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We consider the asymmetric transmission properties of a Discrete NonlinearSchr{\"o}dinger type dimer with a saturable nonlinear intersite couplingbetween the dimer sites, in addition to a cubic onsite nonlinearity andasymmetric linear onsite potentials. In contrast to previously studied caseswith pure onsite nonlinearities, the transmission coefficient for stationarytransmission is shown to be a multivalued function of the transmittedintensity, in regimes of low saturability and small or moderate transmittedintensity. The corresponding backward transfer map is analyzed analytically andnumerically, and shown to have either one or three distinct solutions forsaturable coupling, and zero or two solutions for the purely cubic nonlinearcoupling. As saturation strength is increased, the multi-solution regimesdisappear through bifurcations and the single-valued regime of the onsite modelis recovered. The existence of multiple solution branches yields novelmechanisms for asymmetric left/right stationary transmission: in addition toshifts of the positions of transmission peaks, peaks for transmission in onedirection may correspond to nonexistence of stationary solutions propagating inthe opposite direction, at the corresponding branch and transmitted intensity.Moreover, one of these transmission channels behaves as a nearly perfect mirrorfor incoming signals. The linear stability of the stationary solutions isanalyzed, and instabilities are typically observed, and illustrated by directnumerical simulations, in regimes with large transmission coefficient.Intersite nonlinearities are found to prevent the formation of a localizeddimer mode in the instability-induced dynamics. Finally, the partial reflectionand transmission of a Gaussian excitation is studied, and the asymmetrictransmission properties are compared to previously studied onsite models.

Multichannel asymmetric transmission through a dimer defect with saturable inter-site nonlinearity