Beam splitting of a double-groove fused-silica grating under normal incidence

Double-groove fused-silica gratings for 1 x 5 and 1 x 7 TE-polarization beam splitting under normal incidence are studied. The grating profiles are optimized by use of the rigorous coupled-wave analysis (RCWA) and the simulated annealing (SA) algorithm. The average diffraction efficiencies of the two gratings are both more than 95% with uniformity of better than 2%. The diffraction efficiencies of these gratings are approximately 15% more than the conventional Dammann gratings. The physical understanding of the diffraction behaviors taking place inside the beam splitter gratings is presented by the modal method. The mode eigenvalue equation of the double-groove grating is derived theoretically. The eigenmodes of 1 x 5 and 1 x 7 TE-polarization beam splitter gratings are obtained from the eigenvalue equation. Then, we calculate the overlap integral and modal propagation constants. We also present the mode profiles of the propagating modes for TE polarization. The proposed method of analyzing beam splitters under normal incidence should be helpful for developing new double-groove grating-based devices.