Multiaxial super-geometric mode laser.

Structured light was usually studied by two-dimensional (2D) transverse eigenmodes. Recently, the three-dimensional (3D) geometric modes as coherent superposed states of eigenmodes opened new topological indices to shape light, that optical vortices can be coupled on multiaxial geometric rays, but only limited to azimuthal vortex charge. Here, we propose a new structured light family, multiaxial super-geometric modes, enabling full radial and azimuthal indices coupled to multiaxial rays, and they can be directly generated from a laser cavity. Exploiting combined intra- and extra-cavity astigmatic mode conversions, we experimentally verify the versatile tunability of complex orbital angular momentum and SU(2) geometry beyond the limit of prior multiaxial geometric modes, opening new dimensions to revolutionize applications such as optical trapping, manufacturing, and communications.