  Mechanical motion can break the symmetry in which sound travels in a medium,
but significant non-reciprocity is typically achieved only for very large
motion speeds. Here we combine moving media with zero-index acoustic
propagation, yielding extreme non-reciprocity and induced bianisotropy for
modest applied speeds. The metamaterial is formed by an array of waveguides
loaded by Helmholtz resonators, and it exhibits opposite signs of the
refractive index sustained by asymmetric Willis coupling for propagation in
opposite directions. We use this response to design a non-reciprocal acoustic
lens focusing only when excitation from one side, with applications for imaging
and ultrasound technology.
