Synopsis: Transformation optics by the slice

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Credit: B. Popa et al., Phys. Rev. A (2010)

Design of layered transformation-optics devices of arbitrary shape

Bogdan-Ioan Popa and Steven A. Cummer

Published September 30, 2010

The field of transformation optics, where optical materials are tailored to direct the trajectory of light, has led to astonishing devices previously thought to be impossible. Now, perfect lenses fabricated from flat pieces of material, invisibility cloaks, and illusion devices that make an object appear as something else, all appear feasible. The catch is that transformation optics designs, which call for inhomogeneous and anisotropic optical materials, are far ahead of what it is practical to fabricate.

In some cases, it is possible to make the desired optical device by simply layering materials. This approach works for building invisibility cloaks with a spherical geometry, where layering spherical shells of different materials and different thicknesses gives the desired result. Unfortunately, this type of layered design recipe is not available for transformation optics devices with other functionalities.

Writing in Physical Review A, Bogdan-Ioan Popa and Steven Cummer at Duke University in the US have now shown how general devices can be designed such that the material parameters have level sets of identical shape. This allows a convenient “by the slice” solution to device construction based on combining identically shaped layers, each with different, but homogeneous, material parameters. Their design methodology, which in most cases relies on solutions to the eikonal equation of optics, is general and can be applied to yield a layered design for any type of transformation device and geometry. – Mark Saffman

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