Anomalous Refraction of Light Colors by a Metamaterial Prism

A prism of glass separates white light into its spectral components in such a manner that colors associated with shorter wavelengths are more refracted than the colors associated with longer wavelengths. Here, we demonstrate that this property is not universal, and that a lossless metamaterial prism with a suitable microstructure may enable a broadband regime of anomalous dispersion, where the spectral components of light are separated in an unconventional way, so that “violet light” is less refracted than “red light.” This phenomenon is fundamentally different from conventional anomalous dispersion effects, which are invariably accompanied by significant loss and are typically very narrow band.

Figure 1

(a) Refraction of light by a conventional dielectric prism. (b) Refraction of light by the metamaterial prism proposed in this Letter. Notice that the palette of refracted colors is reversed. (c) and (d) Perspective views of the metamaterial prism. The metamaterial is formed by nonconnected crossed metallic wires that lie in planes normal to the $y$ direction.

Figure 2

Normalized radiation intensity $I$ of the refracted beam (calculated at a distance $R=30.0{\lambda }_0$ from the output interface) as a function of the elevation angle $\phi$, for a metamaterial prism with $\alpha ={15}^{°}$ and (a) $\omega =0.25c/a$, (b) $\omega =0.35c/a$, and (c) $\omega =0.40c/a$. The dashed lines correspond to the results obtained using physical optics [Eq. (6)], whereas the solid lines were obtained by solving Maxwell’s equations using the periodic MoM. The vertical grid lines mark the theoretical angle of transmission ${\theta }_t$ for each of the considered cases. The inset shows ${\theta }_t$ as a function of normalized frequency and different values of $\alpha$.

Figure 3

Amplitude and phase of the transmission coefficient $T$ of a planar metamaterial slab, as a function of the thickness of the slab $L$. The slab is illuminated by a plane wave propagating along the normal direction. The normalized frequency of operation is $\omega a/c=0.22$, and the radius of the wires is $r_w=0.05a$. Solid lines: full wave calculation with the periodic MoM. Discrete symbols: results obtained using the homogenization model developed in Ref. 9. The inset represents the geometry of the problem. The wires are tilted by $\pm {45}^{°}$ with respect to the interfaces, and lie in planes normal to the $y$ direction.

Figure 4

Normalized $|E_x{|}^2$ (which is roughly proportional to the beam intensity) in the vicinity of the prism, calculated by solving Maxwell’s equations using the periodic MoM. Panel (a): $\omega a/c=0.25$. Panel (b): $\omega a/c=0.40$.