Polarization-Induced Interaction as a Perturbation within Orbital Angular Momentum(OAM) Modes of an Optical Fiber

We investigate the role of polarization effects in orbital angular momentum modes of an optical fiber. Specifically, we revisit the removal of the degeneracy of the $HE$ and the $EH$ vector modes that exists within the weakly guiding approximation (WGA); within WGA, these two vector modes coalesce into a single spatial (scalar) orbital angular momentum (OAM) mode, defined by a common topological charge and associated with left or right circular polarization. While the polarization term of the vector wave equation acting as a Hermitian perturbation operator accounts for the splitting of the $HE$ and the $EH$ vector modes, its extension to explain the accompanying field correction, called the polarization-induced field, encounters hurdles; this field is characterized by a topological charge differing by two in magnitude. The problems are critically examined with a possible remedy and its implications.