Total angular momentum coherent state fields

Structured light fields exploit spin and orbital angular momentum for precision manipulation, advanced imaging, and high-capacity communication. We develop a paraxial modal framework that couples the circular polarization basis, a spin-1/2 representation of su(2), with finite-dimensional Laguerre-Gaussian modal subspaces at fixed order that carry spin-j representations. The Clebsch-Gordan decomposition of our product representation yields paraxial total angular momentum fields, and the action of an SU(2) rotation on the lowest-weight state of each subspace defines total angular momentum coherent state fields. A single complex parameter controls polarization and spatial structure jointly. Our fields propagate self-similarly, preserving their transverse polarization and spatial structure up to a scale factor. We present a proof-of-principle experiment to support the feasibility of our construction.