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While roton dispersion relations had been restricted to correlated quantumsystems at low temperature, recent works show the possibility of obtaining thisunusual dispersion in acoustic and elastic metamaterials. Such phenomenon hasbeen demonstrated in periodic structures by means of beyond-nearest-neighborinteractions, following the formulation firstly developed by Brillouin in the$'50s$. In this paper, we demonstrate both numerically and experimentally thatbeyond-nearest-neighbor connections are not a necessary condition to obtainthis unusual dispersion relation in elasticity. Leveraging the intrinsiccomplexity of elastic systems supporting different types of waves, wedemonstrate that mode locking can be applied to obtain roton dispersion,without the need of elastic or magnetic interactions between non nearestneighbors. Moreover, the combination of roton dispersion and rainbow physicsenables spatial separation of the energy fluxes with positive and negativegroup velocity.

Roton-like dispersion via polarisation change for elastic wave energy control in graded delay-lines