Reply to Comment on Reply to Comment on `Perfect imaging without negative refraction'

TL;DR

This paper clarifies that Maxwell's fish eye can still produce perfect imaging despite causal solutions, emphasizing that causality does not preclude perfect resolution in optical systems.

Contribution

It demonstrates that perfect imaging is compatible with causal solutions in Maxwell's fish eye, correcting misconceptions about causality and imaging quality.

Findings

Maxwell's fish eye can produce perfect images.

Causality does not prevent perfect resolution.

Both causal and non-causal solutions can exist in the system.

Abstract

Kinsler and Favaro point out correctly that Blaikie's numerical solution of Maxwell's equations in Maxwell's fish eye is causal and hence valid, a solution where no perfect image is formed. It is wrong to conclude from the existence of a causal solution with perfect imaging that one without perfect resolution is not causal; both are allowed by causality. However, Maxwell's fish eye can still perfectly image, as the Reply shows.