${\hbox {Q}}$ Factor Analysis of Reflectarray Elements Investigating the Effects From Angle of Incidence Using Floquet Modes

A theoretical approach to investigate the effects of incidence angle on reflection properties of reflectarray elements is developed for the first time. Utilizing coupled-mode theory and Floquet analysis, the dependence of reflection coefficient on incidence angles and plane of incidence is presented in terms of Q factors. A unit cell excited by a plane wave at different incidence angles is shown to have varying coupling conditions and reflection properties. Emphasis is laid on elements located on planes where extremities in performance tend to occur. Anomalous phase characteristics are observed for particular polarization and incidence angles. The antenna element properties are assessed in terms of maximum reflection loss and slope of the reflection phase. A thorough analysis is performed at K a band and the results obtained are verified using full-wave simulations. Reflection coefficients over a 749-element reflectarray aperture for a broadside radiation pattern are presented for a couple of cases and the effects of coupling conditions in conjunction with incidence angles are demonstrated. The presented theory provides explicit physical intuition and guidelines for efficient and accurate reflectarray design.