## Abstract

The ability of the Finite-Difference Time-Domain method to model a perfect lens made of a slab of homogeneous left-handed material (LHM) is investigated. It is shown that because of the frequency dispersive nature of the medium and the time discretization, an inherent mismatch in the constitutive parameters exists between the slab and its surrounding medium. This mismatch in the real part of the permittivity and permeability is found to have the same order of magnitude as the losses typically used in numerical simulations. Hence, when the LHM slab is lossless, this mismatch is shown to be the main factor contributing to the image resolution loss of the slab.

© 2005 Optical Society of America

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### Equations (7)

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(1)
$$\oint \overline{E}\xb7d\overline{l}=-\frac{\partial}{\partial t}\oint d\stackrel{\xaf}{s}\xb7\stackrel{\xaf}{B}-\oint d\overline{s}\xb7\overline{M}$$
(2)
$${E}_{y}^{n+\frac{1}{2}}\left(I,K\right)-{E}_{y}^{n+\frac{1}{2}}\left(I-1,K\right)=-\frac{\Delta x{\mu}_{o}}{\Delta t}[{H}_{z}^{n+1}\left(I,k+\frac{1}{2}\right)$$
(3)
$$\phantom{\rule{16.em}{0ex}}-{H}_{z}^{n}(I,K+\frac{1}{2})]\frac{\Delta x}{2}{M}_{z}^{n+\frac{1}{2}}\left(I,K\right)$$
(4)
$${H}_{z}^{n+1}(I,K)={H}_{z}^{n}(I,K)-\frac{\Delta t}{2{\mu}_{o}}{M}_{z}^{n+\frac{1}{2}}(I,K)-\frac{\Delta t}{\Delta x{\mu}_{o}}\left({E}_{y}^{n+\frac{1}{2}}\left(I,K\right)-{E}_{y}^{n-\frac{1}{2}}\left(I-1,K\right)\right)$$
(5)
$$\nabla \times \overline{H}=\frac{\partial}{\partial t}{\epsilon}_{0}\overline{E}+{\overline{J}}_{e}=\frac{\partial}{\partial t}{\epsilon}_{o}{\epsilon}_{r}\overline{E}$$
(6)
$$\frac{\partial {\overline{J}}_{e}}{\partial t}+{\Gamma}_{e}{\overline{J}}_{e}={\epsilon}_{0}{\omega}_{\mathit{pe}}^{2}\overline{E}$$
(7)
$${\epsilon}_{r}=1-\frac{{\omega}_{\mathit{pe}}^{2}}{4\mathrm{sin}\frac{\left(\frac{{\omega}_{o}\Delta t}{2}\right)}{{\left(\Delta t\right)}^{2}}}$$