Broadband epsilon-near-zero metamaterials with steplike metal-dielectric multilayer structures

The concept of the broadband epsilon-near-zero meta-atom consisting of layered stacks with specified metallic filling ratio and thickness is proposed based on the Bergman spectral representation of the effective permittivity. The steplike metal-dielectric multilayer structures are designed to achieve realistic broadband epsilon-near-zero meta-atoms in optical frequency range. These meta-atoms can be integrated as building blocks for unconventional optical components with exotic electromagnetic properties over a wide frequency range, such as the demonstrated broadband directional emission and phase front shaping.

Figure 1

The schematic diagram of the broadband ENZ meta-atom and the designed broadband near-zero effective permittivity. (a) The effective-medium meta-atom with three homogenous layers composed by gold and silica, and the realistic meta-atom with a steplike metal-dielectric multilayer structure. (b) The theoretical values (solid curves) and the FDTD retrieved values (dashed curves) of the real part (red curves) and the imaginary part (blue curves) of the effective permittivity ${\varepsilon }_x$ of the effective medium meta-atom, with the ENZ frequencies (yellow dots) listed at the right bottom.

Figure 2

The distributions of the absolute value of the electric field in the effective medium meta-atom (upper panel) and the realistic meta-atom array (lower panel) at different ENZ frequencies, corresponding to the incident electromagnetic wave indicated by the coordinates.

Figure 3

The schematic diagram and IFC analysis about the directional emission with respect to the broadband ENZ response. (a) The diagram of the directional emission through the ENZ prism represented by the electromagnetic waves inside and outside the prism. (b) The flat elliptical IFC (red curve for ${\varepsilon }_x=0.05$ and ${\varepsilon }_y=3.0$) of the meta-atom under lossless condition. (c) The elliptical-like IFC (red curve for ${\varepsilon }_x=0.05+0.5i$ and ${\varepsilon }_y=3.0+0.002i$) of the meta-atom under lossy condition. The IFC of air is plotted as blue circle.

Figure 4

Simulation results about the directional emission of the broadband ENZ prism with the ${15}^{\circ }$-oblique upper interface, represented by the distribution of the electric field amplitude $E_x$ and the power flow (hollowed arrows), for (a) the effective medium made prism and (b) the realistic meta-atom made prism. (c) The angle of refraction (in degrees) as a function of the frequency, based on the theoretical effective permittivity (blue curve), and the simulation results of the effective medium made prism (blue dots) and the realistic meta-atom made prism (black circles). The average angle of refraction is $6.3^{\circ }$ (red line) in the ENZ frequency range.

Figure 5

Simulation results about the phase front shaping of the broadband ENZ $S$-shape lens with the radius of curvature of $3\mu \mathrm{m}$, represented by the distribution of the electric field amplitude $E_x$, for (a) the effective medium made $S$-shape lens and (b) the realistic meta-atom made $S$-shape lens. (c) The average phase variation (in radians) as a function of the frequency, with respect to the effective medium made $S$-shape lens (blue dots) and the realistic meta-atom made $S$-shape lens (black circles). The mean value of the average phase variation is $0.7\mathrm{rad}$ (red line) in the ENZ frequency range.

Figure 6

Robustness analysis of the designed parameters in the realistic meta-atom with solid curves indicating theoretical results in the main text based on six-digit values of the fraction and the thickness, while the dashed curves indicating the approximated results based on two-digit values.

Figure 7

The impedance of the designed broadband ENZ metamaterials.