  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.
