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.
Recently, the transverse mode locking (TML) effect has been attracting increasing attention, due to its possible use to generate various beam patterns possessing optical vortices. The TML effect is mostly focused on the laser physics area to investigate beam pattern formation and temporal dynamics.1–6 At the same time, with the wide attention of laser technology scientists, research on extended properties of TML laser beams is a new direction for the laser technology field. Currently, TML is studied with solid state lasers such as microchip cavities,7 diode lasers such as vertical-cavity surface-emitting lasers (VCSELs),8,9 and fiber lasers for both temporal and spatial mode locking.10 For the solid-state microchip lasers and VCSELs, single longitudinal mode operation of the TML mode can be achieved for quite short cavity lengths and the consequent large longitudinal frequency spacing. These two types of cavities share quite similar outputs of TML beam patterns under large Fresnel number pumping conditions. So far, the investigations of the TML effect are limited to the fundamental frequency of the laser cavity. Its nonlinear frequency conversion phenomenon was rarely reported.