  Metagratings (MGs), sparse (periodic) composites of subwavelength polarizable
particles (meta-atoms), have demonstrated highly efficient diffraction
engineering capabilities via meticulous tailoring of the interaction between
individual scatterers. To date, MGs at microwave frequencies have mostly been
devised for either transverse electric (TE) or transverse magnetic (TM)
polarized scenarios, which limits their use in many practical applications.
Herein, we bridge this gap and present a comprehensive semianalytical design
method for dual-polarized MGs with a separable response for TE and TM waves.
First, by relating a printed circuit board (PCB) compatible array of dog-bone
elements with the canonical dipole line analytical model, we establish a
meta-atom for TM-polarized MGs, featuring negligible interaction with TE waves.
Subsequently, we integrate the proposed configuration with a systematic
synthesis scheme to implement a TM beam splitter MG, harnessing the equivalent
dipole line model to resolve analytically the optimal meta-atom coordinates and
dog-bone polarizability, without resorting to full-wave optimization. Finally,
we show that a dual-polarized MG beam splitter can be conveniently synthesized
correspondingly, combining the TM-polarized structure as is with previously
reported TE-polarized MG designs. This work paves a clear path towards
integration of sparse, semianlaytically synthesized, efficient MGs in practical
dual-polarized communication and imaging applications.
