Conservation laws of generalized angular momentum by second-harmonic generation in underdense plasmas harmonic generation

Light beams exhibit two intrinsic quantized degrees of freedom: spin angular momentum (SAM) and orbital angular momentum (OAM) whose manipulation enables precise control over the topological characteristics of electromagnetic fields. Recently, structured fields formed from a non-separable combination of SAM and OAM have attracted significant interest. These fields correspond to eigenstates of the generalized angular momentum (GAM), an operator merging SAM and OAM components which can yield remarkable fractional eigenvalues. The conservation of GAM, observed through harmonic generation, suggests its potential significance as a fundamental quantum number. In this work, we extend the analysis by examining its conservation laws through second- harmonic generation within an underdense, isotropic, and inhomogeneous plasma; a process governed by dipole-forbidden interaction which implies spin-orbit coupling. Our findings indicate that the symmetry and topological properties of the field are disrupted, leading to conservation of the GAM charge only on average. This symmetry breaking provides an easily detectable signature of the driving field’s topology.