Engineered optical nonlocality in nanostructured metamaterials

We analyze dispersion properties of layered metal-dielectric structures, which can be considered as a simple example of nanostructured metamaterials. We demonstrate that, in sharp contrast to the results of the theory of effective media, the layered structure demonstrates strong optical nonlocality due to excitation of surface plasmon polaritons. Such nonlocality can be engineered by changing a ratio between the thicknesses of metal and dielectric layers. Importantly, the nonlocality leads to the existence of an additional extraordinary wave that manifests itself in the splitting of the transverse-magnetic polarized beam refracted at an air-metamaterial interface.

Figure 1

Effective medium model. Permittivity tensor components as functions of normalized frequency for three types of periodic layered metal-dielectric nanostructures with the fixed lattice spacing $D=d_1+d_2$, but formed by pairs of metal and dielectric layers with the thicknesses (1) $d_2=1.5d_1$, (2) $d_1=d_2$, and (3) $d_1=1.5d_2$, respectively.

Figure 2

Dispersion diagrams and the geometries of the periodic nanostructures composed of alternating metal and dielectric layers. Thicknesses of the layers are (a) $d_2=1.5d_1$, (b) $d_1=d_2$, and (c) $d_1=1.5d_2$. Two dispersion branches corresponding to the actual structures are numbered by Roman numerals.

Figure 3

Diagrams of beam refraction at the air-MDN interface in the case of Fig. 2c at three different frequencies: (a) $D/\lambda =0.085$, (b) $D/\lambda =0.094$, and (c) $D/\lambda =0.106$. Wave vectors ${\mathbf{k}}_i,\hspace{0.5em}{\mathbf{k}}_r$ of incident and refracted waves, respectively, and group velocity vectors ${\mathbf{v}}_g$ are plotted by means of the isofrequency contours method. The first Brillouin zone is rendered.

Figure 4

Numerical studies of the beam refraction in the three cases corresponding to Figs. 3a, 3b, 3c, respectively. Layers are normal to the interface. Incident wave is TM polarized.