Limits on the amplification of evanescent waves of left-handed materials

TL;DR

This paper analyzes the limitations of evanescent wave amplification in left-handed materials using FDTD and transfer matrix simulations, revealing how discretization affects super-resolution capabilities.

Contribution

It introduces a model explaining how discretization limits evanescent wave transfer in perfect lenses, supported by FDTD and TMM simulation comparisons.

Findings

Finite discretization causes exponential decay in transfer function.

Peak transfer function is affected by finite time artifacts.

Maximum parallel momentum depends logarithmically on mesh size.

Abstract

We investigate the transfer function of the discretized perfect lens in finite-difference time-domain (FDTD) and transfer matrix (TMM) simulations; the latter allow to eliminate the problems associated with the explicit time dependence in FDTD simulations. We argue that the peak observed in the FDTD transfer function near the maximum parallel momentum $k_{\|,\mathrm{max}}$ is due to finite time artifacts. We also find the finite discretization mesh acts like imaginary deviations from $\mu=\epsilon=-1$ and leads to a cross-over in the transfer function from constance to exponential decay around $k_{\|,\mathrm{max}}$ limiting the attainable super-resolution. We propose a simple qualitative model to describe the impact of the discretization. $k_{\|,\mathrm{max}}$ is found to depend logarithmically on the mesh constant in qualitative agreement with the TMM simulations.