Fig. 3: Results of the optimization of seven axially symmetric nanogratings to excite the fundamental mode in the individual cores of the MCF at different incident angles (λ0 = 1.55 μm).

a Angular distribution of the respective coupling efficiencies. Each colored curve corresponds to an optimized angle of incidence θ−1, i.e. a single grating. The vertical gray dashed lines indicate the respective target optimization angle. The black curve shows the distribution in the absence of a nanostructure. b Dependence of the numerically optimized geometric parameters (colored dots) on targeted incident angle θ−1 [blue: pitch (Λ), green: distance from the center of the first ring to the origin (r0), red: width of the rings (w)]. The solid lines were calculated using the expressions from steps 1 to 3 of the proposed optimization procedure (corresponding equations are Eqs. (3)–(5) and are given in the legend).