Thin metamaterial Luneburg lens for surface waves

By suitably patterning a metasurface, the phase velocity of surface waves may be manipulated. Here, a low-loss, thin (1/14th of the free-space wavelength), omnidirectional Luneburg lens, based upon a Sievenpiper “mushroom” array [Sievenpiper et al., IEEE Trans. Microwave Theory Tech. 47, 2059 (1999)], is fabricated and characterized at microwave frequencies. Surface waves excited using a near-field point source on the perimeter of the lens, exit the opposite side of the lens as planar wave fronts. The electric field of the surface wave is mapped out experimentally and compared to numerical simulations.

Figure 1

(a) Numerical predictions (Ref. 31) of the dispersion relation of a surface wave on an array of identical mushrooms, where each line corresponds to a different patch length, $a$. (b) Surface wave mode index $n_{SW}$ as a function of patch length at 13.0 GHz. Inset: Schematic of the mushroom unit cell.

Figure 2

A comparison between the ideal Luneburg lens mode index profile and the stepped mode index profile of the fabricated device taken along a radial distance parallel to the lattice, where the discrete steps are a consequence of the finite pitch of individual mushroom elements. Inset: Schematic of a section of the thin Luneburg lens from above, demonstrating the change in mushroom patch length $a$, throughout the device. The scale bar provides a comparison of the size of the device to the wavelength of surface waves as they traverse the background medium ${\lambda }_{SW}$.

Figure 3

(a) Electric field magnitude data taken in a plane $\sim$1 mm above the surface wave Luneburg lens sample, using a near-field antenna as a point source for surface waves at ($x$ $=$ 0 mm, $y$ $=$ 50 mm) at 13 GHz. (b) Simulation of the instantaneous magnitude of the $E_z$ field above the same device at 13 GHz, using an impedance sheet approximation in the finite element method model. Both plots were normalized to the same color magnitude scale using the magnitude of the cylindrical wave fronts in the top corners of the two plots as a reference; regions where the surface waves do not traverse the Luneburg lens.