We report for the first time the generation of optimized space‐invariant fan‐out elements, so‐called Dammann gratings [H. Dammann and K. Go¨rtler, Opt. Commun.3, 312 (1971)] in plasma silicon nitride. Diffraction efficiencies as high as 65% have been achieved. Using simulated annealing and the greedy algorithm, grating structures with fan‐out as large as 201×201 can readily be calculated. Low absorption and high optical quality together with its ease of structuring make silicon nitride an ideal medium for the construction of phase‐only optical elements.