Optical vortices are promising for increasing the bandwidth of optical communications by encoding information in the topological charge. For this purpose, it is essential to develop efficient and compact systems for generating and detecting vortex beams of different topological charges. We present the design and the theoretical and experimental analysis of a 2D liquid-crystal geometric-phase diffraction grating based on the optimal triplicator profile. The grating generates an array of 3x3 equi-energetic optical vortices of different integer topological charges and with the maximum theoretical diffraction efficiency. The performance of this grating as a vortex detector is demonstrated by illuminating it with vortex beams of different topological charges. In a recent work we mathematically proved a π/2 phase shift between the zero and the two lateral first diffraction orders generated by the optimal triplicator design. Here, we show the implications that this factor has in the polarization of the diffraction orders when the optimal triplicator is encoded as a geometric-phase element.