Mode-cleaning in antisymmetrically modulated non-Hermitian waveguides

We demonstrate all-optical spatial mode-cleaning in non-Hermitian waveguides. The effect is accounted by a unidirectional coupling among the modes resulting from a simultaneous modulation of the refractive index and the gain/loss along graded index multimodal waveguides. Depending on the spatial delay between the real and imaginary part of the potential modulation, higher or lower order modes are favored, which in latter case eventually leads to an nearly-monomode propagation. In this way, for any arbitrary initial field distribution an antisymmetric non-Hermitian modulation results in an effective mode-cleaning. The effect is demonstrated analytically, based on coupled mode theory in 1D waveguides, and numerically proven by solving the wave propagation equation with the antisymmetric non-Hermitian potential. The proposal is also generalized to the more involved case of 2D waveguides, leading to a significant reduction of the beam quality factor and improvement of beam spatial quality.