Laguerre-Gaussian Expansion of Step-Index Multimode Fiber Beams in Free-Space

We show that the complex conjugate of the overlap integrals between the fiber end-facet field and the Laguerre-Gaussian modes provides the expansion coefficients for the step-index multimode fiber beams. We also show that the fractional power in different azimuthal mode orders remains unchanged from fiber to free-space propagation.