A Study on Scattering Performance of Reflectarray Element Covered by Dielectric Superstrate

Abstract

In this article, effect of a dielectric superstrate on scattering performance of reflectarray elements is clarified. At first, analytical electric field expressions of an infinite line current backed by a ground plane with the dielectric superstrate and so-called resonance conditions derived by Sugio et al., are reviewed. According to the electric field expressions and reciprocity, enhancement of the scattering field strength by the dielectric superstrate under the resonance conditions is expressed analytically. Since the scatterers are illuminated by the incident wave arriving from outside of the scatterers, the effect of its incident angle <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\theta _{i}$ </tex-math></inline-formula> on the scattering field strength is also studied. Based on inequalities that are derived from the electric field expressions, range of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\theta _{i}$ </tex-math></inline-formula> for enhancing the scattering field strength by the dielectric superstrate under the resonance conditions is found. As a result, it is found that the range of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\theta _{i}$ </tex-math></inline-formula> is independent of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\varepsilon _{r}$ </tex-math></inline-formula> when <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\varepsilon _{r} \gg 1$ </tex-math></inline-formula> , where <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\varepsilon _{r}$ </tex-math></inline-formula> is relative permittivity of the dielectric superstrate. Numerical simulation is performed, and it is demonstrated that the analytical formulae derived here are useful for predicting the effect of the dielectric superstrate on practical reflect array elements such as dipole, patch, and loop elements. Results and theories demonstrated in this article give quantitative guidelines on designing the reflectarray elements covered by the superstrate from the viewpoints of angle dependence, geometry, and permittivity of the superstrate.