Analysis and design of metamaterial reflectarray using combination of multilayer mushroom-structure

We have previously proposed to use reflectarrays to eliminate blind zones in a propagation area of very high-speed wireless communication systems and have shown that one candidate of such reflectarrays is metamaterial reflectarray which has mushroom structure. The reflection phase of mushroom structure can be calculated applying a parallel resonant circuit model with inductance L and capacitance C. The value of reflection phase is equal to zero at LC resonant frequency and the value of reflection phase at given frequency is changed using inductance L and capacitance C because the resonant frequency is changed by these. There are typically three control methods for L and C changing. The first method employs varactor diodes and changing the voltage, the second method changes the resonant frequency depending on the position of the mushroom structure, and the third involves changing the patch length of the mushroom structure to achieve a difference in capacitance. Although, it is necessary to achieve a reflection phase range from + π to π at the desired frequency for the strict design of a reflectarray, it is difficult to achieve this because of manufacturing limitation. On the other hand, a multi-layered mushroom structure is used to increase the capacitance in order to achieve low frequency resonance. To address this issue, this paper proposes novel metamaterial reflectarray which has combination of multi-layer mushroom structures and can achieve arbitrary desired inductance L and capacitance C. Since the value of Inductance L is determined by patch height from ground plane, we adopt several kind of thicknesses for substrate and combine them. To eliminate manufacturing difficulty when we make patches closer to each other for achieving large capacitance value, we slightly change adjacent patches height using multi-layer structure. By using proposed method, we design 45 degree beam control reflectarray. Theoretical result using LC resonant circuit model agrees with simulation result using finite element method.