Figure 1

(Color online) Various unit-cell designs for LH behavior consisting of metals (dark regions) and dielectrics (light semitransparent regions). (a) The design proposed by Pendry et al. and implemented by Smith et al.: Two single split metallic rings have been deposited on a dielectric on the back side of which a continuous metallic wire is attached. (b) Single ring with one or more cuts (the 4-cut is shown). (c) The cut slab design assisted by continuous wires. (d) The fishnet structure and [(e) and (f)] some of its variations.Reuse & Permissions

Figure 2

(Color online) Measured (solid lines) and simulated (dashed lines) electromagnetic (EM) wave transmission $\left(S_{21}\right)$ through a set of three unit cells along the propagation direction of the fishnet structure, shown in the right panel of the figure. The unit-cell side along the propagation direction, $a_{\mathbf{k}}$, is $2.6\mathrm{mm}$ for panel (a) and $3.1\mathrm{mm}$ for panel (b). The other unit-cell sides are $a_{\mathbf{E}}=9.5\mathrm{mm}$ and $a_{\mathbf{H}}=7\mathrm{mm}$. The structure parameters are as follows: continuous wires’ width (necks in the fishnet), $w_n=1.5\mathrm{mm}$; metal thickness, $t_m=30\mu \mathrm{m}$; slabs’ length, $l_s=7\mathrm{mm}$; thickness of the dielectric FR4 board separating the metallic elements in each unit cell, $t=1.6\mathrm{mm}$. The board dielectric constant and conductivity used in the simulations are ${ϵ}_b=4$ and ${\sigma }_b=0.022\mathrm{S}∕\mathrm{m}$. The metal conductivity used is ${\sigma }_m=5.88\times {10}^7\mathrm{S}∕\mathrm{m}$.Reuse & Permissions

Figure 3

(Color online) Effective material parameters, impedance $\left(z\right)$, refractive index $\left(n\right)$, permittivity $\left(ϵ\right)$, and permeability $\left(\mu \right)$ for the fishnet structure of Fig. 2b. The solid lines show the real part of the parameters, the dashed lines the imaginary part, and the dotted horizontal lines are guides for the eyes.Reuse & Permissions

Figure 4

(Color online) Transmission vs frequency (simulated) for a set of five unit cells along the propagation direction of the fishnet structure shown in Fig. 1d (solid line), the modified fishnet design shown in Fig. 1e (dashed line), and the isotropic-like fishnet design shown in Fig. 1f (dotted dashed line). The parameters for the fishnet and the modified fishnet designs are those mentioned in Fig. 2b, except that the substrate here has been considered as lossless; the width of the short slabs in the modified fishnet is $5\mathrm{mm}$. For the isotropic-like fishnet design, the width of the continuous wires is $3.6\mathrm{mm}$, the length of the short slabs $l_s$ is $8\mathrm{mm}$, and the unit-cell sides $a_{\mathbf{H}}=a_{\mathbf{E}}$ are $9.5\mathrm{mm}$. The rest of the parameters are those mentioned in connection with Fig. 2b.Reuse & Permissions

Figure 5

(Color online) Comparison of the simulated transmission vs frequency of the short slabs (of width of $1.6\mathrm{mm}$) combined with continuous wires as shown in Fig. 1c (solid line) with the fishnet design of Fig. 1f (dashed line). The dotted dashed line shows the transmission for only the short slabs (of width of $1.6\mathrm{mm}$); the dip at $\sim 11\mathrm{GHz}$ is due to the negative permeability response of the slabs. The parameters here are as follows: Substrate thickness (pair separation), $t=0.3\mathrm{mm}$; unit-cell length along the propagation direction, $a_{\mathbf{k}}=2.3\mathrm{mm}$; width of the continuous wires, $w=1\mathrm{mm}$; lossless substrate [note that case 1(c) involves two pairs of wires per unit cell, while the fishnet, 1(f), one pair]. The rest of the parameters are those mentioned in connection with Fig. 2.Reuse & Permissions

Figure 6

(Color online) Effective material parameters $ϵ$ and $\mu$, for the slab and wire structures of Fig. 5. Solid lines are for the structure of the nonconnected slabs and wires [shown in Fig. 1c], while dashed lines are for the fishnet structure [shown in Fig. 1d]. The dotted horizontal lines are guides for the eyes. Note that the antiresonances in the parameters are artifacts coming from the periodicity of the structure, which imposes an upper limit to the retrieved refractive index from which $ϵ$ and $\mu$ are simulated (Ref. 17).Reuse & Permissions

Figure 7

(Color online) Surface current distribution for the fishnet structure presented in Fig. 2b (single pair along the propagation direction) at frequency just above the magnetic resonance. The incoming EM field meets first the surface indicated as 1st in the plot.Reuse & Permissions

Figure 8

(Color online) The magnetic-field component $H_x$ for the fishnet structure of Fig. 2b (left panel) and the electric-field component $E_z$ (right panel) just above the magnetic-resonance frequency of the structure. Propagation is along the $z$ direction. Red color indicates strong positive values and blue strong negative values. The displayed fields are calculated at an $x\text{−}y$ plane located in the middle between the two sheets of the pair along the $z$ direction and at a frequency just above the magnetic-resonance frequency of the structure.Reuse & Permissions

Figure 9

An $LC$ circuit model for the fishnet structure. $L_s$ and $L_n$ denote the loop inductances at the slabs and necks, respectively, and $C$ the capacitance of the structure. The right panel results from left panel after taking into account the periodicity and thus the equivalence of the points $A$ and $A^{\prime }$ and $B$ and $B^{\prime }$.Reuse & Permissions

Figure 10

(Color online) The magnetic-field component $H_x$ (left panel) and the electric-field component $E_z$ (right panel) just above the magnetic-resonance frequency $({\omega }_m\approx 9\mathrm{GHz})$ for a fishnet structure with those parameters mentioned in Fig. 2, except the unit-cell side $a_{\mathbf{E}}$, which here is $16.5\mathrm{mm}$, thus increasing the length of the neck part of the structure. The displayed fields are calculated at an $x\text{−}y$ plane located in the middle between the two sheets of the pair, and at a frequency just above the magnetic-resonance frequency of the structure. Propagation is along the $z$ direction. Red color indicates large positive values and blue color large negative values.Reuse & Permissions

Figure 11

(Color online) (a) Schematics of one unit cell of the fishnet design. Dashed lines show the boundaries of the unit cell. Due to the periodicity, the lines $AB$ and $A^{\prime }{B}^{\prime }$ are equivalent. Panels (b) and (c) are redrawings of the metallic sheet of panel (a) taking advantage of the periodicity, and drawing also the two possibilities for current flow: (b) topologically opposite direction current flow and (c) topologically same direction flow.Reuse & Permissions