Fig. 1 Section of the refractive index profile in the radial direction for (a) a straight fiber and (b) a bent fiber using conformal mapping. The horizontal red line corresponds to the fundamental mode’s effective mode index. The blue curve illustrates its intensity distribution.

Fig. 2 (a) Difference of transmission spectra of the investigated fiber with and without a bend around a mandrel yielding an LP₁₁ mode cut-off at λ_c = 1209 nm. (b) The reflection spectrum from the fiber Bragg grating with peaks at λ_LP01 = 1079.86 nm and λ_LP11 = 1077.96 nm. Additionally the plots include (blue) the material refractive indices n_core, n_clad including dispersion [28], as well as the effective mode indices n_LP01, n_LP11, and (black) the Bragg condition Eq. (9).

Fig. 3 Hologram illumination with pure modes and resulting correlation signals for the LP₀₁, LP_11e, and LP_11o modes (dots and arrows mark the position of the intensity signals I_LP01, I_LP11e, and I_LP11o being proportional to the mode powers ${\rho }_{{\text{LP}}_{01}}^2$, ${\rho }_{{\text{LP}}_{11\text{e}}}^2$, and ${\rho }_{{\text{LP}}_{11\text{o}}}^2$). (a) Measured near field of a pure LP₀₁ mode beam. (b) Corresponding measured correlation signals. (c) Simulation of the diffraction of a LP₀₁ mode beam illuminating a hologram encoding the LP_11e mode only, and propagation through a 2f -setup. (d) Measured near field of a pure LP_11e mode beam. (e) Corresponding measured correlation signals. (f) Simulation of the diffraction of a LP_11e mode beam illuminating a hologram encoding the LP_11e mode only, and propagation through a 2f -setup. Intensities are normalized.

Fig. 4 Experimental setup. (a) LS - laser source, MO_1,2 - microscope objectives, D_B -bending diameter, P - polarizer, L_1,2 - lenses, BS - beam splitter, CGH - computer-generated hologram, CCD_1,2 - cameras. (b) Scheme of the metal plate with half-circle grooves. (c) Scheme of the fiber coiled around a mandrel with a stable loop at the end.

Fig. 5 Relative modal powers as a function of bending diameter D_B (dashed lines to guide the eye). The mode intensity distributions are depicted on the right for the straight and bent fiber (D_B = 1.5cm, bending in x-z-plane with bending center in direction of −x). The corresponding measured beam intensities (CCD₁ in Fig. 4) as a function of bending diameter are shown in Media 1.

Fig. 6 Modal power loss 2α as a function of bending diameter D_B for (a) the fundamental mode LP₀₁ and (b) the higher-order modes LP_11e and LP_11o. (CGH) modal decomposition measurements, (FEM) rigorous loss simulations by FEM, (ana) analytically calculated loss after Eq. (6).