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.
