Phase gratings to couple several input beams into one output beam

Phase gratings with certain continuous grating profiles are shown to be excellent devices for beam coupling, that means to couple N input beams into a single output beam. These gratings are also known as N-to-one-interconnection gratings. We prove in this paper that if the relative phases of the incoming beams are chosen properly coupling efficiencies over 90% are achieved. Only thin phase-only gratings are considered. The input angles of the incoming waves may be freely chosen. The effects of noise in phases and in grating profiles are also numerically calculated and discussed.