Orbital angular momentum coherent state beams

Paraxial propagation through isotropic, homogeneous, linear media exhibits invariance under rotations around the propagation axis, a symmetry described by the su(2) Lie algebra. We explore a family of paraxial beams that exploit this symmetry, constructed as linear superpositions of Laguerre-Gaussian beams (LGBs), serving as optical analogs of generalized SU(2) Lie group coherent states. A single complex parameter controls a smooth transition between Laguerre-Gaussian and Hermite-Gaussian beams (HGBs), producing intermediate beams that blend the characteristics of both families. Our beams exhibit propagation-invariant properties, up to a scaling factor, a highly desirable feature for optical applications. Experimental validation via digital holography demonstrates the practical feasibility of our approach.