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We propose an all-optical control of the mode dynamics in GRaded INdex (GRIN) multimode waveguides, by a Non-Hermitian potential (simultaneous modulation of the refractive index and of the gain/loss coefficient). Such potential induces a unidirectional mode-coupling. Depending on the modulation parameters it yields to the enhancement/ reduction of the excitation of higher order transverse modes. In the latter case, this leads to an all-optical mode-cleaning. The proposal is supported by analytical predictions based on a coupled mode theory for 1D waveguides, which is numerically proven solving the wave propagation equation. The proposal is generalized to the more involved case of 2D waveguides for different geometries controlling the unidirectional mode-coupling and final beam shape.
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