On subwavelength imaging with Maxwell's fish eye lens

TL;DR

This paper analyzes the limitations of Maxwell's fish eye lens for subwavelength imaging, showing it cannot achieve perfect imaging due to high order mode attenuation, but zeroth order mode can produce limited subwavelength images.

Contribution

The study provides explicit analysis and numerical simulations demonstrating the inability of Maxwell's fish eye lens to produce perfect images and clarifies the role of different modes in imaging.

Findings

High order modes are suppressed, preventing perfect imaging.

Subwavelength images are possible only with zeroth order mode.

Time-domain simulations confirm the analysis.

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 subwavelength 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 imaging for a single object point is also demonstrated.