Abstract
We propose to use morphing algorithms to deduce some approximate wave pictures of scattering by cylindrical invisibility cloaks of various shapes deduced from the exact computation (e.g. using a finite element method) of scattering by cloaks of two given shapes, say circular and elliptic ones, thereafter called the source and destination images. The error in L(2) norm between the exact and approximate solutions deduced via morphing from the source and destination images is typically less than 2 percent if control points are judiciously chosen. Our approach works equally well for rotators and concentrators, and also unveils some device which we call rotacon since it both rotates and concentrates electromagnetic fields. However, it breaks down for superscatterers (deduced from non-monotonic transforms): the error in L(2) norm is about 25 percent. We stress that our approach might greatly accelerate numerical studies of 2D and 3D cloaks.
Highlights
In the early 90’s, there was a very fashionable special effect called “morphing” which consisted in transforming an image into another with a succession of intermediate images
We propose to use morphing algorithms to deduce some approximate wave pictures of scattering by cylindrical invisibility cloaks of various shapes deduced from the exact computation of scattering by cloaks of two given shapes, say circular and elliptic ones, thereafter called the source and destination images
The error in L2 norm between the exact and approximate solutions deduced via morphing from the source and destination images is typically less than 1 percent if control points are judiciously chosen
Summary
In the early 90’s, there was a very fashionable special effect called “morphing” which consisted in transforming an image into another with a succession of intermediate images This computer graphic technique [1], notably used in the heroic fantasy movie Willow and the musical video clip Black or White of Michael Jackson is fairly underrated in other contexts, such as photonics.
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