Short period undulators are an essential component of a compact free electron laser (FEL) and medium energy storage rings for the production of hard X-rays. The use of ReBCO high temperature superconductors (HTS) in a staggered array undulator geometry is expected to yield a magnetic undulator flux density above 2 T for a 10 mm period and a 4 mm magnetic gap, thus substantially increasing the lasing performance of existing FEL and storage ring facilities.The optimization of the design for a staggered array undulator with FEM simulations and a critical analysis of its working principles are discussed in this paper. Specifically, the maximization of the undulator field and the minimization of the required HTS material are the two main objectives of this study, which is performed with realistic material parameters of commercially available bulks materials.Finally, the outcome of the applied optimization technique is discussed and the intrinsic limits of this undulator geometry are highlighted.