Inverse problem in transformation optics

TL;DR

This paper presents an inverse approach in transformation optics that derives material parameters directly from electromagnetic fields in a cloak, bypassing the need for coordinate transformations, thus aiding cloak design.

Contribution

It introduces a method to determine permittivity and permeability tensors directly from fields, offering a new way to design cloaks without prior knowledge of coordinate transformations.

Findings

Allows direct derivation of material parameters from fields

Eliminates the need for coordinate transformation in cloak design

Facilitates inverse design of electromagnetic cloaks

Abstract

The straightforward method of transformation optics implies that one starts from the coordinate transformation, determines the Jacobian matrix, the fields and material parameters of the cloak. However, the coordinate transformation appears as an optional function: it is not necessary to know it. We offer the solution of some sort of the inverse problem: starting from the fields in the invisibility cloak we directly derive the permittivity and permeability tensors of the cloaking shell. The approach can be useful for finding material parameters for the specified electromagnetic fields in the cloaking shell without knowing coordinate transformation.