With the development of ultra-intense laser technology, the manipulation of relativistic laser pulses has become progressively challenging due to the limitations of damage thresholds for traditional optical devices. In recent years, the generation and manipulation of ultra-intense vortex laser pulses by plasma has attracted a great deal of attention. Here, we propose a new scheme to produce a relativistic vortex laser. This is achieved by using a relativistic Gaussian drive laser to irradiate a plasma binary phase square spiral zone plate (BPSSZP). Based on three-dimensional particle-in-cell (3D-PIC) simulations, we find that the drive laser has a phase difference of π after passing through the BPSSZP, ultimately generating the vortex laser with unique square symmetry. Quantitatively, by employing a drive laser pulse with intensity of 1.3 × 1018~W/cm2, a vortex laser with intensity up to 1.8 × 1019~W/cm2, and energy conversion efficiency of 18.61% can be obtained. The vortex lasers generated using the BPSSZP follow the modulo-4 transmutation rule when varying the topological charge of BPSSZP. Furthermore, the plasma-based BPSSZP has exhibited robustness and the ability to withstand multiple ultra-intense laser pulses. As the vortex laser generated via the BPSSZP has high intensity and large energy conversion efficiency, our scheme may hold potential applications in the community of laser-plasma, such as particles acceleration, intense high-order vortex harmonic generation, and vortex X/γ-ray sources.
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