Flat lens without optical axis: Theory of imaging

TL;DR

This paper develops a comprehensive theory for flat lenses without optical axes, showing how anisotropic and inhomogeneous media can achieve imaging, including sub-wavelength resolution, with both positive and negative refractive indices.

Contribution

It introduces a general theoretical framework for flat lens imaging without optical axis, encompassing anisotropic media and photonic crystals, expanding beyond traditional isotropic negative index lenses.

Findings

Imaging requires elliptic dispersion with negative group refraction.

Both negative and positive refractive indices can be used for imaging.

Numerical examples demonstrate sub-wavelength imaging capabilities.

Abstract

We derive a general theory for imaging by a flat lens without optical axis. We show that the condition for imaging requires a material having elliptic dispersion relations with negative group refraction, equivalent to an effective anisotropic refractive index n(theta). Imaging can be achieved with both negative (n<0) and positive (n>0) refractive indices. The Veselago-Pendry lens is a special case with isotropic negative refractive index of n(theta)=-1. Realizations of the imaging conditions using anisotropic media and inhomogeneous media, particularly photonic crystals, are discussed. Numerical examples of imaging and requirements for sub-wavelength imaging are also presented.