Mechanism for Designing Metallic Metamaterials with a High Index of Refraction

We introduce a mechanism for creating artificial high refractive index metamaterials by exploiting the existence of subwavelength propagating modes in metallic systems. As an example, we investigate analytically and numerically metal films with a periodic arrangement of cut-through slits. Because of the presence of TEM modes in the slits, for TM polarization such a system can be rigorously mapped into a high refractive index dielectric slab when the features are smaller than the wavelength of light. The effective refractive index is entirely controlled by the geometry of the metal films, is positive, frequency independent, and can be made arbitrarily large.

Figure 1

(a) Schematic of the metal film with periodic slits. The parameters are defined as in the figure: $a$ is the width of the slit, $d$ is the periodicity, and $L$ is the thickness of the metal film. The black regions indicate the metal parts, and the white regions are the vacuum. The film is extended in the $x-y$ plane. (b) The equivalent effective dielectric slab corresponding to (a). The effective refractive index is $n\equiv d/a$, and the thickness is $\overline{L}\equiv L/n$.

Figure 2

The transmission coefficient of the metal film (black lines) and the corresponding effective dielectric slab (red lines). The thickness of the metal film is $L/d=25/4$. The effective refractive index of the slab is $n=d/a=4$. (a) Spectrum at normal incidence. (b) Transmission at oblique incidence for the frequency $\omega =0.05\times d/\lambda$.

Figure 3

Dispersion curves of the waveguide modes in the first Brillouin zone. Shown in the figures are the first three even modes of the metal films (black lines) and the corresponding effective dielectric slabs (red lines). The dashed lines are the light lines in vacuum and in the slab waveguides, respectively. $L/d=25/4$. (a) $n=4$; (b) $n=16$. (The odd modes, not shown here, are located between the even bands and behave similarly.)

Figure 4

Snapshots of the $H_y$ field distributions of the fundamental waveguide modes of the metal film [shown in (a)] and the corresponding effective dielectric slab [shown in (b)] for $n=d/a=4$, $L/d=25/4$. The red color indicates positive amplitude, while the blue color indicates negative amplitude. The white lines in (a) and (b) outline the film and the slab, respectively. The normalized excitation frequency is $\omega =d/\lambda =0.0516$. The arrows indicate the periodicity of the field.