Focussing Light Using Negative Refraction

TL;DR

This paper introduces a method using negative refraction and coordinate transformation to focus light and produce perfect, magnified images, including complex geometries, revealing subwavelength details.

Contribution

It extends negative refraction focusing to arbitrary geometries and introduces coordinate transformation as a powerful design technique.

Findings

Negative slabs focus images at twice their thickness.

Coordinate transformation enables focusing in complex geometries.

Images can be magnified and reveal subwavelength details.

Abstract

A slab of negatively refracting material, thickness d, can focus an image at a distance 2d from the object. The negative slab cancels an equal thickness of positive space. This result is a special case of a much wider class of focussing: any medium can be optically cancelled by an equal thickness of material constructed to be an inverted mirror image of the medium, with, $\epsilon$ and $\mu$ reversed in sign. We introduce the powerful technique of coordinate transformation, mapping a known system into an equivalent system, to extend the result to a much wider class of structures including cylinders, spheres, and intersecting planes and hence show how to produce magnified images. All the images are perfect in the sense that both the near and far fields are brought to a focus and hence reveal sub wavelength details.