Analyzing coherent phonon mode conversion in gradient multilayers with atomistic wave-packet simulations

Atomistic phonon wave-packet simulations are used to investigate coherent phonon transmission and mode conversion in gradient multilayers (GMLs), in which locally periodic bilayer domains vary systematically in period size along the transport direction. We examine how coherent transport is affected by the number of distinct period sizes Ns, the number of repetitions Np of each period size, and the direction of the thickness gradient, with periodic superlattices (SLs) and random multilayers (RMLs) serving as limiting reference structures. The results show that GMLs exhibit coherent-transport characteristics intermediate between those of periodic SLs and RMLs. Increasing Ns progressively fragments the transmission spectrum and weakens or redistributes the reciprocal-space mode-conversion signatures, shifting the behavior toward that of randomized multilayers. Varying Np changes the spatial development of coherent modes: shorter locally periodic domains produce broader wavevector distributions, whereas longer domains permit more distinct, stepwise mode conversion associated with the local multilayer periodicity. In contrast, reversing an ascending GML to its descending counterpart produces only modest changes in transmission, consistent with reciprocal elastic transport. These results demonstrate that coherent phonon propagation in nonuniform multilayers is governed by the spatial organization and persistence of local periodicity rather than by gradient direction alone, and establish coherent mode conversion as a useful framework for understanding wave-like phonon transport in structurally complex multilayers.