Analytical Study of Sub-Wavelength Imaging by Uniaxial Epsilon-Near-Zero Metamaterial Slabs

TL;DR

This paper provides an analytical framework for understanding sub-wavelength imaging using uniaxial epsilon-near-zero metamaterial slabs, including the effects of tilted optical axes, validated by numerical solutions.

Contribution

It derives a closed-form Green's function for these metamaterials, enabling efficient and insightful modeling of their imaging properties.

Findings

Analytical Green's function derived for uniaxial ENZ slabs.

Validation against full-wave simulations confirms accuracy.

Enhanced tools for designing sub-wavelength imaging systems.

Abstract

We discuss the imaging properties of uniaxial epsilon-near-zero metamaterial slabs with possibly tilted optical axis, analyzing their sub-wavelength focusing properties as a function of the design parameters. We derive in closed analytical form the associated two-dimensional Green's function in terms of special cylindrical functions. For the near-field parameter ranges of interest, we are also able to derive a small-argument approximation in terms of simpler analytical functions. Our results, validated and calibrated against a full-wave reference solution, expand the analytical tools available for computationally-efficient and physically-incisive modeling and design of metamaterial-based sub-wavelength imaging systems.