Cloaking and anamorphism for light and mass diffusion
arXiv:1701.03090 · doi:10.1088/2040-8986/aa7df8
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.
42 pages, Latex, 14 figures. V2: Major changes : some formulas corrected, some extra cases added, overall length extended from 21 pages (V1) to 42 pages (present version V2). The last version will appear at Journal of Optics
References in corpus (16)
- Achieving transparency with plasmonic coatings
- Hiding Under the Carpet: a New Strategy for Cloaking
- Illusion optics: The optical transformation of an object into another object
- Silicon nanostructure cloak operating at optical frequencies
- Acoustic cloaking theory
- Cloaking of Matter Waves
- Achieving control of in-plane elastic waves
- Electromagnetic wormholes and virtual magnetic monopoles
- Hyperelastic cloaking theory: Transformation elasticity with pre-stressed solids
- Controlling solid elastic waves with spherical cloaks
- Transformation seismology: composite soil lenses for steering surface elastic Rayleigh waves
- Scattering problems in elastodynamics
- Non-singular cloaks allow mimesis
- Transformation Optics, Generalized Cloaking and Superlenses
- Theory of diffusive light scattering cancellation cloaking
- Enhanced propagation of photon density waves in random amplifying media