Fig. 2. Laser concept.

a A 2D planar representation of the desired geometric mode, where the mode evolves from wave-like fringes (at z = 0 and ±z_R) to a ray-like trajectory. The means to create this mode in the cavity is illustrated in b, where completed oscillation orbits can be described by the direction states $∣+⟩$ and $∣-⟩$ (equivalently the sub-orbits shown in black and pink, respectively, in the dashed-line boxes), as well as paths originating from ray positions $∣1⟩$ and $∣2⟩$ (equivalently the sub-orbits shown in orange and green, respectively). c The planar mode is converted to the skewed version with a pair of cylindrical lenses. d A 3D schematic of a skewed (vortex) SU(2) geometric mode propagating in free space, with e experimental beam images shown at example propagation distances