Modeling and analysis of quasi-periodic arrays

Planar quasi-periodic arrays are widely used in many electromagnetic devices such as metasurfaces, reflectarray antennas, nano particle arrays, etc. They comprise similar elements located on periodic grids. In this work, we compare the reflection phase of elements in the array between the designed value and the practical one. This difference is mainly because real quasi-periodic arrays break the periodicity assumption used in computing the designed element phase. To study this error, we develop a formulation based on Floquet theory to compute the reflection phase of a unit-cell in a practical array. We observe that the error can be significant for elements with high-Q resonances and can deteriorate the performance of reflectarray antennas or metasurfaces. As a remedy, we develop a workflow for element phase correction based on full-wave simulation of the entire array. An improvement in performance is observed for arrays with high-Q resonances.