Unveiling the Properties of Metagratings via a Detailed Analytical Model for Synthesis and Analysis

Abstract

We present detailed analytical modelling and in-depth investigation of wide-angle reflect-mode metagrating beam splitters. These recently introduced ultrathin devices are capable of implementing intricate diffraction engineering functionalities with only a single meta-atom per macro-period, making them considerably simpler to synthesize than conventional metasurfaces. We extend upon recent work and focus on electrically-polarizable metagratings, comprised of loaded conducting wires in front of a perfect elecric conductor, excited by transverse-electric polarized fields, which are more practical for planar fabrication. The derivation further relates the metagrating performance parameters to the individual meta-atom load, facilitating an efficient semianalytical synthesis scheme to determine the required conductor geometry for achieving optimal beam splitting. Subsequently, we utilize the model to analyze the effects of realistic conductor losses, reactance deviations, and frequency shifts on the device performance, and reveal that metagratings feature preferable working points, in which the sensitivity to these non-idealities is rather low. The analytical relations shed light on the physical origin of this phenomenon, associating it with fundamental interference processes taking place in the device. These results, verified via full-wave simulations of realistic physical structures, yield a set of efficient engineering tools, as well as profound physical intuition, for devising future metagrating devices, with immense potential for microwave, terahertz, and optical beam-manipulation applications.

Omega-bianisotropic metasurface for converting a propagating wave into a surface wave

“…As a concluding remark, metasurfaces may not represent the best solution for the matter at hand and other strategies have to be considered. For instance, a recently emerged concept of metamaterials-inspired diffraction gratings (or metagratings) have demonstrated unprecedented efficiency in manipulating scattered waves with sparse arrays (contrary to metasurfaces) of polarizable particles [45][46][47]. Due to the sparseness, metagratings inherently possess strong spatial dispersion, what (together with a straightforward design procedure [48]) can be beneficial for solving the conversion problem.…”

Arbitrary Diffraction Engineering With Multilayered Multielement Metagratings

“…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].…”

“…The third term accounts for the fields produced by the kth wire on its shell. Similar to [23], [44], [45], [60], due to the singularity of the Hankel function at the origin, it is not possible to use (7)- (13) as is at (y, z) → (d k , h k ), and a more subtle treatment is required.…”

“…Lastly, after evaluating the load impedancesZ k of (18) that would lead to the desired induced currents I k of (17), we harness our previous work to calculate the printed capacitor width W k [ Fig. 1(c)] that would realize the required distributed load impedanceZ k = 1/(jωlC k ), where C k is the load capacitance of the kth wire, and l is the periodicity along the x axis [44], [45]. Specifically, when the trace width is equal to the gap between traces w = s as in our case, we can approximate the capacitor width following W k = 2.85K corr C k /ε eff,r [mil/fF] [65], where K corr is a frequency dependent correction factor (at 20GHz and w = s = 4mil utilized in Section III it was previously found that K corr = 0.947), and the effective permittivity is given by ε eff,r = (ε n k + ε n k +1 )/(2ε 0 ), where z = h k = t n k is the vertical coordinate of the wire [45].…”

“…Subsequently, we devise an additional set of nonlinear constraints, guaranteeing that the required currents could be generated by loading the conducting wires with reactive (capacitive) elements, such that each meta-atom is passive and lossless. Resolving these two sets of linear and nonlinear equations while minimizing power dissipation in realsitic conducting wires, estimated analytically following [44], yields the complete conductor layout, i.e. the wire positions and the capacitor widths, to implement the desirable diffraction pattern.…”