Design of Pauci-Adaptive, Spirally Tiled Mirrors for Large Size Optical Vortex Generation

We propose the optical design of an adaptive and flexible 4-quadrant, or N-facet, spirally tiled mirror setup, to generate an optical vortex on large diameter laser systems. From a far-field analysis, we derive the optimal angular parameters that generate the highest contents of the targeted Laguerre-Gaussian mode. The modal purities thus obtained are close to those obtained with standard segmented spiral phase plates or mirrors. The intensity behavior in the focal Rayleigh zone is regular, and the effect of a small laser astigmatism, known to break the circularity of the ring intensity profile at focus, can be corrected. This pauci-adaptive faceted mirror setup appears well suited for use on ultra-high intensity or high energy laser systems.