Second harmonic generation of laser beams in transverse mode locking states

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