Generation of vector Bessel beams with diffractive phase elements based on the Jacobi-Anger expansion.

We report the design and optimization of a diffractive phase element whose phase modulation is derived from the Jacobi-Anger relation, which allows the simultaneous generation of multiple scalar Bessel beams of different integer orders. In addition, by the appropriate treatment of a couple of such Bessel beams, we generate a vector Bessel beam of arbitrary order m. This beam is constructed by the collinear superposition of the scalar Bessel beam modes of orders m-1 and m+1, with circular orthogonal polarizations. We demonstrate experimentally both the simultaneous generation of the multiple scalar Bessel beams and the generation of vector Bessel beams of orders m=0 and m=1. These tasks are performed in an optical setup based on a pixelated liquid-crystal spatial light modulator.