Harnessing Selective State Space Models to Enhance Semianalytical Design of Fabrication-Ready Multilayered Huygens' Metasurfaces: Part I - Field-based Semianalytical Synthesis

Abstract

Planar metasurfaces can profoundly control electromagnetic scattering. At microwave frequencies, such devices are typically implemented using multilayer cascades of patterned metallic sheets, whose design often requires time-consuming full-wave optimization. Here, we extend analytical models originally developed for sparse loaded-wire metagratings to accurately describe densely packed Jerusalem-cross meta-atoms embedded in standard printed circuit board (PCB) dielectric stacks. The model captures both near- and far-field coupling within and between layers, enabling efficient prediction of the dual-polarized response. Using this framework, we identify highly transmissive meta-atoms whose phase is controlled by the leg lengths of the Jerusalem crosses (microscopic design stage). This (phase)-(leg-length) "lookup table" allows rapid synthesis of Huygens' metasurfaces (macroscopic design stage), demonstrated through a full-wave-validated metalens exhibiting low-reflection beam manipulation. Notably, we implement a judicious scaling method to further extend the model to predict wideband meta-atom responses. In the companion paper (Part II), a hybrid machine-learning approach leverages this semianalytical framework to enhance accuracy without requiring the conventional exhaustive full-wave training, enabling ultrafast inverse design across the full parameter space. Overall, the presented methodology -- the standalone semianlytical scheme (Part I) and the machine-learning enhanced version (Part II) -- establishes an effective open-source toolkit for versatile, rapid, and highly accurate synthesis of fabrication-ready dual-polarized transmissive Huygens' meta-atoms and metasurfaces.

Figures (12)

• Figure 1: (a) Parallel arrays of periodic capacitively loaded wires affixed to laminates in a multilayer PCB configuration, illuminated by a transverse electric (TE) polarized plane wave. The goal to eliminate the reflected propagating wave is indicated by the cross on the corresponding red arrow. (b) The top view of layer 1, displaying the distributed impedance $\tilde{Z}$ of its wires. Although illustrated as short discrete reactive components, the wire is modeled as having a continuous, distributed impedance per unit length along the wire. For TE polarization, these wires are oriented in the direction of the electric field vector. (c) The same surface as (b), but including additional wires resulting in $90^\circ$ rotational symmetry of the system about the $y$-axis.
• Figure 2: (a) The reactive loading of the wires in Fig. \ref{['figIntro']}c represented by planar parallel plate capacitors. The unit cell is defined about a JC-shaped structure. A new "effective" loaded wire is shown in the red dashed box. The brown wires indicate the realization of the original capacitive loading in Fig \ref{['figIntro']}a. (b) Enlarged view of the unit cell. The distributed impedance of the "effective" wire is a function of the length $W$ of the leg of the JC.
• Figure 3: (a) A multilayered unit cell containing JCs at each of the five interfaces. The length $W_n$ of the leg of each JC can be varied to control the value of $Z_n$, and subsequently $T$ and $R$. (b) Example of a single interface ($n=2$) utilized to determine $Z_n(W_n)$.
• Figure 4: Distributed impedance $Z_n(W_n)$ as a function of the JC leg length $W_n$ for wires at the five interfaces of the MS, utilizing the parameters in Section \ref{['sec:DetZkWk']}. (a) $\Re(Z_n)$. (b) $\Im(Z_n)$. The data obtained using \ref{['eqTZW']} are indicated by the markers. The narrow solid curves are fifth degree polynomial fits for this data that are utilized by LAYERS. $W_n$ values are provided to 80 mil since beyond that value, proper solutions of \ref{['eqTZW']} were not found.
• Figure 5: Values of $|T_\ell|^2e^{i\phi_\ell}$ located in a complex unit circle for the meta-atom defined in Section \ref{['sec:DetZkWk']}. The dashed radials are drawn every $30^{\circ}$, and the solid circles are drawn at intervals of 0.1. (a) Results as calculated by LAYERS of an exhaustive sampling, $\Delta_W=2$ mil, with only $|T_\ell|^2>0.2$ displayed. The circled dots represent the two largest values of $|T_\ell|^2$ (i.e. the two closest values to the red circle $|T|^2=1$) in every phase interval of $5^{\circ}$. (b) The two largest LAYERS-computed values of $|T_\ell|^2$ in every phase interval of $5^{\circ}$ that were circled in (a) (blue dots), and the corresponding full-wave-computed values of $|T_\ell|^2e^{i\phi_\ell}$ for the same sets $\textbf{W}_\ell$. (c) The final lookup table consisting of the full-wave-calculated values of $|T_\ell|^2e^{i\phi_\ell}$ of (b), but with smaller values of $|T_\ell|^2$ removed.