Perfect imaging without negative refraction

TL;DR

This paper demonstrates that perfect imaging is achievable with positive refraction media like Maxwell's fish eye, challenging the belief that negative refraction is necessary, and provides practical methods for implementation.

Contribution

It provides a mathematical proof that Maxwell's fish eye can produce perfect images in two-dimensional optics, expanding the understanding of wave focusing beyond negative refraction.

Findings

Maxwell's fish eye achieves perfect imaging in 2D optics.

The method can be adapted for practical perfect imaging devices.

Potential applications extend to acoustics, fluid mechanics, and quantum physics.

Abstract

Perfect imaging has been believed to rely on negative refraction, but here we show that an ordinary positively-refracting optical medium may form perfect images as well. In particular, we establish a mathematical proof that Maxwell's fish eye in two-dimensional integrated optics makes a perfect instrument with a resolution not limited by the wavelength of light. We also show how to modify the fish eye such that perfect imaging devices can be made in practice. Our method of perfect focusing may also find applications outside of optics, in acoustics, fluid mechanics or quantum physics, wherever waves obey the two-dimensional Helmholtz equation.