Density-Based Topology Optimization for Characteristic Modes Manipulation

TL;DR

The work addresses manipulating characteristic modes of conducting structures by integrating density-based topology optimization with characteristic mode analysis (CMA) in a MoM framework. It introduces an auxiliary loss term and adjoint sensitivity to compute material gradients, combined with density and projection filters to drive a gradient-based optimization toward near-binary designs. The method decouples geometry from feeding synthesis, enabling optimization of modal resonance, bandwidth, and multi-mode performance without prespecifying excitation. Results across single- and multi-mode scenarios demonstrate improved computational efficiency, reveal thresholding-induced resonance shifts, and highlight practical considerations such as area and bandwidth constraints for antenna design.

Abstract

A density-based topology optimization framework is developed to manipulate characteristic modes of conducting surfaces. The adjoint sensitivity analysis provides an efficient computation of the material gradient utilized by the local optimizer to update the material distribution. The modal approach naturally separates geometry and feeding synthesis, demonstrating its ability to optimize modal quantities while maintaining computational efficiency through gradient-based updates. The framework's properties and performance are illustrated through several examples, including single-mode resonance control, modal Q-factor, and multi-mode optimization.

Figures (12)

• Figure 1: The structure used to investigate the behavior of the material model. The region is divided into three parts: a passive region (white) with $\rho_t = 0$ (vacuum), a fixed region (black) with $\rho_t = 1$ (PEC), a design region (gray) with variable $\rho \in[0,1]$, which translates to $R_\mathrm{s}(\rho)$ through \ref{['eq:Interpolation']}. Hence, $\rho=0$ leads to a meander line antenna, while $\rho=1$ results in a slot-loaded plate.
• Figure 2: Contour plots showing magnitudes of the both parts $\lambda_1$ and $\delta_1$ of the first characteristic number $\xi_1=\lambda_1-\mathrm{j}\delta_1$ as a function of electrical size $ka$ and design variable $\rho$ which relates the surface resistivity $R_\mathrm{s}(\rho_t)$ through \ref{['eq:Interpolation']}. The structure transitions between two geometries as $\rho$ varies from 0 to 1 and is represented by each marker, see snapshots above the axis. The minimum values of the color bars are truncated to improve the readability. The top panes show the characteristic angles $\alpha_1$ of both extreme cases with $\rho = \{0,1\}$ to highlight the resonance.
• Figure 3: Flowchart adapted from tucek2023TopOptMoM_minQ illustrates the density-based topology optimization process for manipulating characteristic modes.
• Figure 4: The convergence history of three runs of the topology optimization task \ref{['eq:MakeModeResonant1']} with different values of heuristic parameter $\nu$ included in the objective. The parameter $\nu$ influences the magnitude of the imaginary part of the characteristic number and allows the optimizer to converge to different results. A few snapshots of the density distribution from selected iterations of the run with $\nu=0.1$ are included below the convergence plots and highlighted by the red markers.
• Figure 5: The frequency sweep of of characteristic angle $\alpha_1$ for all three designs optimized at electrical size $ka=0.5$ (black lines). These near-binary solutions are hard-thresholded, impacting performance as shown by the red lines. The thresholded designs are shown as the bottom panes.