Fathnan Ashif A, Powell David A
Opt Express. 2018 Oct 29;26(22):29440-29450. doi: 10.1364/OE.26.029440.
Metasurfaces can implement a wide variety of wave-manipulation functions with sub-wavelength layers. They are typically created from resonant elements, thus their refraction properties depend strongly on frequency. The resulting chromatic aberration is undesirable for most applications, motivating recent efforts in the development of achromatic metasurfaces. However, it remains unclear whether there are any physical limits on the achievable operating bandwidth of achromatic metasurfaces. Here we address this question, considering a common microwave metasurface geometry based on three metallic layers, separated by dielectric substrates. Since each of these metallic layers is modeled as an impedance, we apply Foster's reactance theorem to determine the bandwidth over which they are physically realizable using passive, causal and lossless structures. We derive limits for the bandwidth and total size of the metasurface, showing that there is a trade-off between these two parameters. A higher angle of refraction, corresponding to a larger numerical aperture for a lens, further limits the realizable bandwidth. We consider both Huygens' and Omega-bianisotropic metasurface types, and show that the limit is more severe for bianisotropic metasurfaces, making them less suitable for broadband achromatic designs.
超表面可以通过亚波长层实现各种各样的波操纵功能。它们通常由谐振元件构成，因此其折射特性强烈依赖于频率。对于大多数应用而言，由此产生的色差是不理想的，这推动了近期在消色差超表面开发方面的努力。然而，尚不清楚消色差超表面可实现的工作带宽是否存在任何物理限制。在此，我们考虑一种基于三个金属层且由电介质基板隔开的常见微波超表面几何结构来解决这个问题。由于这些金属层中的每一层都被建模为一个阻抗，我们应用福斯特电抗定理来确定使用无源、因果和无损结构在物理上可实现它们的带宽。我们推导了超表面带宽和总尺寸的限制，表明这两个参数之间存在权衡。更高的折射角对应于透镜更大的数值孔径，这进一步限制了可实现的带宽。我们考虑了惠更斯型和欧米伽双各向异性超表面类型，并表明双各向异性超表面的限制更为严格，这使得它们不太适合宽带消色差设计。
