Two dimensional invisibility cloaking via transformation optics

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journalpeer-review

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Original languageEnglish
Pages (from-to)525-543
Journal / PublicationDiscrete and Continuous Dynamical Systems
Issue number2
Publication statusPublished - Oct 2011
Externally publishedYes


We investigate two-dimensional invisibility cloaking via transformation optics approach. The cloaking media possess much more singular parameters than those having been considered for three-dimensional cloaking in literature. Finite energy solutions for these cloaking devices are studied in appropriate weighted Sobolev spaces. We derive some crucial properties of the singularly weighted Sobolev spaces. The invisibility cloaking is then justified by decoupling the underlying singular PDEs into one problem in the cloaked region and the other one in the cloaking layer. We derive some completely novel characterizations of the finite energy solutions corresponding to the singular cloaking problems. Particularly, some 'hidden' boundary conditions on the cloaking interface are shown for the first time. We present our study for a very general system of PDEs, where the Helmholtz equation underlying acoustic cloaking is included as a special case. © 2021 American Institute of Mathematical Sciences

Research Area(s)

  • Finite energy solutions, Invisibility cloaking, Singularly weighted sobolev space, Transformation optics