  The coupling feature of helical gratings (HGs) has been studied on flexible
conversion between two orbital angular momentum (OAM) modes by both the
transverse and longitudinal modulation of HGs. Apart from one to one OAM
exchange, HGs can achieve OAM transfer among multiple modes, provided both the
helix and phase matching conditions are well satisfied for successive coupling.
It is contributed from the fold number of modulation fringes of HGs and the
difference multiplication of propagation constants between two of the
successive modes. Based on the coupled mode theory, we investigate the mode
conversion and OAM transfer among three modes using a 3 fold HGs in a ring core
fiber, and numerically simulate it by transmission matrix. Our work about the
multiple modes transferring can be regarded as an extension of mode coupling
for optical gratings, and might flourish the mode conversion, as well as OAM
manipulation in optics fields.
