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This paper deals with phase gratings working in the paraxial domain. The profile of the optimum-efficiency beam multiplier with an arbitrary number of output diffraction orders is derived in an analytic form by exploiting methods from the calculus of variation. The output beams may be equi-intense or with arbitrary distribution of power. Numerical examples are given for different values of the number of output beams. Keywords—beam multipliers, diffractive optical elements, gratings, periodic structures.

The Optimum-efficiency Beam Multiplier for an Arbitrary Number of Output Beams and Power Distribution