  Space Division Multiplexing (SMD) is a very attractive technique for
addressing the ever-growing demands in transmission capacity by enabling the
use of a new parameter \textemdash\ space \textemdash\ to increase the number
of channels in multi-mode fibers. One key component to build a spatially
multiplexed-based optical network is a spatial multiplexer and demultiplexer
combining signals from multiple single-mode fibers into as many channels in a
multi-mode fiber. In this article, we report the fabrication and
characterization of a pair of 45-mode spatial multiplexer and demultiplexer
saturating all the modes of a standard 50~$\mu$m core graded-index (OM2)
multi-mode fiber. The multiplexers are based on Multi-Plane Light Conversion
(MPLC), a technique that enables the control of the transverse shape of the
light by multiple reflections on specifically designed phase plates. We show
that by using a separable variable basis of modes, such as Hermite-Gaussian
(HG) modes, we are able to drastically reduce the number of reflections hence
reducing the insertion losses and modal crosstalks. The multiplexers typically
show an average 4~dB insertion loss and -28~dB cross-talk across the C band.
Finally, we emphasize the use of this higher-order modes multiplexer to explore
the propagation properties inside multi-mode fibers and more specifically the
mode group crosstalks as well as the impact of fiber bending.
