Analytical Design of Printed Circuit Board (PCB) Metagratings for Perfect Anomalous Reflection

Abstract

We present an analytical scheme for the design of realistic metagratings for wide-angle engineered reflection. These recently proposed planar structures can reflect an incident plane wave into a prescribed (generally non-specular) angle with very high efficiencies, using only a single meta-atom per period. Such devices offer a means to overcome the implementation difficulties associated with standard metasurfaces (consisting of closely-packed subwavelength meta-atoms) and the relatively low efficiencies of gradient metasurfaces. In contrast to previous work, in which accurate systematic design was limited to metagratings unrealistically suspended in free space, we derive herein a closed-form formalism allowing realization of printed-circuitboard (PCB) metagrating perfect reflectors, comprised of loaded conducting strips defined on standard metal-backed dielectric substrate. The derivation yields a detailed procedure for the determination of the substrate thickness and conductor geometry required to achieve unitary coupling efficiencies, without requiring even a single full-wave simulation. Our methodology, verified via commercial solvers, ultimately allows one to proceed from a theoretical design to synthesis of a full physical structure, avoiding the time-consuming numerical optimizations typically involved in standard metasurface design.

Arbitrary Diffraction Engineering With Multilayered Multielement Metagratings

“…The longitudinal wavenumbers corresponding to the mth mode in the nth layer are given by β m,n = k 2 n − k 2 t,m , {β m,n } ≤ 0. Given the period Λ and the incident angle θ in , the indices of the propagating modes in the nth layer m n,prop must satisfy [45] −…”

“…As shall be detailed in Sections II-D and II-E, this choice would provide the sufficient number of degrees of freedom to obtain the desired diffraction control with a passive lossless device. As in [42], [44], [45], [58], [60], we analyze the problem by expressing the fields in space as a superposition of two sets: one corresponding to the incident field scattered off the stratified media configuration in the absence of the loaded wires (external field); the other is produced by the current induced in the wires by the polarizing impinging wave. In contrast to this previous work, however, dealing with the multilayer PCB MG configuration requires accounting for multiple reflections at the boundaries between the various layers, similar to [11], [61]- [64].…”

“…1). We utilize capacitively-loaded wires as meta-atoms in our multilayered printed-circuit-board (PCB) device, extending our previously developed [44], [45] (and experimentally verified [46]) detailed rigorous analytical model to relate the scattered fields to the individual wire positions and capacitor geometries. In the extended model, incorporating an arbitrary number of elements and an arbitrary stack of different dielectric layers, the full electromagnetic coupling between the meta-atoms (including multiple reflections and near field phenomena) is taken into account, allowing reliable resolution of the currents induced on the various wires in response to the incident fields, and subsequently the scattered ones.…”

Accurate Metasurface Synthesis Incorporating Near-Field Coupling Effects

“…This has motivated the development of deeply subwavelength meta-atoms [7,12], with feature sizes on the order of λ/200. For metasurfaces operating at Wband frequencies (75 -110 GHz) and higher, the resulting feature sizes are too small for conventional printed circuit board fabrication techniques, so simpler geometries such as dogbone [13][14][15] must be used. This frequency range is of interest for applications such as wireless communication [16] and radar [17,18], and metasurfaces should enable devices such as efficient transmitarray antennas [19,20].…”

“…Early works on near-field interaction in metamaterials aimed to model the propagation of magneto-inductive waves in arrays of split ring resonators [23], to analyze tunability through modifying lattice parameters [24] and to analyze optical activity of twisted dimers [25,26]. Furthermore, several recent works propose analytical de-sign approaches for metagratings based on rigorous descriptions of the mutual interaction of individual particles [15,[27][28][29][30]. While these works on near-field coupling in metagratings provide full insight into the interaction of individual scatterers and demonstrate highly efficient devices, they have been largely restricted to reflective operation at large angles.…”