The discovery that light beams with a helical phase front carry orbital angular momentum (OAM) has enabled applications in many fields ranging from optical manipulation to quantum information processing and, recently, free-space information transfer and communications. Here, a novel three-dimensional fabrication process by electron beam lithography was finely tuned in order to realize high-quality spiral phase plates (SPPs) for the generation of OAM-carrying optical beams. Single-and multi-step SPPs have been realized for the generation of high-order Laguerre-Gaussian beams with different values of topological charge and radial index. The optical response of these optical elements was experimentally investigated and compared with theoretical models.