Direct Ink Writing(DIW) for Fabrication of Gradient Dielectric Metamaterials with Designable Permittivity

With the growing demand for electronic devices operating within specific frequency bands—such as X-band dielectric resonator antennas—research on materials with precisely tunable dielectric constants has gained significant momentum. Metamaterials featuring artificially designed microstructures offer the potential to tailor their effective permittivity to meet specific application requirements.

Recently, Prof. Hong Wang and her team from the Southern University of Science and Technology (SUSTech) published a paper in Advanced Functional Materials (Impact Factor: 19.0) titled “Graded Dielectric Metamaterial with Designable Permittivity Fabricated by 3D Printing.

In this study, the researchers leveraged the high precision of Direct Ink Writing (DIW) 3D printing to achieve accurate control over the effective dielectric constant by precisely adjusting the geometric parameters of the metastructures. Furthermore, they established a predictive model for the dielectric constant of composite materials based on effective medium theory, enabling rational design of gradient dielectric materials for advanced electronic applications.
 

Research Highlights

In this study, the research team designed a ceramic metamaterial featuring an internal periodic waffle-like and honeycomb porous structure. Based on effective medium theory, they simulated the dielectric constant of the metamaterial and established a mathematical relationship between the dielectric constant and the geometrical parameters. By precisely tuning these geometrical parameters, the team achieved accurate control over the material’s permittivity.

Subsequently, ceramic metamaterial substrates with various dielectric constants were fabricated using Direct Ink Writing (DIW) technology. The experimentally measured dielectric constant values showed excellent agreement with the theoretical predictions.

Moreover, the study explored the application of tunable dielectric constants in antenna design, successfully fabricating a dielectric resonator antenna with a gradually varying permittivity. The antenna demonstrated broadband performance, covering the entire X-band frequency range, and exhibited remarkably high gain.

This approach to precisely controlling and designing dielectric constants provides a new pathway for developing high-performance electronic devices. The use of graded dielectric metamaterials holds great promise for significantly enhancing the overall performance of next-generation electronic systems.

Here are the research methods and data from the article:

Figure 1. Structural model of the metamaterial and comparison between simulated and calculated dielectric constants. (a) Three-dimensional models of the waffle and honeycomb metamaterial substrates. The electric field distributions were simulated using HFSS software, with the substrate material having a dielectric constant of 10. All structural units have an edge length of 3 mm and a thickness of 1.2 mm. (b) Dielectric constant variation curves of MgMoO₄-based waffle and honeycomb metamaterial substrates in the 4–6 GHz range, simulated using the effective medium theory with different A values. Five A values were used for the waffle structure and four for the honeycomb structure. (c) Calculation formula for the dielectric constant of the MgMoO₄-based metamaterial under the conditions W = L = 50 mm, b = 0.5 mm, h = 1.2 mm, and H = 1.7 mm. The curve represents the calculated results, and the scatter points represent the simulated results.

Figure 2. Fabrication and dielectric constant measurements of the metamaterials (n = 3). (a) 3D-printed anatase TiO₂-based waffle metamaterial with W = L = 50 mm, b = 0.5 mm, h = 1.2 mm, H = 1.7 mm, and a = 2 mm, sintered at 900 °C. (b) Comparison between predicted and measured dielectric constants of the anatase TiO₂-based waffle metamaterial. Three points were measured. The curve represents the theoretical values from the formula, while the scatter points represent the measured values. (c) 3D-printed MgMoO₄-based honeycomb metamaterial with W = L = 50 mm, b = 0.5 mm, h = 1.2 mm, H = 1.7 mm, and a = 2.3 mm, sintered at 850 °C. (d) Comparison between designed and measured dielectric constants of the MgMoO₄-based honeycomb metamaterial. Three points were measured. The curve represents the derived formula, and the scatter points correspond to the measured dielectric constants of samples with a = 0.9, 1.3, and 2.3 mm. (e) 3D-printed rutile TiO₂-based honeycomb metamaterial with W = L = 50 mm, b = 0.5 mm, h = 1.2 mm, H = 1.7 mm, and a = 4.4 mm, sintered at 1300 °C. (f) Comparison between designed and measured dielectric constants of the rutile TiO₂-based honeycomb metamaterial. Three points were measured. The curve represents the derived formula, and the scatter points correspond to the measured dielectric constants of samples with a = 1.5, 2.4, and 4.4 mm.

Figure 3. Antenna models and simulated results of reflection coefficients and radiation patterns. (a) Antenna using homogeneous MgMoO₄ as the dielectric block. The figure shows the reflection coefficient (S₁₁) in the 5–15 GHz frequency range; the inset depicts a schematic of the antenna structure. (b) E-plane (Φ = 0°) radiation pattern of the homogeneous MgMoO₄ antenna at 12.5 GHz, plotted as a function of θ. (c) Total radiation patterns of the same antenna at θ = 60° for 7.5, 10, and 12.5 GHz, plotted as a function of Φ. (d) Antenna using highly graded MgMoO₄ as the dielectric block; the reflection coefficient in the 5–15 GHz range indicates improved antenna performance. The inset shows the antenna model. (e) E-plane (Φ = 0°) radiation pattern of the highly graded MgMoO₄ antenna at 12.5 GHz, plotted versus θ. (f) Radiation patterns of the highly graded MgMoO₄ antenna at θ = 60° and frequencies of 7.5, 10, and 12.5 GHz, plotted versus Φ. (g) Antenna using MgMoO₄ with both dielectric constant and height gradients as the dielectric block; the reflection coefficient in the 5–15 GHz range shows significantly enhanced performance and greatly widened bandwidth. The inset shows the antenna model. (h) E-plane (Φ = 0°) radiation pattern of the antenna with combined dielectric constant and height gradients at 12.5 GHz, plotted versus θ. (i) Radiation patterns of the same antenna at θ = 60° and frequencies of 7.5, 10, and 12.5 GHz, plotted versus Φ.

Figure 4. Dielectric resonator antenna based on a designable dielectric constant. (a) Antenna model with a total length (l) of 36 mm, flare angle (α) of 30°, and width (w₀) of 6 mm. (b) 3D printing process. (c) 3D-printed antenna prototype, mounted on a copper ground plane and fed by a coaxial probe. (d) Instantaneous electric field distributions in the xy-plane at 8 and 12 GHz, with phases of 0° and 90°. Scale bar: 50 mm. (e) E-plane (Φ = 0°) radiation pattern at 10 GHz, plotted as a function of θ. (f) Total radiation patterns at θ = 60° for 8, 10, and 12 GHz, plotted as a function of Φ. (g) Simulated and measured reflection coefficients. (h) Achieved gain and total efficiency at θ = 60°. (i) Comparison with state-of-the-art antenna designs.

Conclusion

In this study, a novel metamaterial design method based on periodic internal structural units was proposed. By tuning the geometric parameters of the structural units, precise control of the dielectric constant was achieved. Combined with 3D printing technology, this approach enables rapid, cost-effective, and straightforward fabrication of metamaterials with tailored dielectric properties, providing a feasible manufacturing route for complex structures and diverse applications. Experimental results demonstrate that the dielectric constant of the metamaterials is influenced not only by the geometry of the structural units but also by the intrinsic dielectric constant of the substrate. By selecting appropriate substrate materials and optimizing structural designs, a wider range of dielectric constants can be achieved to meet different application requirements.

In the validation of X-band dielectric resonator antennas, the design based on gradient dielectric metamaterials significantly enhanced antenna performance: the bandwidth reached 6.2 GHz, covering the entire X-band (8–12 GHz), far exceeding the 1.7–4.2 GHz of conventional antennas, with a gain of up to 14.7 dB. This demonstrates that the proposed design strategy, combined with 3D printing fabrication, not only has great potential for antenna performance optimization but also provides new design concepts and technical routes for the development of high-frequency RF components, wideband antennas, and frequency-selective devices.

Overall, this study provides a systematic approach for the controllable design and rapid fabrication of high-performance metamaterials, showing broad application prospects and laying the foundation for the future development of multi-material, multifunctional printable metamaterials.