Magic ratio of window width to grating period for van der Waals potential measurements using material gratings

We report improved precision measurements of the van der Waals potential strength (C-3) for Na atoms and a silicon-nitride (SiNx) surface. We studied diffraction from nanofabricated gratings with a particular magic open fraction that allows us to determine C-3 without the need for separate measurements of the width of the grating openings. Therefore, finding the magic open fraction improves the precision of C-3 measurements. The same effect is demonstrated for a grating with an arbitrary open fraction by rotating it to a particular magic angle, yielding C-3=3.42 +/- 0.19 eV angstrom(3) for Na and a SiNx surface. This precision is sufficient to detect a change in C-3 due to a thin metal coating on the grating surface. We discuss the contribution to C-3 of core electrons and edge effects.