Asymmetric acoustic wave scattering by a nonreciprocal and position-dependent mass defect

We investigate the asymmetric wave scattering in a phononic one-dimensional lattice with a nonreciprocal defect and position dependent masses coupled by the defect spring. The nonreciprocal interaction is characterized by a single parameter Δ while the nonlinear contribution due to position-dependent masses are controlled by a parameterχ. The transmission and reflection coefficients are analytically computed and the effects of the nonreciprocity and nonlinearity are detailed. We show that, in opposite with the linear case, the rectification factor has a frequency dependence, which leads to a more efficient diode-like action at large wavevectors. Further, the nonlinearity leads to an asymmetry of the reflected component, absent in the linear regime. We extend our analysis to a system with frictional forces which suppresses the multistability window promoted by the nonlinear mass contribution without compromising the rectification action.