Generation and expansion of Laguerre–Gaussian beams

Laguerre–Gaussian (LG) beams are typical vortex beams with orbital angular momentum (OAM), spiral wavefront phase, and donut-shaped intensity distribution. They are widely used in micro-manipulation, super-resolution microscopy, communication, gravitational wave detection and other fields. LG beam generation methods include passive and active methods. The passive methods are to modulate the Gaussian beams into LG beams outside the resonator through the phase elements; the active methods are to directly excite the high-order transverse modes in the resonant cavity to obtain LG beams. In addition, researchers have also conducted extensive research on the expansion of LG beam parameters in time and frequency domain in recent years. In time domain, optical elements, Q-switched and mode-locked techniques are mainly used to obtain LG pulses with high peak power and short pulse width; in frequency domain, second harmonic generation (SHG), sum-frequency generation (SFG) and optical parametric oscillation (OPO) are mainly used to broaden the spectral range of LG beams. This paper reviews the generation methods of LG beams and the expansion research of LG beam parameters in time and frequency domain, summarizes the LG-mode characteristics obtained by each method, and looks forward to the development trend of LG beams.