  Acoustic bianisotropic materials couple pressure and local particle velocity
fields to simultaneously excite monopole and dipole scattering, which results
in asymmetric wave transmission and reflection of airborne sound. In this work,
we systematically realize an arbitrarily given bianisotropic coupling between
the pressure and velocity fields for asymmetric wave propagation by an acoustic
grating with inversion symmetry breaking. This acoustic bianisotropic grating
is designed by optimizing the unit cells with a finite element method to
achieve the desired scattering wavevectors determined by the bianisotropic
induced asymmetric wave propagation. The symmetry and Bloch wavevectors in the
reciprocal space resulted from the grating are analyzed, which match with the
desired scattering wavevectors. The designed structures are fabricated for the
experimental demonstration of the bianisotropic properties. The measured
results match with the desired asymmetric wave scattering fields.
