  Within the framework of perturbation theory, we explore in detail the mixing
of orbital angular momentum(OAM) modes due to a fiber bend in a step-index
multimode fiber. Using scalar wave equation, we develop a complete set of
analytic expressions for mode-mixing, including those for the $2\pi$ walk-off
length, which is the distance traveled within the bent fiber before an OAM mode
transforms into its negative topological charge counterpart, and back into
itself. The derived results provide insight into the nature of the bend
effects, clearly revealing the mathematical dependence on the bend radius and
the topological charge. We numerically simulate the theoretical results with
applications to a few-mode fiber and a multimode fiber, and calculate
bend-induced modal crosstalk with implications for mode-multiplexed systems.
The presented perturbation technique is general enough to be applicable to
other perturbations like ellipticity and easily extendable to other fibers with
step-index-like profile as in the ring fiber.
