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

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 [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.

submitted to Analysis and Mathematical Physics

References in corpus (4)

• A complementary media invisibility cloak that can cloak objects at a distance outside the cloaking shell
• Notes on Conformal Invisibility Devices
• Solutions in folded geometries, and associated cloaking due to anomalous resonance
• Transformation elastodynamics and active exterior acoustic cloaking

Cited by in corpus (9)

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• Transformation elastodynamics and active exterior acoustic cloaking
• Active Thermal Cloaking and Mimicking
• Sensitivity analysis for active control of the Helmholtz equation
• Analytic Materials
• On Absence and Existence of the Anomalous Localized Resonance without the Quasi-static Approximation
• On quasi-Herglotz functions in one variable
• Active cloaking of finite defects for flexural waves in elastic plates
• Active cloaking of resonant coated inclusions for waves in membranes and Kirchhoff plates