On subwavelength imaging of Maxwell's fish eye lens

TL;DR

This paper analyzes Maxwell's fish eye lens and demonstrates it cannot produce perfect imaging due to limitations in high order mode transmission, but can achieve subwavelength imaging with a larger spot size when only the zero order mode is excited.

Contribution

The study provides explicit analysis and conditions for subwavelength imaging with Maxwell's fish eye lens, clarifying its limitations and capabilities.

Findings

High order modes cannot reach the image point, preventing perfect imaging.

Subwavelength images are possible with zero order mode, but with larger spot size.

Explicit conditions for achieving subwavelength imaging are provided.

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, which has been claimed recently to be able to achieve perfect imaging. We show that such a 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 the Maxwell's fish eye. If only zero order mode is excited, a subwavelength image can be achieved, however, its spot-size is larger than the spot size of the source 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 modified fish eye bounded with perfectly electrical conductor (PEC). Explicit condition is given for achieving a subwavelength image. When this condition is not satisfied, a single line current source may give multiple image spots.