Cloaking

Cloaking is the process of rending objects invisible to electromagnetic fields. This is done using anisotropic materials (built by homogenization) and work for a narrow band of wavelengths. Currently, optical wave invisibility is not possible, but invisibility to radar has been achieved.

Interestingly cloaking is in direct opposition to Compressed Sensing which is about finding ways of detecting hidden objects using randomized samples of wavelengths.

These are partial references...

these papers have anisotropic metrics
Dirichlet Neumann map for the wave equation
singular metrics
Uhlmann's web page
bulletin of ams review paper

Controlling Electromagnetic Fields J. B. Pendry, D. Schurig, D. R. Smith Science 23 June 2006: Vol. 312. no. 5781, pp. 1780 - 1782 [1]

Building the cloaking device requires anisotropic meta-materials, which can be constructed by homogenization using layers of materials, as in figure 1 of

Metamaterial Electromagnetic Cloak at Microwave Frequencies D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, D. R. Smith Science 10 November 2006: Vol. 314. no. 5801, pp. 977 - 980 [2]