Far field imaging by a planar lens: diffraction versus superresolution

TL;DR

This paper clarifies the conditions under which a planar lens made of left-handed media can achieve superresolution, highlighting the roles of absorption, wavelength, and surface plasmon resonance in far-field imaging.

Contribution

It provides a theoretical resolution of the controversy by identifying the fundamental factors that determine diffraction versus superresolution in planar lenses.

Findings

Diffraction governs the image at small wavelengths regardless of absorption.

A critical absorption threshold exists for superresolution at finite wavelengths.

Surface plasma wave resonance influences the transition between regimes.

Abstract

We resolve the long standing controversy regarding the imaging by a planar lens made of left-handed media and demonstrate theoretically that its far field image has a fundamentally different origin depending on the relationship between losses {inside} the lens and the wavelength of the light $\lambda$. At small enough $\lambda$ the image is always governed by diffraction theory, and the resolution is independent of the absorption if both Im$\epsilon \ll 1$ and Im$\mu \ll 1$. For any finite $\lambda$, however, a critical absorption exists below which the superresolution regime takes place, though this absorption is extremely low and can hardly be achieved. We demonstrate that the transition between diffraction limited and superresolution regimes is governed by {the} universal parameter combining absorption, wavelength, and lens thickness. Finally, we show that this parameter is related to the resonant excitation of the surface plasma waves.