In recent years, the Pr3+: YLF lasers pumped by blue laser diodes (LDs) have obtained significant progress due to the rich energy level spectrum of the praseodymium ions (Pr3+) in the visible wavelength band [[1], [2], [3]], which are widely used in medicine [4,5], display [6], laser machining [7,8], optical communication [9,10], biology [11] and so on. Meanwhile, with the development of structured light [12], the visible vortex beams demonstrate significant advantages in laser material processing [13], optical trapping [14,15] and optical communication [16], of which each photon carries the OAM of lћ [17]. Thus, the generation of vortex beams based on the Pr3+: YLF laser has attracted much attentions [18,19].

Currently, the generations of vortex beams in the Pr3+: YLF lasers are usually based on the off-axis pump [20], tilt imbalance [21], and annular pump [22], which have the compact resonant cavity structure and high beam quality comparing with the passive method by using spatial light modulator (SLM) [23], and digital micromirror device (DMD) [24] outside the cavity. However, these vortex Pr3+: YLF lasers typically output the vortex beam with OAM of ±1 [[20], [21], [22]]. Relatively speaking, the insertion of helical phase plates [25] and Q-plates [26,27] inside the cavity can achieve the vortex beams with larger OAM in the near-infrared and mid-infrared solid-state lasers, but the insertion of optical elements leads to the elongation of the cavity length, which is not favorable for the Pr3+: YLF laser with the shorter wavelengths. Because, the longer cavity structure, as well as the insertion of the Q-plate, will dramatically increase the loss of the resonator and raise the threshold of the laser, making it difficult to obtain laser output. Therefore, a more suitable and flexible method is needed for the generation of vortex beams from the Pr3+: YLF laser.

In this paper, we reported and demonstrated a blue LD-pumped Pr3+: YLF laser for the controlled generation of OAM-switchable vortex beams at 639 nm. To begin with, the quantitative tilt imbalance of the resonator was introduced to select the higher-order Hermite-Gaussian (HG) modes by utilizing the eigenvector method and introducing the concept of mode discriminant factor. Moreover, the mode converter, composed of two cylindrical mirrors, was applied to convert the HG modes into the Laguerre-Gaussian (LG) modes with the orbital angular momentum. Then, the OAM-switchable vortex beams can be obtained by tuning the quantitative tilt imbalance of the resonator.