Infrared beam-splitting transmission gratings that utilize anisotropic
ally etched v-grooves on silicon wafers are proposed. With scalar diff
raction theory to find the amplitudes of the different diffraction ord
ers, a numerical search is used to find optimum designs for 1:3, 1:5,
and 1:7 splitters with efficiencies greater than 70% with a standard d
eviation in intensity of no more than 7%.