Antireflection and Wavefront Manipulation with Cascaded Metasurfaces

Layered structures are widely used in optics to control wave reflection and propagation at interfaces but their thickness relative to the wavelength hinders their application in the radio-frequency regime. Here, we design and experimentally demonstrate cascaded metasurfaces with deeply subwavelength thickness that provide both antireflection and wavefront manipulation. We describe the systematic synthesis of the metasurface layers from a prescribed scattering response and demonstrate designs capable of providing near-perfect microwave transmission through glass as well as antireflection focusing of wireless signals from air into water.

Figure 1

Cascaded metasurfaces for antireflection and wavefront manipulation. (a) An illustration of a three-layer cascaded metasurface placed on the interface between two media. (b) A model for the transmission through the cascaded $n$-layer metasurface.

Figure 2

Antireflection from air into dielectric media. (a) The calculated sheet admittances $\mathrm{Im}(Y_i)$ for antireflection of a normally incident plane wave into media with relative permittivity ${\epsilon }_2$ and a phase change $\phi$. The admittances are all purely imaginary. (b),(c) Full-wave simulations of the magnetic field transmitted from air into media with (b) constant phase change $\phi =\pi /3$ and ${\epsilon }_2=10$, 40, and 70 (top to bottom) and (c) ${\epsilon }_2=78$ and phase changes $\phi =\pi /3$, $5\pi /12$, and $3\pi /4$ (top to bottom).

Figure 3

Wavefront manipulation using a metasurface that focuses a normal incident plane wave from air into different media (from ${\epsilon }_2=1$ to ${\epsilon }_2=80$) at 5-cm ($\lambda /2.5$) depth. The metasurface, having a total length of 10.4 cm ($0.83\lambda$), is evenly divided into 60 unit cells along the $x$ axis. (a) An example of the magnetic field for a metasurface that focuses a normal incident plane wave from air into water (${\epsilon }_2=78$). (b) The phase change across the metasurface as a function of its location. (c) The sheet admittances of the metasurface for focusing.

Figure 4

Wave impedance matching between air and glass. (a) A perspective view of the unit cell. The substrate is made of FR4 (${\epsilon }_2=4.2$). The thickness of the substrate between two metallic patterns is 2 mm and that of the outermost substrate is 1 mm. The cell size is $6\times 6\times 5{\mathrm{mm}}^3$. (b)–(d) The structures and dimensions of each impedance sheet: (b) the first sheet, $Y_1=0.0193j{\mathrm{\Omega }}^{-1}$; (c) the second sheet, $Y_2=0.0107j{\mathrm{\Omega }}^{-1}$; (d) the third sheet, $Y_3=0.0356j{\mathrm{\Omega }}^{-1}$. All units are in millimeters. (e) A photograph of the fabricated metasurface: scale bars 6 mm. (f) An image of the experimental setup. (g) The experimentally measured transmission between two panel antennas in air, with a 3-cm-thick glass placed in the center and having metasurfaces on the two surfaces of the glass as shown in (f). The graphs show the mean $\pm$ s.d. ($n=3$ technical trials). (h) The enhancement in transmission between the antennas obstructed by the glass slab, for the case in which the metasurfaces are placed on the glass slab. The theoretical calculations are based on Fabry-Perot resonance and the numerical simulations use an infinite periodic structure.

Figure 5

The unit-cell design of the antireflection metasurface focusing a normal incident plane wave from air into water at 5-cm ($\lambda /2.5$) depth. (a) A discretization study of the transmission and focusing efficiency as a function of the number of unit cells with ${\phi }_0=0$. (b),(c) The theoretical designed and physically realized (b) transmission efficiency and (c) phase changes for the eight unit cells. The shaded region area shows the area for $2\pi$ phase wrap. (d) The geometry of the unit cells from cell 1 to cell 8 (left to right) and from sheet 1 to sheet 3 (top to bottom), respectively: the units are millimeters. The corresponding sheet admittances and specific dimensions for each cell are stated in Tables 1 and 2, respectively. The water is simulated with a relative permittivity of ${\epsilon }_2=78$.

Figure 6

Antireflection focusing from air into 5-cm ($\lambda /2.5$) depth in water. (a) A perspective view of the metasurface using eight unit cells distributed in a circular ring form. Cells occupying the same background color are identical. (b) A photograph of the fabricated metasurface: a quarter of the metasurface is enlarged on the right. (c) A photograph of the experimental setup. (d) The normalized magnetic field intensity along the focusing depth with and without the metasurface (MS) from simulation (Sim.) and experiment (Exp.). The arrow indicates the full width at half maximum (FWHM) of $0.16\lambda$. (e),(f) The simulated (top) and measured (bottom) magnetic field intensity at the $x$-$z$ plane (e) without and (f) with the metasurface. (g),(h) The simulated (top) and measured (bottom) magnetic field intensity at the 5-cm-deep focal plane ($x$-$y$ plane) (g) without and (h) with the metasurface. The water is simulated with a complex relative permittivity ${\epsilon }_2=78-11.7j$.