Allan Greenleaf et al 2008 New J. Phys. 10 115024 doi:10.1088/1367-2630/10/11/115024
Isotropic transformation optics: approximate acoustic and quantum cloaking
Focus on Cloaking and Transformation OpticsAllan Greenleaf1,5,6, Yaroslav Kurylev2, Matti Lassas3 and Gunther Uhlmann4
Show affiliationsPart of Focus on Cloaking and Transformation Optics
Transformation optics constructions have allowed the design of electromagnetic, acoustic and quantum parameters that steer waves around a region without penetrating it, so that the region is hidden from external observations. The material parameters are anisotropic, and singular at the interface between the cloaked and uncloaked regions, making physical realization a challenge. We address this problem by showing how to construct isotropic and nonsingular parameters that give approximate cloaking to any desired degree of accuracy for electrostatic, acoustic and quantum waves. The techniques used here may be applicable to a wider range of transformation optics designs. For the Helmholtz equation, cloaking is possible outside a discrete set of frequencies or energies, namely the Neumann eigenvalues of the cloaked region. At these frequencies or energies the ideal cloak supports trapped states, vanishing outside of the cloaked region; near these energies, an approximate cloak supports almost trapped states. This is in fact a useful feature, and we conclude by giving several quantum mechanical applications.
- PACS
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43.20.Bi Mathematical theory of wave propagation
- Subjects
- Dates
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Issue 11 (November 2008)
Received 31 May 2008
Published 27 November 2008
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