Overlap relation between free-space Laguerre Gaussian modes and step-index fiber modes.

We investigated the overlap relation of the free-space Laguerre-Gaussian modes to the corresponding linearly polarized modes of a step-index fiber. To maximize the overlap for an efficient coupling of the free-space modes into a fiber, the scale-dependent overlap was theoretically and experimentally determined. The presented studies pave the way for further improvement of free-space to fiber optical connections.