  We combine two different fields, topological physics and graded metamaterials
to design a topological metasurface to control and redirect elastic waves. We
strategically design a two-dimensional crystalline perforated elastic plate,
using a square lattice, %consisting of bore holes, that hosts symmetry-induced
topological edge states. By concurrently allowing the elastic substrate to
spatially vary in depth, we are able to convert the incident slow wave into a
series of robust modes, with differing envelope modulations. This adiabatic
transition localises the incoming energy into a concentrated region where it
can then be damped or extracted. For larger transitions, different behaviour is
observed; the incoming energy propagates along the interface before being
partitioned into two disparate chiral beams. This "topological rainbow" effect
leverages two main concepts, namely the quantum valley-Hall effect and the
rainbow effect usually associated with electromagnetic metamaterials. The
topological rainbow effect transcends specific physical systems, hence, the
phenomena we describe can be transposed to other wave physics. Due to the
directional tunability of the elastic energy by geometry our results have
far-reaching implications for applications such as switches, filters and
energy-harvesters.
