Enhancing Angular Stability in Magnitude and Phase of Frequency Selective Slabs Using Partial Derivatives Expansion Based on Equivalent Medium Theory

This article presents a novel partial derivatives expansion (PDE) based on equivalent medium theory for designing frequency selective slabs (FSSlabs) with excellent angular stability in both magnitude and phase. First, the change in phase under oblique incidence is mapped to the partial derivatives of the electromagnetic parameters using Taylor expansion. The angular stability of homogeneous slabs and 2-D frequency selective surfaces (2D-FSSs) are discussed based on the corresponding partial derivatives. Then, the ranges of normalized impedance and refractive index satisfying the angular stability condition under large-angle incidence are deduced. At last, using this condition, an FSSlab is designed and fabricated, and the measured results show that the FSSlab has excellent angular stability up to 60
$^{\circ}$
in the
$-$
3 dB passband from 3.0 to 4.1 GHz, with a fraction bandwidth (FBW) of 30.1%: 1) the insertion loss (IL) ripple is less than 0.8 dB and 2) the phase difference between normal and oblique incidences is less than 14
$^{\circ}$
and the phase difference between TE and TM polarizations is under 13
$^{\circ}$
. Remarkably, the profile of the FSSlab is only 0.19 wavelength at the center frequency. Compared with previous counterparts, the FSSlab designed by the proposed method shows lower IL and phase differences while maintaining a compact profile.