Angular Dispersion Analysis of Frequency-Selective Surfaces Based on Wavevector Domain Equivalent Impedance

For the angular dispersion issue of frequency-selective surfaces (FSSs), a novel analysis method based on wavevector domain equivalent impedance is proposed. The main concept is to change the view from the usual (x, y) space to the wave vector (kx, ky) space. Comprehensive analyses and comparisons are conducted regarding the resonant frequency shifts of dipole and loop FSSs under oblique incidence. The total equivalent impedance of the FSS is treated as the aggregate of equivalent impedances corresponding to numerous Floquet modes. A hierarchical relationship is established among the 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">$\boldsymbol {\theta }$ </tex-math></inline-formula>, wave vector (kx, ky), equivalent impedance <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$Z_{eq}$ </tex-math></inline-formula>, and reflection coefficient <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$S_{11}$ </tex-math></inline-formula>. The variation of the 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">$\boldsymbol {\theta }$ </tex-math></inline-formula> is observed to exert a discernible influence on the tangential wave vector, denoted as <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$k_{0}\textit {sin}\theta $ </tex-math></inline-formula>. This influence subsequently instigates a modification in the equivalent impedance, ultimately resulting in a shift in the resonant frequency of the FSS. Given the rapid convergence of higher order modes, a focused analysis of two primary modes proves sufficient for comprehending the overall behavior. The calculated S-parameters are essentially consistent with the simulated results, which demonstrates the accuracy of the proposed method.