Design of Rectangular Waveguide-fed Metasurfaces for Near-Field Shaping using a Coupled Dipole Model

TL;DR

This paper tackles near-field shaping with rectangular waveguide-fed metasurfaces by accounting for strong inter-element coupling through a coupled-dipole model (CDM). Radiators are represented as magnetic $m_z$ and electric $p_y$ dipoles along the waveguide, and their interactions are captured by a matrix equation $\mathbf{G}^{mm}_{zz}\mathbf{G}^{me}_{zy}\mathbf{G}^{em}_{yz}\mathbf{G}^{ee}_{yy}\mathbf{m}_{z}\mathbf{p}_{y}=\mathbf{H}^{i}_{z}\mathbf{E}^{i}_{y}$, with polarizabilities $\alpha_{yy}^{ee}$ and $\alpha_{zz}^{mm}$ extracted from $S$-parameters; a surrogate optimization with $N_m=30$ slots spaced at $8.5$ mm ($\sim 0.28\lambda_0$) targets specific near-field patterns, including equal- and unequal-amplitude two-beam configurations and frequency-scanned beams. Experimental validation using substrate-integrated waveguides (SIWs) and planar near-field measurements shows good agreement with CDM predictions, confirming the approach’s accuracy and computational efficiency. The work delivers a fast, physics-informed design workflow for near-field control in wireless power transfer, imaging, and communications, with future avenues to include transition effects in the model and to deploy resonant radiators for richer phase control.

Abstract

We present the design of rectangular waveguide-excited metasurfaces for near-field shaping using a coupled dipole framework. Waveguide-fed metasurfaces are array-like radiating systems typically constructed from one or more waveguides loaded with a series of subwavelength metamaterial apertures that function as radiators. The use of subwavelength radiating elements distributed across the aperture enables electromagnetic field control with subwavelength precision, offering significant potential for near-field shaping. Leveraging these capabilities, we demonstrate that the near-field patterns of rectangular waveguide-fed metasurfaces can be tailored using the coupled dipole model, which accounts for mutual interactions between metamaterial radiating elements. The validity and effectiveness of the proposed approach are verified through full-wave simulations and experiments in the X-band.

Figures (4)

• Figure 1: Schematic of a rectangular waveguide-fed metasurface for near-field shaping. The geometry of individual metamaterial elements (e.g., rectilinear slots) is tuned to generate a desired field profile along the line defined by $\left(x,y=y_{tar},z=0\right)$.
• Figure 2: The extracted effective magnetic polarizability (left) and electric (right) polarizability as functions of frequency and slot length $s$ (inset).
• Figure 3: (a) Schematic of the designed metasurface example generating two beams at the target plane, realized with the substrate-integrated waveguide and grounded coplanar waveguide-to-SIW transition feeds. (b) Photo of the fabricated metasurface examples, each with $N_{m}=30$ rectangular slot radiators (photo edited for compact illustration). The metasurfaces are designed to generate two near-field focused beams with the same and different amplitudes (top, middle rows), and frequency-scanned beams (bottom row). (c) Measurement setup using a planar near-field scan system. The cross-sectional plots of the normalized squared electric field along the line $y=y_{ref}$ for (d) the equal-amplitude design, (e) the different peak-amplitude design, and (f) the frequency-scanned beam design.
• Figure 4: The evolution of the cost function for (a) the equal-amplitude design, (b) the different peak-amplitude design, and (c) the frequency-scanned beam design.