Nonreciprocal wave transmission through an extended discrete nonlinear Schrödinger dimer

We analyze a one-dimensional extended discrete nonlinear Schrödinger (DNLS) dimer model for nonreciprocal wave transmission. The extension corresponds to the addition of a nonlocal or intersite nonlinear response in addition to a purely cubic local (on-site) nonlinear response, which refines the purely cubic model and aligns to more realistic situations. We observe that a diodelike action persists in the extended case; however, the inclusion of nonlocal response tends to reduce the diode action. We show that this extension results in achieving the diode effect at lower incoming intensities as compared to the purely cubic case. We also report that a nearly perfect diode action is possible in the extended case for a higher level of asymmetry between on-site potentials than its cubic counterpart. Moreover, we vary different site-dependent parameters to probe for regimes of a better diode effect within this extended model. We also present the corresponding stability analysis for the exact stationary solutions to the extended DNLS equation, we discuss the bifurcation behavior in detail, and we explicitly give the regions of stability.