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Novel fundamental notions helping in the interpretation of the complexdynamics of nonlinear systems are essential to our understanding and ability toexploit them. In this work we predict and demonstrate experimentally afundamental property of Kerr-nonlinear media, which we name mode rejection andtakes place when two intense counter-propagating beams interact in a multimodewaveguide. In stark contrast to mode attraction phenomena, mode rejection leadsto the selective suppression of a spatial mode in the forward beam, which iscontrolled via the counter-propagating backward beam. Starting from thisobservation we generalise the ideas of attraction and rejection in nonlinearmultimode systems of arbitrary dimension, which paves the way towards a moregeneral idea of all-optical mode control. These ideas represent universal toolsto explore novel dynamics and applications in a variety of optical andnon-optical nonlinear systems. Coherent beam combination inpolarization-maintaining multicore fibres is demonstrated as example.

Mode attraction, rejection and control in nonlinear multimode optics