Calculation of material properties for arbitrary shape transformation media

TL;DR

This paper introduces a numerical method to determine material parameters for arbitrary shape transformation media, enabling the design of complex devices like cloaks and rotators with flexible boundaries.

Contribution

A general approach using Laplace's equations to evaluate material properties for arbitrary shape transformation media, including devices with non-fixed outer boundaries.

Findings

Method successfully computes deformation fields for arbitrary shapes.

Designs of cloaks, rotators, and concentrators demonstrated with simulations.

Analysis of wave velocity and energy changes in transformation media.

Abstract

We propose a general method to evaluate the material parameters for arbitrary shape transformation media. By solving the original coordinates in the transformed region via Laplace's equations, we can obtain the deformation field numerically, in turn the material properties of the devices to be designed such as cloaks, rotators or concentrators with arbitrary shape. Devices which have non-fixed outer boundaries, such as beam guider, can also be designed by the proposed method. Examples with full wave simulation are given for illustration. In the end, wave velocity and energy change in the transformation media are discussed with help of the deformation view.