Mathematical analysis of the two dimensional active exterior cloaking in the quasistatic regime

Details Mathematical analysis of the two dimensional active exterior cloaking in the quasistatic regime Mathematical analysis of the two dimensional active exterior cloaking in the quasistatic regime

2011-09-16

arxiv.org/abs/1109.3526v1

Physics

Mathematical Physics

submitted to Analysis and Mathematical Physics

Scientific paper

We design a device that generates fields canceling out a known probing field inside a region to be cloaked while generating very small fields far away from the device. The fields we consider satisfy the Laplace equation, but the approach remains valid in the quasistatic regime in a homogeneous medium. We start by relating the problem of designing an exterior cloak in the quasistatic regime to the classic problem of approximating a harmonic function with harmonic polynomials. An explicit polynomial solution to the problem was given earlier in [Phys. Rev. Lett. 103 (2009), 073901]. Here we show convergence of the device field to the field needed to perfectly cloak an object. The convergence region limits the size of the cloaked region, and the size and position of the device.

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