Title: Cloaking and anamorphism for light and mass diffusion,
Abstract: We first review classical results on cloaking and mirage effects for
electromagnetic waves. We then show that transformation optics allows the
masking of objects or produces mirages in diffusive regimes. In order to
achieve this, we consider the equation for diffusive photon density in
transformed coordinates, which is valid for diffusive light in scattering
media. More precisely, generalizing transformations for star domains introduced
in [Diatta and Guenneau, J. Opt. 13, 024012, 2011] for matter waves, we
numerically demonstrate that infinite conducting objects of different shapes
scatter diffusive light in exactly the same way. We also propose a design of
external light-diffusion cloak with spatially varying sign-shifting parameters
that hides a finite size scatterer outside the cloak. We next analyse
non-physical parameter in the transformed Fick's equation derived in [Guenneau
and Puvirajesinghe, R. Soc. Interface 10, 20130106, 2013], and propose to use a
non-linear transform that overcomes this problem. We finally investigate other
form invariant transformed diffusion-like equations in the time domain, and
touch upon conformal mappings and non-Euclidean cloaking applied to diffusion
processes.