Asymmetric Cloaking Theory Based on Finsler Geometry ~ How to design Harry Potter's invisibility cloak with a scientific method ~

TL;DR

This paper introduces a novel transformation optics approach based on Finsler geometry to design nonreciprocal invisibility cloaks, enabling the creation of shields that are invisible from outside but see-through from within.

Contribution

It extends conventional transformation optics by incorporating Finsler geometry, allowing the design of nonreciprocal cloaking devices with anisotropic media.

Findings

Finsler geometry-based theory enables nonreciprocal cloaking.

Method for designing permittivity and permeability distributions.

Includes conventional transformation optics as a special case.

Abstract

Is it possible to actually make Harry's invisibility cloaks? The most promising approach for realizing such magical cloaking in our real world would be to use transformation optics, where an empty space with a distorted geometry is imitated with a non-distorted space but filled with transformation medium having appropriate permittivity and permeability. An important requirement for true invisibility cloaks is nonreciprocity; that is, a person in the cloak should not be seen from the outside but should be able to see the outside. This invisibility cloak, or a nonreciprocal shield, cannot be created as far as we stay in conventional transformation optics. Conventional transformation optics is based on Riemann geometry with a metric tensor independent of direction, and therefore cannot be used to design the nonreciprocal shield. To overcome this problem, we propose an improved theory of transformation optics that is based on Finsler geometry, an extended version of Riemann geometry. Our theory shows that nonreciprocal shielding can be realized by covering cloaking space with transformation medium having anisotropic, nonreciprocal permittivity and permeability. This theory includes conventional transformation optics as special cases. We show the method for designing the spatial distribution of the permittivity and permeability required to make the nonreciprocal shield.