  Polarization is a key ingredient of all waves, including the electromagnetic
wave, the acoustic wave, as well as the spin wave. Due to the fixed
ferromagnetic order, the spin wave in ferromagnet is limited to the right
circular polarization. The spin wave in antiferromagnet, however, is endowed
with the full polarization degree of freedom because of the two identical
magnetic sublattices. In the synthetic antiferromagnet, the two magnetic
sublattices are spatially separated into two sublayers. The circular
polarization of spin wave is partially locked to the magnetic sublattice of the
antiferromagnet, thus to the sublayer in synthetic antiferromagnet. Based on
this unique polarization-sublayer locking mechanism, we show that both the
circular spin wave polarizer and retarder (wave-plate) can be straightforwardly
realized using synthetic antiferromagnets by restructuring the sublayers, e.g.
by removing or capping a portion of a sublayer. Manipulating spin wave
polarization by geometrical engineering provides a simple yet powerful paradigm
in harnessing the spin wave polarization for spin information processing.
