  We show that the simultaneous modulation of the propagation constant and of
the gain/loss coefficient along the multimode fibers results in unidirectional
coupling among the modes, which, depending on the modulation parameters, leads
to the enhancement or reduction of the excitation of higher order transverse
modes. In the latter case, effective mode-cleaning is predicted, in ideal case
resulting in single-mode spatially coherent output. The effect is
semi-analytically predicted on a simplified Gaussian beam approximation and
numerically proven by solving the wave propagation equation introducing the
modulated potential.
