3D geometrically isotropic metamaterial for telecom wavelengths

We present a new design for a unit cell with the cubic symmetry and sizes less than one sixth of the vacuum wavelength possessing a negative refractive index in the IR region. The main challenges in designing and fabricating metamaterials nowadays are in obtaining isotropic electric and magnetic responses keeping in the same time the cell dimensions within the effective medium approximation.

Several approaches have been made to develop such a structure in the microwave region [1, 2], nevertheless, there is still a lack of structures to be used in the IR and visible diapasons. Since the dimension of the unit cell is not infinitely small, certain geometrical constraints have to be fulfilled to obtain an isotropic response of the material [3].

These conditions and the metal behaviour close to the plasma frequency increase the design complexity. Our unit cell is composed of two main parts. The first part generates the electric response, thus providing the negative real part of permittivity in the desired spectral range. The usual way is to utilize a set of metallic wires, so called diluted metal that exhibits a Drude-like behaviour.

Our study shows that this behaviour is obtainable if the wires are arranged in a cage-like structure. For the magnetic response we use metallic plates forming an open cube located inside the “cage”. For this topology the plates can be thought of as capacitors in a resonant LC circuit [4]. By adjusting the resonant circuit frequency in the IR range a double negative response is obtained in a certain bandwidth.

The proposed unit cell has the cubic point group of symmetry and being repeatedly placed in space can effectively reveal isotropic optical properties. We use the CST commercial software to characterise the “cube-in-cage” structure. Reflection and transmission spectra are shown in Fig.1a. The effective refractive index is retrieved accordingly to the standard algorithm [5] (see Fig.1b).

After several cycles of naïve optimizations, the refractive index reaches -2.4 at 1.55μm (ca. 192.5THz). The maximum FOM in the band, where Re(n) <0 is 2.4 at 1.54μm (ca. 195.2THz). At this wavelength the refraction index is equal to -1.44. These values together with the effective cubic symmetry of the unit cell entitle us to assume the high potential of the suggested design as a constitutive block for an isotropic, relatively low-loss, metamaterial in the near IR region.