Metamaterials are artificial materials designed with specific unit cell configurations and/or geometric structures. They can be engineered to achieve new properties, such as special values of permittivity and permeability. These characteristics can also lead to negative and zero refractive indices, as well as super and hyper lenses that go beyond the diffraction limit. Extra-thin metamaterials—or metasurfaces—have recently attracted substantial attention because of their easy fabrication, relatively low effective surface refractive index loss, and more compact size of traditional bulk metamaterials.1–6 Surface plasmon polaritons (SPPs) are special surface waves (in the optical frequency) that exist on the interface between metal and dielectric materials. Due to the tight binding ability and strong confinement of electromagnetic fields, many optical applications (e.g., biological sensing, super-resolution imaging, opto-electronics, and nanophotonics) have been developed based on SPPs. It has been more difficult, however, to create highly confined surface waves at lower frequencies.
The concept of spoof SPPs7,8 has been proposed to lower the plasmon frequency of SPPs from the optical region to terahertz and microwave regions. Since metasurfaces are planar materials, it is thought that they can be used to control spoof SPPs and other surface waves. Transformation optics (TO) can be applied to metamaterials and facilitate new methods for manipulating electromagnetic waves. Together with geometrical optics (GO), i.e., the description of propagating light rays, new systematic tools for the design of complex devices that use gradient index metamaterials (materials with gradual variation in refractive index) are now available.
We incorporated TO and GO theories into the designs of novel metasurface lenses. With these lenses, we adopted the concept of spoof SPPs to obtain highly confined surface waves at microwave and terahertz frequencies. We chose U-shaped metallic patches—shown in Figure 1(a)—as the constituent units for these metasurface lenses. The metallic patches can support spoof SPPs, and they possess very low plasmon frequencies.
The first metasurface lens that we designed is based on a Luneburg (spherically symmetric gradient-index) lens, but the circular focusing curve is flattened through the application of quasi-conformal mapping.5 The transformed distribution of the metasurface lens surface refractive index is shown in Figure 1(b). The U-shaped unit cells are asymmetric structures. Therefore, the 2D surface refractive index is anisotropic. The degree of anisotropy (α), however, is small and close to an intrinsic value—see Figure 1(c)—that is a result of the quasi-conformal mapping. We thus used the y component of the surface refractive index to design the metasurface lens: see Figure 1(d).
Figure 1. Design process for the transformation optics (TO) metasurface lens. (a) Schematic of the U-shaped unit cell. (b) Distribution of the surface refractive index calculated through quasi-conformal mapping. (c) Parametric curves of the surface refractive index, n, and the anisotropic degree, α. Dashed red line shows the intrinsic anisotropic value of the lens. (d) Schematic of the TO metasurface lens.
We used a Vivaldi antenna array as the source of the metasurface lens. When the lens is excited by the different array antennae, it emits beams in different directions and with high directivity (see Figure 2). Our near electric-field distribution simulations and measured results for the lens are in good agreement. The results also showed that the metasurface lens has a broad bandwidth (8–10GHz) centered on the designed frequency of 9GHz.
Figure 2. Comparison of near electric-field distribution (x components) simulations (top panels) and measurements (bottom panels) for the TO metasurface lens, at (a) 8GHz, (b) 9GHz, and (c) 10GHz. Simulation and measurement results are shown when the right (I and IV), central (II and V), and left (III and VI) antennae are excited.
We designed our second metasurface lens based on GO theory.6 Unlike for our first case, we did not ignore the anisotropy of the U-shaped unit cells. Instead with this metasurface lens we used the anisotropy to combine a Maxwell fisheye lens and a Luneburg lens into a single lens. The design principle for this bi-functional metasurface lens (see Figure 3) is based on the fact that the anisotropy decreases as the distance between the U-shaped unit cell to the lens center increases. Furthermore, the light path is nearly parallel to the principle axis of the lens—see Figure 3(b) and (c)—when the anisotropy is strong. Consequently, we were able to separate the two principle components of the surface refractive index tensor and realize different functions for different directions. We varied the depth of the U-shaped unit cell to fit both the Luneburg lens refractive index profile (x component of the surface refractive index tensor) and the fisheye lens (y component of the tensor). The bi-functional metasurface lens, therefore, performs like a Luneburg lens along the horizontal optical axis and like a Maxwell fisheye lens along the vertical optical axis. We conducted numerical simulations and experiments in the microwave frequency range that clearly show the bi-functional characteristics of our lens (see Figure 4).
Figure 3. (a) Schematic diagram of the bi-functional anisotropic metasurface lens. The blue and red arrows indicate the directions of the two optical axes. (b) Ray tracing diagrams for the anisotropic metasurface lens when nx satisfies the ideal Luneburg distribution for a source on the horizontal optical axis and (c) fisheye distribution for a source on the vertical axis. When observed from the horizontal optical axis, the metasurface is a Luneburg lens, and when observed from the vertical optical axis it is a fisheye lens. (d) Comparison of the ideal surface indices of refraction for Luneburg and fisheye lenses with those for the realistic metasurface lens (nx and ny).
Figure 4. Full-wave (a) simulation and (c) measured results of the electric- field (Ex)distributions on an observation plane that is 1mm above the metasurface when the electric dipole is on the horizontal optical axis. (b) The simulated Ex distribution on a vertical observation plane passing through the horizontal optical axis, showing the nature of the surface wave inside the metasurface lens. Full-wave (d) simulation and (f) measured results of the Eydistributions on the observation plane that is 1mm above the metasurface. (e) The simulated Eydistribution on a vertical observation plane passing through the vertical optical axis.
Using TO and GO theories, we designed and built two metasurface lenses that feature U-shaped metallic patches as the unit cells. The anisotropy of the unit cell can be used to realize a bi-functional lens design. Our design approach can now be applied to other metasurface devices. So far we have conducted experimental testing on our materials in the microwave frequency range, but similar tests can be extended into terahertz frequencies. We also plan to combine holographic optics theory with TO and GO to produce planar or conformal integrated systems using metasurfaces.
Tie Jun Cui, Xiang Wan
Tie Jun Cui received his PhD in 1993 and is currently a Cheung-Kong professor in the Department of Radio Engineering. His research interests include metamaterials, computational electromagnetics, and millimeter wave technologies. He has published more than 200 peer-reviewed journal papers.
1. N. Yu, P. Genevet, M. A. Kats, F. Aieta, J.-P. Tetienne, F. Capasso, Z. Gaburro, Light propagation with phase discontinuities: generalized laws of reflection and refraction, Science 334, p. 333-337, 2011.
2. S. Sun, Q. He, S. Xiao, Q. Xu, X. Li, L. Zhou, Gradient-index meta-surfaces as a bridge linking propagating waves and surface waves, Nat. Mater. 11, p. 426-431, 2012.
3. A. Pors, M. G. Nielsen, R. L. Eriksen, S. I. Bozhevolnyi, Broadband focusing flat mirrors based on plasmonic gradient metasurfaces, Nano Lett. 13, p. 829-834, 2013.
4. X. Ni, N. K. Emani, A. V. Kildishev, A. Boltasseva, V. M. Shalaev, Broadband light bending with plasmonic nanoantennas, Science 335, p. 427, 2012.
5. X. Wan, W. X. Jiang, H. F. Ma, T. J. Cui, A broadband transformation-optics metasurface lens, Appl. Phys. Lett. 104, p. 151601, 2014.
6. X. Wan, X. Shen, Y. Luo, T. J. Cui, Planar bifunctional Luneburg-fisheye lens made of an anisotropic metasurface, Laser Photon. Rev.
, 2014. doi:10.1002/lpor.201400023
7. J. B. Pendry, L. Martín-Moreno, F. J. Garcia-Vidal, Mimicking surface plasmons with structured surfaces, Science 305, p. 847-848, 2004.
8. F. J. Garcia-Vidal, L. Martín-Moreno, J. B. Pendry, Surfaces with holes in them: new plasmonic metamaterials, J. Opt. A: Pure Appl. Opt. 7, p. S97-S101, 2005.