Design Method for Electromagnetic Cloak with Arbitrary Shapes Based on Laplace's Equation

TL;DR

This paper presents a method to design electromagnetic cloaks of arbitrary shapes by solving Laplace's equation, enabling precise control of material parameters for complex cloaking geometries validated through simulations.

Contribution

The paper introduces a novel approach using Laplace's equation to design transformation media for electromagnetic cloaks with arbitrary shapes, including irregular geometries.

Findings

Analytical solutions for spherical and elliptical cloaks.

Numerical determination of parameters for irregular shapes.

Full-wave simulations confirm the effectiveness of the designed cloaks.

Abstract

In transformation optics, the space transformation is viewed as the deformation of a material. The permittivity and permeability tensors in the transformed space are found to correlate with the deformation field of the material. By solving the Laplace's equation, which describes how the material will deform during a transformation, we can design electromagnetic cloaks with arbitrary shapes if the boundary conditions of the cloak are considered. As examples, the material parameters of the spherical and elliptical cylindrical cloaks are derived based on the analytical solutions of the Laplace's equation. For cloaks with irregular shapes, the material parameters of the transformation medium are determined numerically by solving the Laplace's equation. Full-wave simulations based on the Maxwell's equations validate the designed cloaks. The proposed method can be easily extended to design other transformation materials for electromagnetic and acoustic wave phenomena.