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We analyze and design the reflection phase characteristics in metasurface based asymmetric Fabry-Perot cavities, consisting of a metallic metasurface backed by a ground metal plane. The metamaterial cavity is modeled using transmission line theory and effective surface admittance approach, where the free space and substrate are described by equivalent transmission lines. The individual metasurface is modeled by an equivalent surface admittance connected at the junction of the transmission lines. Analysis using the above model reveals that the effective metasurface susceptence and cavity thickness govern the resonance frequency of the cavity structure. While, the effective metasurface conductance at that frequency determines whether the overall cavity resonator is in under coupled, critically coupled or over coupled regimes. Therefore by appropriately controlling the metasurface effective conductance and the cavity thickness, the metasurface cavity can be designed to have desired resonant regime. In under and critically coupled regimes, the cavity resonator exhibits a reflection phase variation limited between 90° and 270°. While in over coupled regime, reflection phase variation from 0° to 360° is exhibited. We demonstrate and verify the above results using full wave EM simulations. Using an example metasurface consisting of cross shaped resonators, we demonstrate controlling effective metasurface conductance to realize any desired reflection amplitude and phase. The presented results provide important guidelines for realizing phase control devices such as lenses or beam deflectors. This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (Ministry of Science, ICT and Future Planning) (No. 2017R1A2B3004049).
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