Figure 2.

(a) All-dielectric cube with a = 10 mm. (b) Sphere of air of radius $r_a$. (c) Unit cell obtained from the dielectric cube and the air sphere. (d) One of the spherical shells composing the Luneburg lens. (e) Effective permittivity of the unit cells composed of an air sphere in the host dielectric material. A parametric analysis is performed to extract the effective permittivity value according to the radius $r_a$ of the air sphere in the dielectric cube. The yellow shaded zone represents the region where the value of radius $r_a$ is less or equal to a/2 ($r_a\le a/2$). The continuous trace corresponds to approximate values calculated using the Bruggeman’s model and the dashed trace corresponds to accurate values retrieved from homogenization procedure at 6 GHz.