# Cloaking and anamorphism for light and mass diffusion

## TL;DR

This paper explores how transformation optics can be used to create cloaking effects for diffusive light and mass, demonstrating numerical methods and proposing new designs for external cloaks with spatially varying parameters.

## Contribution

It extends transformation optics to diffusive regimes, introduces a non-linear transform to address non-physical parameters, and explores cloaking in time domain and non-Euclidean geometries.

## Key findings

- Infinite objects of different shapes scatter diffusive light identically.
- A design for an external diffusion cloak with spatially varying parameters is proposed.
- Transformation methods can be applied to time-dependent diffusion equations.

## 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.