mmi 100 according to fig1 may be part of an integrated circuit which comprises further optical and or electronic components fig2 shows the refractive index n x of an mmi on the ordinate and a spatial coordinate x on the abscissa in a direction running substantially perpendicular to the direction of the supply waveguide 108 in the illustration selected in fig2 13 the spatial coordinate x is standardized to the geometrical width w of a previously known mmi with the refractive index n 0 x in this case fig2 illustrates the profile of the refractive index at least in one section of the region 112 of the mmi 100 in some embodiments of the invention the refractive index profile illustrated is established over the entire propagation direction y of the region 112 the curve designated a illustrates the profile of the refractive index n 0 x of a known mmi the refractive index profile according to a is constant in sections this means that a first refractive index n 0 2 6 in the example illustrated prevails in the region 112 of the mmi with the width w a material having a second refractive index 1 44 in the exemplary embodiment is arranged to the right and to the left of the region 112 the invention now proposes configuring the refractive index n x as illustrated in curve b the index profile optimized according to curve b has an alternating profile in the waveguide core the amplitude between minima and maxima being smallest in the center.