Comment on "Perfect imaging with positive refraction in three dimensions"

TL;DR

This paper critiques a proof claiming perfect imaging with Maxwell's fish-eye lens, arguing that the claimed unlimited resolution is due to an unphysical assumption, and that realistic focusing adheres to the diffraction limit.

Contribution

It clarifies that the previously claimed perfect imaging is an artifact caused by an unphysical drain, emphasizing the importance of realistic boundary conditions.

Findings

Unlimited resolution is an artifact of an unphysical drain.

Realistic focusing aligns with the diffraction limit.

The original proof does not hold under physically realistic conditions.

Abstract

Leonhard and Philbin [Phys. Rev. A 81, 011804(R) (2010)] have recently constructed a mathematical proof that the Maxwell's fish-eye lens provides perfect imaging of electromagnetic waves without negative refraction. In this comment, we argue that the unlimited resolution is an artifact of having introduced an unphysical drain at the position of the geometrical image. The correct solution gives focusing consistent with the standard diffraction limit.