## 1 Introduction  
The use of optical fibers with a core having a few spatial propagation modes is a promising possibility of spatial division-multiplexing (SDM) to increase the transmission information rate of optical communications in order to meet future traffic demands [1, 2]. Ideally, SDM must be orthogonal to polarization multiplexing and wavelength division multiplexing currently used, that is, each spatial mode must contain both polarizations and many wavelength channels spanning a few tens of nanometers in the spectrum. However, the crosstalk due to random mode mixing during the propagation along the fiber is an issue. It can be compensated by coherent detection and extensive use of multi-input-multiple-output (MIMO) digital signal processing (DSP) [3], although this solution requires carefully designed FMFs to obtain a low modal differential group delay. A more recent approach that is valid for short propagation distances is the use of elliptical core (EC) few mode fibers (FMF). These fibers not only significantly reduce crosstalk between both polarizations of the same mode (polarization maintaining) but also within the same spatial mode group, such as LP\({}_{11a}\) and LP\({}_{11b}\), since they are no longer degenerate. Therefore, MIMO and DSP can be removed from the detection stage. This solution has been proposed to improve the cabling footprint, bandwidth and link length of internal communications in data centers, while avoiding expensive and power-consuming detectors [4; 5; 6]. As MIMO is not present in these systems, a low mode crosstalk is also mandatory in mode (de)multiplexers. Multiplexing can be carried out in multiple ways, for instance by beam-splitters [7], Bragg gratings [8], directional couplers [9], photonic lanterns [10], multiplane light converters [11], or Mach-Zehnder interferometers (MZI) including Dove prisms to rotate the modes [12], a mirror image inverter [13], a refractive inverter [14] or a refractive Gouy's phase retarder [15]. However, most of these methods have drawbacks for this application as shown in Table 1. Beam-splitters introduce high losses, the launched power being inversely proportional to the number of modes. Bragg gratings are wavelength sensitive. Directional couplers need 3D structures which are difficult to fabricate, or include mode rotators that are wavelength sensitive. Photonic lanterns currently have a notable crosstalk (around \(-6.5\) dB) Multiplane light conversion uses a complex phase plate which is difficult to design and fabricate; when implemented with a spatial light modulator, each polarization must be processed apart. Moreover, very large spectral ranges seem challenging to achieve with a diffractive method. Finally, multiplexers based on MZI are vibration-sensitive, difficult to align and bulky since they often need almost as many interferometers as modes to be multiplexed; besides, those based on reflections are polarization sensitive. In this work, we propose a new interferometric spatial mode (de)multiplexer for FMF. Besides the optical criteria (low light losses, achromatism, low crosstalk...), we also pay attention to other ones, such as number of elements, robustness, compactness and cost, in order to obtain a more attractive design for a practical use. On the contrary, we do not deal the issue of coupling efficiency of the modes to the fibres [16; 17]. In Section 2, we present a modified Michelson interferometer with a mirror image inverter to demultiplex two spatial modes. In comparison with its MZI counterpart [13], it comprises less elements, it is monolithic and easier to align and especially it can manage both polarizations simultaneously in a no possible way with MZI. The modes coming from a fiber must be collimated before entering in the interferometer. The collimating system is dealt in Section 3 where we show that its focal length is fixed by the size of the interferometer. Next, in Section 4, the interferometer is used as a multiplexer adding a binary phase plate in one of its ports.