Generation of high-order picosecond optical vortices up to the 17^th order from a mode-locked Hermite-Gaussian laser

Vortex beams, characterized by their helical phase front and orbital angular momentum, have attracted significant attention in recent research. Generating high-order ultrafast optical vortices in a mode-locked Hermite-Gaussian (HG) laser presents significant challenges due to the inherent contradiction between achieving high-order mode output and maintaining the mode-locking threshold. In achieving high-order mode locking with non-collinear pumping, increasing the non-collinear angle will reduce the pump threshold of the high-order mode and make it easy to output the high-order mode, but it will also increase the spot size and cause the mode-locking to fail. This study designed an asymmetric resonator structure to weaken the contradiction between high-order mode output and mode-locking and achieved 17^th-order mode output. Meanwhile, the properties of vortex beams were investigated in a laser diode (LD) non-collinear pumped Nd: YVO₄ passively mode-locked laser. By carefully controlling the non-collinear angle and mode-locking threshold, up to 17^th-order HG mode was achieved with a maximum average output power of 662 mW. The pulse width was 38.5 ps at a repetition rate of about 81.2 MHz. Subsequently, a cylindrical lens mode converter was used to convert the 1^st to the 17^th order HG modes into the corresponding Laguerre-Gaussian (LG) modes. To the best of our knowledge, this is the highest-order picosecond mode-locked vortex beam reported to date, which provides theoretical guidance for realizing high-order ultrafast optical vortices.