Total Transmission and Total Reflection by Zero Index Metamaterials with Defects

We theoretically investigate microwave transmission through a zero-index metamaterial loaded with dielectric defects. The metamaterial is impedance matched to free space, with the permittivity and permeability tending towards zero over a given frequency range. By simply varying the radii and permittivities of the defects, total transmission or reflection of the impinging electromagnetic wave can be achieved. The proposed defect structure can offer advances in shielding or cloaking technologies without restricting the object’s viewpoint. Active control of the observed exotic transmission and reflection signatures can occur by incorporating tunable refractive index materials such as liquid crystals and ${\mathrm{BaSrTiO}}_3$.

Figure 1

Schematic of the proposed vacuum-MIZIM-vacuum metamaterial structure containing an arbitrary arrangement of $N$ defects (region 2). The propagation direction of the EM wave is along the $x$ axis. The central MIZIM layer (with ${ϵ}_1$ and ${\mu }_1$) in region 1 has thickness $d$ in the $x$ direction and width $w$ in the $y$ direction. The $i$th cylindrical defect has radius $R_i$, permittivity ${ϵ}_{2,i}$, and permeability ${\mu }_{2,i}$. The upper and lower boundaries correspond to a perfectly conducting metal or perfect magnetic boundary, depending on the polarization of the incident wave.

Figure 2

Perfect reflection. (a) The magnetic field distribution for an arrangement of three defects embedded in a MIZIM. The radii are $R_1=4\mathrm{mm}$, $R_2=8\mathrm{mm}$, and $R_3=12\mathrm{mm}$ with respective materials ${ϵ}_{2,1}=3.7$, ${ϵ}_{2,2}=11.9$, and ${ϵ}_{2,3}=15.7$. The $\mathbf{E}$ field magnitude is shown in (b) with its associated vector field distribution (higher field values in the MIZIM occasionally result in some vectors overlapping with an adjacent defect).

Figure 3

Various field profiles illustrating perfect transmission. In  (a) the magnetic field pattern is shown for the same setup as Fig. 2 but with the modifications ${ϵ}_{2,1}=9.3$, ${ϵ}_{2,2}=16.4$, and ${ϵ}_{2,3}=19.1$. In (b) the corresponding $\mathbf{E}$ field is shown (higher field values in the MIZIM occasionally result in some vectors overlapping with an adjacent defect). The power flow is illustrated in (c) with the Poynting vector map (time averaged over one period) and filled contours representing its magnitude.

Figure 4

(a) Transmission ($S21$) versus $K$ (see text) of the 8 mm defect for the three defect system in Fig. 3. The effects of loss are shown in (b) for $\Gamma /{\omega }_p=0.001$ (solid line), 0.01 (dashed line), and 0.05 (dotted line).