Role of propagating modes in a double-groove grating with a +1st-order diffraction angle larger than the substrate–air critical angle

Here we show, analytically and numerically, that in a TiO(2) double-groove grating with two different groove widths per period attached on the SiO(2) substrate, the normally incident light couples to the +1st-order transmission with 96.9% efficiency and with a 50° diffraction angle that is larger than the SiO(2)-air interface critical angle. Modal analysis reveals that three propagating modes for the +1st diffraction order reach the grating back end in phase, while the corresponding propagating modes for the -1st and zeroth orders are added destructively at the grating end. Four optical devices based on this grating characteristic are numerically demonstrated.