Second harmonic generation of laser beams in transverse mode locking states

Nonlinear frequency conversion of structured beams has been of great interest recently.We present an intracavity second harmonic generation(SHG)of laser beams in transverse mode locking(TML)states with a specially designed sandwich such as a microchip laser.The intracavity nonlinear frequency conversion process of a laser beam in a TML state to its second harmonic is theoretically and experimentally investigated,considering different relative phase and weight parameters between the basic modes in the TML beam.Comparison between the far-field SHG beam patterns of fundamental frequency transverse modes in coherently locked and incoherently superposed states demonstrates that the SHG of TML beams can carry more information.Various rarely observed far-field SHG beam patterns are obtained,and they are consistent with the theoretical analysis and numerical simulations.With the obtained SHG beams,the characteristics of the structured fundamental frequency beams can also be conversely investigated or predicted.This work may have important applications in optical 3D printing,optical trapping of particles,and free-space optical communication areas.