Numerical Simulation of an Optical Resonator for the Generation of Radial Laguerre–Gauss LGp0 Modes

The research on high-order transverse modes in lasers is a subject as old as the laser itself and has been largely abandoned. However, recently several studies have demonstrated an interest in using, instead of the usual Gaussian beam, a radial Laguerre–Gauss LGp0 beam, as, for instance, one can observe a strong improvement, for a given power, in the longitudinal and radial forces in optical tweezers illuminated by a LGp0 beam instead of the usual Gaussian beam. Since in most commercial lasers, the delivered laser beam is Gaussian, we therefore think it opportune to consider the problems of forcing a laser to oscillate individually on a higher-order transverse LGp0 mode. We propose a comprehensive analysis of the effects of an intra-cavity phase or amplitude mask on the fundamental mode of a plano-concave cavity. In particular, we discuss the best choice of parameters favouring the fundamental mode of a pure radial Laguerre–Gauss LGp0 model.