  Fabricating patterned nanostructures with matter waves can help to realise
new nanophotonic devices. However, due to dispersion effects, designing
patterns with nanoscale features is challenging. Here, we consider the
propagation of a helium matter wave through different holes in hexagonal boron
nitride (h-BN) as a case study for the weakest dispersion interaction and the
matter wave's diffraction as it passes through the holes. We use a
quantum-mechanical model to calculate the polarisability of edge atoms around
the holes, where we observe polarization ripples of enhanced and reduced
polarisabilities around the holes. We use these values to calculate van der
Waals dispersion coefficients for the scattered helium atoms. We find that the
resulting diffraction patterns are affected by the shape and size of the holes,
where the smallest holes have a radius of just $6$~\AA. These results can be
used to predict the resolution limits of nano-hole patterns on nanophotonic
materials.
