Fig. 1: Illustration of mode attraction and rejection in multimode waveguides.

The input FS (FS_in) and input BCB (BCB_in) are launched at the two opposite ends of an optical fibre. a, b Mode attraction in single-mode isotropic optical fibres. In these fibres, the left and right circular polarisation states play the role of robust attractors. When the BCB is turned off (a), the mode content of the output FS (FS_out) mirrors the input one (right and left-circular polarisations have respectively relative powers P_r and P_l, where P_r and P_l are arbitrary and P_r + P_l = 100%). When the BCB is turned on and has a similar power to the FS (b), their nonlinear interaction modifies the mode content. If the input BCB is coupled to one circular polarisation mode (left circularly polarised in this example), then irrespective of the mode content of the input FS, the output FS is attracted to the mode of the input BCB (100% of the power in the left circularly polarised mode). c, d Mode rejection in multimode optical fibre. In this example the fibre supports 3 modes indicated with M₁,M₂,M₃. When the BCB is turned off (c), the mode content of the output FS mirrors the input one (relative power P₁ for mode M₁, P₂ for M₂ and P₃ for M₃, where P₁, P₂ and P₃ are arbitrary and P₁ + P₂ + P₃ = 100%). When the BCB is turned on and has a similar power to the FS (d), their nonlinear interaction modifies the mode content. If the input BCB is fully coupled to one spatial mode (M₁ in this example), then irrespective of the mode content of the input FS, the output FS rejects the mode of the input BCB (0% power in mode M₁). The specific amount of power on the remaining modes (P_2,out for M₂ and P_3,out for M₃, where P_2,out + P_3,out = 100%) depends on the system parameters.