Giant spatial-dispersion-induced birefringence in metamaterials

We demonstrate experimentally giant spatial-dispersion-induced birefringence in metamaterials. The difference between the reflection coefficients for $(1,\overline{1},0)$- and $(0,0,1)$-polarized light reflected from the $[1,1,0]$ surface of a metamaterial reaches $78\%$. The magnitude of spatial-dispersion-induced birefringence in the transparency windows of the structure reaches $n_{1\overline{1}0}-n_{001}=-0.13$, which is at least three orders of magnitude larger than the typical values reported for natural crystals. Our results elucidate the important role of spatial dispersion effects in a wide class of metamaterials.

Figure 1

(a) The view of the three-dimensional metamaterial under study. The boundary of the structure is parallel to the $[1,1,0]$ plane, and the normal incidence of light is studied. The reflection coefficients are measured for $(1,\overline{1},0)$ and $(0,0,1)$ linear polarizations of the impinging wave. (b) Theoretical results for reflectance of the structure with parameters $A/a^3=0.15, \gamma a/c=1.02\times {10}^{-2}, {\alpha }_b/a^3=0.0279, {\lambda }_0/a=4.5$, where $a$ is the lattice period, ${\lambda }_0=2\pi c/{\omega }_0$, and ${\omega }_0$ is the particle resonance frequency. Particle polarizability is extracted from numerical simulations in Ansoft HFSS.

Figure 2

Effective refractive indices for $(0,0,1)$ and $(1,\overline{1},0)$ linear polarizations of light propagating along the $(1,1,0)$ direction in the metamaterial [Fig. 1]. Calculations are performed by the discrete dipole model. (a) Real part of refractive indices. (b) Imaginary part of refractive indices.

Figure 3

(a) The sketch of the simplified structure used in the experiment. (b) Resonant copper particles isotropic in plane $[1,1,0]$ having the following geometric parameters: $w=0.5$ mm, $R=4.8$ mm, $b=3$ mm, $g=0.5$ mm. (c) The photograph of the manufactured five-layer metamaterial sample composed of resonant meta-atoms. The period of the cubic lattice is $a=16.3$ mm.

Figure 4

The scheme of the experiment on the measurement of the reflection coefficients in an anechoic chamber.

Figure 5

Experimental results on the reflectance of the five-layer structure composed of resonant meta-atoms.