Ultra-short pulses are characterized by short time durations, rich spectra, and high peak power, which enables their extensive applications in areas such as high-field laser physics, micro-nano manipulation, spectral detection, and precision cutting [[1], [2], [3]]. Ultra-short vortex pulses, which combine the benefits of ultra-short pulses with vortex beam, can provide novel approaches for exploring and applying novel physical mechanisms in fields such as high-field laser physics and high-energy density physics [4,5]. Notable applications include vortex particle beam acceleration, ultra-strong terahertz vortices, and vortex high-harmonic generation [[6], [7], [8]]. However, due to the ultra-high peak power and wide bandwidth of ultra-short pulses, directly converting them into vortex modes requires devices with high damage thresholds and low topological charge dispersion [[9], [10], [11]], which limits the development of terawatt (TW) and even petawatt (PW) vortex laser systems and seriously hinders experimental validation and applications of these new physical mechanisms.

In conventional vortex mode converters, spiral phase plates (SPP) [12] have high damage thresholds, low losses, and high conversion efficiency, but require chromatic dispersion compensation designs to address the broad bandwidth of ultra-short pulses. Holographic gratings [13] can provide good dispersion compensation but have complex optical paths and low conversion efficiency. Axially symmetric polarizers [14] can generate high-quality vortex pulses over a wide bandwidth but have low damage thresholds. Diffractive vortex gratings [15] have compact structures and good dispersion compensation, but the component structure is complex and difficult to fabricate. Vortex multi-aperture plates [16] are suitable for broad bandwidth pulses but have low conversion efficiency. Vortex conversion schemes based on Sagnac interferometers [17] are not limited by spectral bandwidth and have high damage thresholds, but can only generate vortices with topological charges of ±1. Fortunately, metasurfaces can flexibly manipulate the amplitude, phase, and polarization of light fields by altering the structural parameters and spatial distribution of their meta-atoms. Metasurfaces are two-dimensional antenna arrays composed of artificially designed subwavelength units [[18], [19], [20]]. With the rapid development of computer technology and micro-nano manufacturing techniques, metasurfaces have been applied in various optical fields, including structured light generation, metalenses, holographic displays, nanolithography, and quantum communication [[21], [22], [23], [24], [25]].Particularly, dielectric metasurfaces have garnered significant attention due to their high damage threshold and low topological charge dispersion [[26], [27], [28]].

The traditional design of metasurfaces often involves extensive trial-and-error simulations, leading to low design efficiency. Consequently, the use of intelligent algorithms for optimization has become a popular approach. Among these, Particle Swarm Optimization (PSO) stands out for its simplicity and ease of implementation, garnering significant attention in the design of metasurfaces. Chengtian Song et al. introduced the PSO algorithm to optimize the phase distribution on metasurface emitter arrays, further reducing the sidelobe level [29]. Ali Lalbakhsh et al. used the PSO algorithm to design a near-field delay equalizer metasurface to improve the directionality and radiation pattern of classic electromagnetic bandgap resonator antennas [30]. Jonathan R. Thompson et al. applied the PSO algorithm to discover different broadband reflector designs, each with its own performance advantages, including ultra-wideband reflection and polarization independence [31]. However, applications of the PSO algorithm for optimizing metasurfaces that generate high-purity ultrashort vortex pulses remain limited. The Starlight-III device [32] is the world's first multi-functional laser system that synchronously outputs pulses with zero jitter, in three different pulse durations: nanoseconds, picoseconds, and femtoseconds, as well as three wavelengths: 527 nm, 1053 nm, and 800 nm. Its diverse physical experimental requirements and the trend of actively controlling the light field on target have also provided a driving force for the development and application of ultrahigh peak power ultrashort vortex pulse technology based on the Starlight-III device. Considering the ultrashort pulses with a central wavelength of 800 nm and a spectral bandwidth of 100 nm produced by the Starlight-III device, we have selected a design bandwidth of 750 nm–850 nm, aiming to convert the injected gaussian pulse into a vortex mode in the front end of the ultrashort pulse device.

In this paper, we propose a metasurface based on the PSO algorithm that can convert ultrashort gaussian pulses into high-purity ultrashort vortex pulses, operating over a broadband wavelength range of 750 nm–850nm. Finite-Difference Time-Domain (FDTD) simulation results demonstrate that the phase and electric field distributions of the ultrashort vortex pulses generated by the metasurface are in excellent agreement with the expected results. The designed metasurfaces with topological charges l = 2 and l = 10 exhibit high purity and good robustness within a 100 nm bandwidth.