On the Aperture Size of Digitally Coded Metasurfaces for Beam Steering Applications using Anomalous Reflection

This paper investigates the minimum size of the metasurface needed for beam steering applications using anomalous reflection. First, using 1-bit and 2-bit digitally coded unit cells, we analytically model a programmable metasurface in MATLAB for a reflected beam direction of
$\theta_{r}=30^{\circ}, \phi_{r}=0^{\circ}$
, and perform the far-field radiation pattern analysis for different aperture sizes. We observe the metasurface size of
$10\lambda_{0}\times 10\lambda_{0}$
(where
$\lambda_{0}$
is the free-space wavelength at 10.5 GHz) provides anomalous reflection in the desired direction having beamwidth of nearly 5° for both 1-bit and 2-bit coding. We verify the reflection angle and half-power beamwidth (HPBW) obtained from the analytical method with the full-wave electromagnetic simulation using CST Microwave Studio. It is also observed that the 2-bit coded metasurface having
$10\lambda_{0}\times 10\lambda_{0}$
size provides a far-field pattern with a reduced sidelobe level (SLL) of nearly −11.54 dB compared to 1-bit.