Total Angular Momentum Coherent State Fields

Structured light fields exploit spin and orbital angular momentum for precision manipulation, advanced imaging, and high-capacity communication. Orbital angular momentum coherent state beams interpolate between Hermite- and Laguerre-Gaussian beams, enabling continuous spatial control. We introduce a symmetry-based framework for joint control of polarization and spatial structure under the shared $su(2)$ Lie algebra of spin and orbital angular momentum. Within this structure, we construct total angular momentum fields as superpositions of circular polarization and Laguerre-Gaussian beams, and define their $su(2)$ coherent states within fixed-angular-momentum subspaces. A single complex parameter controls both polarization and spatial degrees of freedom, enabling continuous, symmetry-preserving tuning.