Non-singular cloaks allow mimesis

Abstract

We design non-singular cloaks enabling objects to scatter waves like objects with smallersize and very different shapes. We consider the Schrödinger equation, which is valid, forexample, in the contexts of geometrical and quantum optics. More precisely, we introduce ageneralized non-singular transformation for star domains, and numerically demonstratethat an object of nearly any given shape surrounded by a given cloak scatterswaves in exactly the same way as a smaller object of another shape. When asource is located inside the cloak, it scatters waves as if it were located somedistance away from a small object. Moreover, the invisibility region actually hostsalmost trapped eigenstates. Mimetism is numerically shown to break down forthe quantified energies associated with confined modes. If we further allow fornon-isomorphic transformations, our approach leads to the design of quantumsuper-scatterers: a small size object surrounded by a quantum cloak describedby a negative anisotropic heterogeneous effective mass and a negative spatiallyvarying potential scatters matter waves like a larger nano-object of different shape.Potential applications might be, for instance, in quantum dots probing. The results inthis paper, as well as the corresponding derived constitutive tensors, are validfor cloaks with any arbitrary star-shaped boundary cross sections, although fornumerical simulations we use examples with piecewise linear or elliptic boundaries.