Self-Cleaning in non-Hermitian Linear Multimode Fibers

We propose a self-cleaning mechanism in linear non-Hermitian graded index multimode fibers. The proposal is based a unidirectional coupling among transverse modes, induced by the introduction of a non-Hermitian potential, i.e. by the simultaneous modulation of the propagation constant and of the gain/loss coefficient along the fiber. The effect is semi-analytically predicted on a simplified Gaussian beam approximation and numerically proven by solving the wave propagation equation. As the main result, we demonstrate a substantial condensation of the radiation into the lowest order mode; resulting in a linear non-Hermitian self-cleaning. The demonstrated scheme could be experimentally realized within the current nanofabrication technologies.