Power scale-up and propagation evolution of structured laser beams concentrated on 3D Lissajous parametric surfaces

We systematically explore the power scale-up and propagation evolution of Lissajous structured beams in a lowly Nd-doped YVO₄ laser with the off-axis pumping scheme. We experimentally found that the average output power can be up to 1.0 W for the output transmission in the range of 1.8-10% at an incident pump power of 6.2 W. It is also found that when the output transmission is greater than 5%, the spatial coherence is considerably reduced to lead to a feature of broken Lissajous figures in transverse patterns. Moreover, transverse patterns varying with propagation direction are remarkably measured to manifest the 3D characteristics of Lissajous structured beams. We also employ the formula of coherent states to make a comparison with experimental observations and to reveal the transverse momentum density varying with propagation direction.