## Abstract

We report on the development and use of a highly anisotropic magnetic metamaterial for near-field imaging. The material consists of an array of Swiss Roll structures, resonant near 21.3 MHz, with a peak value of relative permeability ~35. At this peak, the material transfers an input magnetic field pattern to the output face without loss of intensity and with a spatial resolution equal to the roll diameter. It behaves as a near-field imaging device consisting of a bundle of magnetic wires.

© 2003 Optical Society of America

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### Equations (10)

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(1)
$${\mu}_{z}\left(\omega \right)=1-\frac{F}{\left(1-\frac{{\omega}_{0}^{2}}{{\omega}^{2}}\right)+i\frac{\Gamma}{\omega}},\phantom{\rule{.9em}{0ex}}{\mu}_{x}={\mu}_{y}=1$$
(2)
$$i\mathbf{k}\times \mathbf{E}=i\omega \mathbf{\mu}{\mu}_{0}\mathbf{H},\phantom{\rule{.9em}{0ex}}\phantom{\rule{.9em}{0ex}}i\mathbf{k}\times \mathbf{H}=-i\omega \mathbf{\epsilon}{\epsilon}_{0}\mathbf{E}$$
(3)
$$-\mathbf{k}\times \mathbf{k}\times \mathbf{H}={\omega}^{2}{c}_{0}^{-2}\mathbf{\mu}\mathbf{H}\phantom{\rule{.9em}{0ex}}\mathrm{or}\phantom{\rule{.9em}{0ex}}-\mathbf{k}\left(\mathbf{k}\xb7\mathbf{H}\right)+{k}^{2}\mathbf{H}={k}_{0}^{2}\mathbf{\mu}\mathbf{H}$$
(4)
$$\left[\begin{array}{cc}{\mu}_{x}^{-1}{k}_{z}^{2}& -{\mu}_{z}^{-1}{k}_{x}{k}_{z}\\ -{\mu}_{x}^{-1}{k}_{x}{k}_{z}& {\mu}_{z}^{-1}{k}_{x}^{2}\end{array}\right]\phantom{\rule{.2em}{0ex}}\left[\begin{array}{c}{B}_{x}\\ {B}_{z}\end{array}\right]={k}_{0}^{2}\left[\begin{array}{c}{B}_{x}\\ {B}_{z}\end{array}\right]$$
(5)
$${k}_{z}^{2}={\mu}_{x}{k}_{0}^{2}-\frac{{\mu}_{x}}{{\mu}_{z}}{k}_{x}^{2}$$
(6)
$$\left[\begin{array}{c}{B}_{x}\\ {B}_{z}\end{array}\right]=\left[\begin{array}{c}{\mu}_{z}^{-1}{k}_{x}^{2}-{k}_{0}^{2}\\ {\mu}_{x}^{-1}{k}_{x}{k}_{z}\end{array}\right]$$
(7)
$$\left[\begin{array}{c}{B}_{x}\\ {B}_{z}\end{array}\right]=\left[\begin{array}{c}-{k}_{0}\\ \pm {k}_{x}\end{array}\right]$$
(8)
$${\mu}_{z}\left({\omega}_{\mathit{res}}\right)=i{\beta}^{2}$$
(9)
$${k}_{z}^{2}\approx \frac{i{k}_{x}^{2}}{{\beta}^{2}}$$
(10)
$$\Delta \approx \frac{1}{{k}_{x}}(max)\approx \frac{d}{\beta}$$