Here we show, analytically and numerically, that in a ${\mathrm{TiO}}_2$ double-groove grating with two different groove widths per period attached on the ${\mathrm{SiO}}_2$ substrate, the normally incident light couples to the $+1$ st-order transmission with 96.9% efficiency and with a $50°$ diffraction angle that is larger than the ${\mathrm{SiO}}_2$ –air interface critical angle. Modal anal ysis reveals that three propagating modes for the $+1$ st diffraction order reach the grating back end in phase, while the corresponding propagating modes for the $-1$ st and zeroth orders are added destructively at the grating end. Four optical devices based on this grating characteristic are numerically demonstrated.