# 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 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 Guevara Vasquez et al. (Phys Rev Lett 103:073901, 2009). 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Analysis and Mathematical Physics Springer Journals

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

, Volume 2 (3) – Apr 4, 2012
16 pages

/lp/springer-journals/mathematical-analysis-of-the-two-dimensional-active-exterior-cloaking-nT9Db8Y08X
Publisher
Springer Journals
Subject
Mathematics; Mathematical Methods in Physics; Analysis
ISSN
1664-2368
eISSN
1664-235X
DOI
10.1007/s13324-012-0031-8
Publisher site
See Article on Publisher Site

### Abstract

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 Guevara Vasquez et al. (Phys Rev Lett 103:073901, 2009). 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.

### Journal

Analysis and Mathematical PhysicsSpringer Journals

Published: Apr 4, 2012