnets.
Specifically, we demonstrate that a cyclic set of 90 degree antiferromagnetic
domain walls simultaneously introduce geometric and dynamic phases to spin
wave, and thus leads to asymmetric magnitude of overall phase for
left-/right-circular components. Based on the polarization-dependent phase, we
propose theoretically and confirm by micromagnetic simulations that, a
Mach-Zehner interferometer with cyclic 90 degree domain walls in one arm and
homogenous domain in the other arm, naturally acts as a spin wave circular
polarizer. Moreover, the circular polarizer has intrinsic nonreciprocity, which
filters opposite polarization in opposite propagation direction.
