We experimentally realize a series of incommensurable metasurface stacks that transition from near-field coupling to a far-field regime. Based on a comparison between a semi-analytic model and measurements, we, furthermore, present an experimental study on the validity of the fundamental mode approximation (FMA). As the FMA is a condition for the homogeneity of a metasurface, its validity allows for strong simplification in the design of stacked metasurfaces. Based on this, we demonstrate a method for the semi-analytic design of stacked periodic metasurfaces with arbitrary period ratios. In particular, incommensurable ratios require computational domains of impractically large sizes and are usually very challenging to fabricate. This results in a noticeable gap in parameter space when optimizing metasurface stacks for specific optical features. Here, we aim to close that gap by utilizing the principles of the FMA, allowing for additional parameter combinations in metasurface design.

中文翻译：

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堆叠超表面的基本模式近似的实验验证及其在处理任意周期比率中的应用

我们通过实验实现了一系列不可公度的超表面堆栈，它们从近场耦合过渡到远场区域。基于半解析模型和测量值之间的比较，我们进一步对基模近似 (FMA) 的有效性进行了实验研究。由于 FMA 是超表面均匀性的条件，其有效性允许在堆叠超表面的设计中进行极大的简化。基于此，我们展示了一种具有任意周期比的堆叠周期性超表面的半解析设计方法。特别是，不可公度的比率需要不切实际的大尺寸计算域，并且通常很难制造。当针对特定光学特征优化超表面堆栈时，这会导致参数空间出现明显差距。