Revolution analysis of three-dimensional arbitrary cloaks

TL;DR

This paper extends the design of 3D invisibility cloaks with revolution surfaces using transformation optics, deriving transformation matrices and validating the approach with finite element computations.

Contribution

It introduces a new class of 3D cloaks with revolution surfaces and provides explicit transformation matrix expressions, including eigenvalue analysis.

Findings

Eigenvalues of the transformation matrix vanish at the inner boundary.

Finite element simulations confirm the validity of the cloak design.

The approach applies to non-convex cloaks of varying thickness.

Abstract

We extend the design of radially symmetric three-dimensional invisibility cloaks through transformation optics to cloaks with a surface of revolution. We derive the expression of the transformation matrix and show that one of its eigenvalues vanishes on the inner boundary of the cloaks, while the other two remain strictly positive and bounded. The validity of our approach is confirmed by finite edge-elements computations for a non-convex cloak of varying thickness.