Fractal-informed predictive theoretical framework and design strategy for structured absorbers

Electromagnetic functional metamaterials with multi-scale configurations are widely used in the fields of electromagnetic compatibility, radiation protection and radar stealth. However, conventional transmission line theory is unable to establish an analytical wave impedance model for complex geometric metamaterials, which severely restricts the performance prediction and forward design of broadband microwave-absorbing structures. Herein, we propose a practical predictive theoretical framework for lossy dielectric metamaterial absorbers based on fractal geometry and material-structure coupling effects, which accurately predicts the absorption peak positions, and reveals the intrinsic mechanisms of absorption peak formation and bandwidth expansion. Three typical fractal metamaterial absorbers with the thickness of 10 mm, including gradient honeycomb, multi-layer stepped stack, and multi-layer nested square frame structures, were fabricated via FDM 3D printing technology, exhibiting excellent microwave absorption performance in the ultra-wide frequency range of 2–40 GHz,. Compared with the conventional transmission line theory, the proposed fractal-modified theory significantly reduces the prediction error of electromagnetic performance in the high-frequency bands with the accuracy maximally improved by 64.4%. This work provides a robust theoretical tool and new design strategy for the forward design of ultra-broadband electromagnetic functional metamaterials.