We propose a new light management mechanism in graded index (GRIN) multimode fibers (MMFs) that allow to control the spectral mode distribution of the propagated beam. The effect is achieved through longitudinal non-Hermitian modulations of the complex refractive index, i.e. the refraction index (for instance, a modulation of the core radius) and a periodic gain/loss profile. The applied potential holding a longitudinal spatial period close to the intermodal beat frequency of the parabolic index profile, to strongly influence the transverse mode dynamics. The non-Hermitian potential introduces a unidirectional and controllable coupling between the transverse modes. In turn, the spatial shift between the real and imaginary components of the modulation controls the unidirectional coupling either to higher or lower order modes. The effect is simultaneously demonstrated by solving a (2+1) D Linear Schrodinger Equation (two transverse plus one longitudinal spatial coordinates) as well as it is predicted by a simplified model for an oscillating Gaussian beam ansatz, leading to a system of ordinary differential equations. We demonstrate, both analytically and numerically, a mode cleaning effect, i.e. the improvement of the spatial structure of light in its propagation along the modulated MMFs; in an ideal case resulting in single-mode spatially coherent output. On the contrary, when inducing the coupling towards higher order modes, pulsing is enhanced, which may eventually contribute to super-continuum generation. The proposed scheme could lead to actual applications as it could be experimentally realized within the current nanofabrication technologies.
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