Using the symmetry properties of OAM modes for free space optical communication

Among the many properties of Orbital Angular Momentum (OAM) beams of light, one should mention the resilience under turbulent conditions. This feature has been exploited in the successful transmission of data using increasingly sophisticated encoding and decoding schemes. In this presentation, we use the language of Group Theory and focus on some OAM superpositions that show well-defined invariances with respect to reflections and rotations, and can be associated with subgroups of a large dihedral group. Based on numerical simulations, we use a selection of OAM superpositions that essentially look like light petals throughout the turbulent propagation and can be identified correctly despite some errors in the invariance tests. These ideas are extended to beams with nonuniform polarization such as vector vortex beams.