Physics – Optics
Scientific paper
2008-05-31
New Jour. Phys. 10 (2008) 115024
Physics
Optics
43 pages, 7 figures; revised per referees' comments; new references and figures
Scientific paper
10.1088/1367-2630/10/11/115024
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 {\sl isotropic and nonsingular} parameters that give {\sl 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. For the frequencies or energies corresponding to the Neumann eigenvalues of the cloaked region, the ideal cloak supports trapped states; near these energies, an approximate cloak supports {\sl almost trapped states}. This is in fact a useful feature, and we conclude by giving several quantum mechanical applications.
Greenleaf Allan
Kurylev Yaroslav
Lassas Matti
Uhlmann Gunther
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