  We investigate the effect of inhomogeneous Dzyaloshinskii-Moriya interaction
(DMI) on antiferromagnetic spin-wave propagation theoretically and numerically.
We find that antiferromagnetic spin waves can be amplified at a boundary where
the DMI varies. The inhomogeneous DMI also provides a way to construct a
magnonic crystal with forbidden and allowed antiferromagnetic spin-wave bands
in terahertz frequency ranges. In contrast to ferromagnetic spin waves,
antiferromagnetic spin waves experience a polarization-dependent phase shift
when passing through the inhomogeneous DMI, offering a magnonic crystal that
also serves as a spin-wave polarizer.
