Can Maxwell's fish eye lens really give perfect imaging?

TL;DR

This paper analyzes Maxwell's fish eye lens and concludes it cannot produce perfect imaging due to limitations in high order mode transmission, with only zeroth order mode achieving partial imaging.

Contribution

The study provides explicit analysis and numerical simulations demonstrating the fundamental limitations of Maxwell's fish eye lens in achieving perfect imaging.

Findings

High order modes cannot reach the image point.

Only zeroth order mode can produce a partial image.

Image resolution depends on the zeroth order field spot size.

Abstract

Both explicit analysis and FEM numerical simulation are used to analyze the field distribution of a line current in the so-called Maxwell's fish eye lens [bounded with a perfectly electrical conductor (PEC) boundary]. We show that such a 2D Maxwell's fish eye lens cannot give perfect imaging due to the fact that high order modes of the object field can hardly reach the image point in Maxwell's fish eye lens. If only zeroth order mode is excited, a good image of a sharp object may be achieved in some cases, however, its spot-size is larger than the spot size of the initial object field. The image resolution is determined by the field spot size of the image corresponding to the zeroth order component of the object field. Our explicit analysis consists very well with the FEM results for a fish eye lens. Time-domain simulation is also given to verify our conclusion. Multi-point images for a single object point are also demonstrated.