A beam-splitting reflection grating

A metallic grating made of triangular grooves filled with penetrable material is considered. A plane wave normally incident and polarized perpendicular to the grooves produces three plane waves, one backreflected and two obliquely reflected, for certain ratios between groove dimensions and wavelength. This geometrical optics solution is exact. In particular, if the material filling the grooves is isorefractive to the surrounding medium, then the backreflected field is zero.