Nearly non-scattering electromagnetic wave set and its application

Abstract

For any inhomogeneous compactly supported electromagnetic (EM) medium, it is shown that there exists an infinite set of linearly independent electromagnetic waves which generate nearly vanishing scattered wave fields. If the inhomogeneous medium is coated with a layer of properly chosen conducting medium, then the wave set is generated from the Maxwell-Herglotz approximation to the interior PEC or PMC eigenfunctions and depends only on the shape of the inhomogeneous medium. If no such a conducting coating is used, then the wave set is generated from the Maxwell-Herglotz approximation to the generalised interior transmission eigenfunctions and depends on both the content and the shape of the inhomogeneous medium. We characterise the nearly non-scattering wave sets in both cases with sharp estimates. The results can be used to give a conceptual design of a novel shadowless lamp. The crucial ingredient is to properly choose the source of the lamp so that nearly no shadow will be produced by the surgeons operating under the lamp.

18 pages, 1 figure

References in corpus (4)

• Acoustic cloaking theory
• Virtual reshaping and invisibility in obstacle scattering
• Mosco convergence for H(curl) spaces, higher integrability for Maxwell's equations, and stability in direct and inverse EM scattering problems
• Non-scattering wavenumbers and far field invisibility for a finite set of incident/scattering directions

Cited by in corpus (3)

• On vanishing and localizing of transmission eigenfunctions near singular points: a numerical study
• On local and global structures of transmission eigenfunctions and beyond
• Electromagnetic interior transmission eigenvalue problem for inhomogeneous media containing obstacles and its applications to near cloaking