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.
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