Generalized Bimode Equivalent Circuit of Arbitrary Planar Periodic Structures for Oblique Incidence

This work presents, for the first time, a generalized bimode Foster’s equivalent circuit for characterization of 2-D planar periodic structures (PPSs) with arbitrary geometry at oblique incidence. It considers the interactions between the fundamental TE and TM modes without any restriction within the bimode bandwidth of the geometry. The proposed circuit is only composed of frequency-independent LC elements, which can be extracted systematically from electromagnetic (EM) simulations. The reactive immittances obtained in the process fulfill Foster’s theorem, enabling the design process of PPS-based devices using standardized synthesis techniques from the circuit theory. To demonstrate its viability and general nature, equivalent circuits are extracted for different single-layer and multilayer PPS composed of rotated dipoles under oblique incidence
$\theta $
= 20° and
$\varphi $
= 30° and including dielectrics. Excellent agreement is found between the response of the circuit model and the EM simulation in all cases. Finally, to validate experimentally the proposed equivalent circuit and highlight its applicability, a 90° reflective linear-polarization (LP) rotator centered at 25 GHz and under oblique incidence,
$\theta $
= 30° and
$\varphi $
= 0° (TE), is designed, manufactured, and tested. The agreement between the circuit response, the EM simulation, and the measurement underlines the potential of the new equivalent circuit for PPS design under oblique incidence.