Figure 1

Geometry of the unit cell of our periodic system along the $y$ direction; the unit cell consists of an ENZ region (1) and an embedded dielectric cylinder [region (2)]. The left and right materials surrounding region (1) are considered as air. The upper and bottom boundary conditions of the unit cell are equivalent to a perfect magnetic conductor (PMC) in the case of TE polarization. The geometrical values are typically as follows: $R=4$ μm, $d=30$ μm, and $a=100$ μm.Reuse & Permissions

Figure 2

Comparison of the results for the transmission amplitude $\left|\overline{t}\right|$ based on Eqs. (8a) to (10f) with the numerical results based on the Microwave Studio (MWS) for the system of the unit cell which is shown in Fig. 1 with $R=4$ μm, ${\varepsilon }_1=0.001{\varepsilon }_0$, ${\varepsilon }_2=40{\varepsilon }_0$, and $a=100$ μm. (a) Large $d$, $d=100\mu \mathrm{m}$, MWS. (b) Large $d$, formulas (8a) to (10f). (c) $d=30\mu \mathrm{m}$, MWS. (d) $d=30\mu \mathrm{m}$, formulas (8a) to (10f) including the renormalization due to couplings along the $y$ direction (see text). The incident wave is a TE polarized wave (i.e., $\vec{E}$ along the axis of the cylinder). Dashed line shows the corresponding transmission for the system with no cylinder. The sharpness of the resonance is due to the large ratio ${\varepsilon }_2/{\varepsilon }_1$ and the omission of any losses. The inset shows the displacement currents and the electric field distribution of the sharp resonant mode at the frequency 4.54 THz.Reuse & Permissions

Figure 3

Electric $E_z$ (a) and magnetic $H_y$ (b) field distribution for the first resonant mode associated with the first zero of $J_0\left(k_{2}R\right)$ (at frequency 4.54 THz) of a single cylinder of radius $R=4$ μm, the permittivity of which is ${\varepsilon }_2$ $=$ 40ε${}_0$ embedded in an ENZ matrix with ${\varepsilon }_1$ $=$ 0.001ε${}_0$, for a plane TE wave incident on the cylinder according to Microwave Studio.Reuse & Permissions

Figure 4

Electric $E_z$ field distribution at the frequency 4.55 THz for: (a) a waveguide based on cylinders of radius $R=4$ μm, distance $a_0=12$ μm, and permittivity ${\varepsilon }_2=40{\varepsilon }_0$, embedded in an ENZ matrix of permittivity ${\varepsilon }_1=0.001{\varepsilon }_0$; (b) a corner 45° angle structure based on the waveguide shown in (a). The field distribution has been obtained using the Microwave Studio.Reuse & Permissions

Figure 5

Dispersion characteristics of a waveguide based on cylinders of radius $R=4$ μm and permittivity ${\varepsilon }_2=40{\varepsilon }_0$, embedded in an ENZ matrix of permittivity ${\varepsilon }_1=0.001{\varepsilon }_0$; the distance between the cylinders is $a_0=12$ μm. The black curve shows the mode of this waveguide and the red curve the light line of $\omega =ck$. The inset shows a schematic of the waveguide.Reuse & Permissions

Figure 6

(a) The $E_z$ field distribution for a metamaterial “lens” composed of five layers (along propagation direction) of subwavelength cylindrical inclusions of radius $R=4$ μm$,$ and permittivity ${\varepsilon }_2=40{\varepsilon }_0$, embedded in an ENZ matrix with ${\varepsilon }_1=0.001{\varepsilon }_0$${}_{.}$ The distances between the cylinders are 12 and 15 μm, along $x$ and $y$ axes, respectively. The incident wave has frequency 4.55 THz. (b) Transmission coefficient $\left|\overline{t}\right|$ through the system depicted in (a); $\left|\overline{t}\right|$ has been calculated through Microwave Studio. Note that the peaks below 3 THz correspond to Fabry-Perot resonances, occurring when the system length (along the $x$ direction) equals an integer multiple of the effective half-wavelength.Reuse & Permissions

Figure 7

Transmission coefficient $\left|\overline{t}\right|$ as a function of frequency for a hexagonal lattice of LiF cylinders with radius $R=1$ μm and separation (from center to center) 4 μm, embedded in a KCl matrix. The material parameters for KCl (see text) show an ENZ response around 6 THz (at which a peak in the transmission appears), while for the LiF the permittivity is positive in the frequency range 4–8 THz.Reuse & Permissions