Phase Analysis for a Three-Layer Focusing Metasurface with Impedance Boundary Conditions

In this paper, we propose a method to theoretically analyze the phase shift limit of focusing metasurface. Particularly, impedance boundaries are used instead of lens units with multiple metal patterns for the maximum phase shift limit of the three-layer metal and double-layer dielectric structure. It is found that the phase is limited as no more than 400° by changing the capacitance value of the parallel equivalent circuit of capacitors and inductors. Based on this three-layer structure, a focusing lens with dimension of 480 mm×480 mm×7.5 mm (≈ 7.8λ×7.8λ×0.1225λ) operating at 4.9 GHz is proposed. The lens, consisting of 1600 units arranged in a 40×40 arrangement, can focus a vertically incident plane wave at a position z = 205 ~ 279 mm. The peak of the electric field along the oz-axis is 8 times higher than without it, revealing the exceptional focusing performance of the lens.