  Assuming weakly guiding approximation, we examine orbital angular momentum
(OAM) mode mixing on account of ellipticity in a fiber and derive a complete
set of analytic expressions for spatial crosstalk, using scalar perturbation
theory that incorporates fully the existing degeneracy between a spatial OAM
mode and its degenerate partner characterized by a topological charge of
opposite sign. These expressions, consequently, include an explicit formula for
calculating the 2 pi walk-off length over which an input OAM mode converts into
its degenerate partner, and back into itself. We further explore the
applicability of the derived expressions in the presence of spin-orbit
interaction. The expressions constitute a useful mathematical tool in the
analysis and design of fibers for spatially-multiplexed mode transmissions.
Their utility is demonstrated with application to a few mode and a multimode
step-index fiber.
