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Permittivity Characterization of 3D-Printed Materials at Millimeter Waves

This study characterizes the permittivity of various commercial 3D-printed materials in the 70–110 GHz millimeter-wave range using an open-waveguide extraction method, providing essential data to support the development of novel antennas and metasurfaces for 6G and beyond wireless communication technologies.

Original authors: Kamil Anıl Işık, Mohammad Mahdi Asgari, Xuchen Wang, Maxim Masyukov, Irina Nefedova, Zachary Taylor, Viktar S. Asadchy

Published 2026-07-21

📖 4 min read☕ Coffee break read

CC BY 4.0

Original authors: Kamil Anıl Işık, Mohammad Mahdi Asgari, Xuchen Wang, Maxim Masyukov, Irina Nefedova, Zachary Taylor, Viktar S. Asadchy

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine the invisible ocean of radio waves that surrounds us, carrying everything from your favorite songs to the next generation of internet. For decades, engineers have built antennas and lenses using standard materials like glass or plastic, knowing exactly how these materials interact with those waves. But now, a new technology called 3D printing is shaking things up. It allows us to build complex shapes layer by layer, like a high-tech printer creating a sculpture out of melted plastic or liquid resin. The problem? While we know how to print a cool-looking vase, we don't always know how the plastic inside that vase behaves when hit by super-fast, high-frequency waves.

To understand this, think of "permittivity" as a material's "personality" when it meets an electromagnetic wave. Some materials are like shy introverts that let the waves pass right through without much fuss, while others are like energetic party-goers that absorb the waves or slow them down significantly. If you want to build a super-fast antenna for the future of wireless communication (often called 6G), you need to know exactly which "personality" your 3D-printed material has. Without this knowledge, your antenna might be like a radio tuned to the wrong station—static and useless. This is the puzzle scientists are trying to solve: figuring out the electromagnetic personality of the colorful plastics and resins we use to print our world.

In this study, a team of researchers decided to test the "personalities" of various 3D-printed materials using a specific slice of the radio spectrum known as millimeter waves, specifically between 70 and 110 GHz. This range is like the high-speed highway of the future, where data travels incredibly fast, but it's also a tricky place to measure things because the waves are so short. To do this, the team used a clever trick called the "open-waveguide" method. Imagine a tunnel (the waveguide) designed to guide waves like water through a pipe. Instead of trying to perfectly fit a 3D-printed block into this tiny tunnel—which is hard because the tunnel is so small and the block might be slightly uneven—they simply placed the material right at the mouth of the tunnel. They then tightened the tunnel's flanges (like clamps) around the material just enough to hold it in place.

The researchers treated the material like a gatekeeper in an electrical circuit. By measuring how the waves bounced off and passed through this gate, they could mathematically figure out the material's permittivity without needing a perfect fit. They tested a colorful lineup of materials: seven different types of PLA plastic (in Green, Blue, Red, Silver, White, Black, and Transparent) and two types of liquid resin (Black and White). To make sure their measurements were fair, they used a torque meter to tighten the clamps with the exact same force every time, preventing the material from bending or getting squished, which would have messed up the results.

The results revealed some surprising differences. Even though many of the plastics came from the same brand and were just different colors, they didn't all act the same. The Silver PLA and Black Resin turned out to be the most "interactive" with the waves, showing the highest permittivity values, averaging above 2.7. In contrast, the Blue PLA was the most "shy," with the lowest value near 2.45. When it came to how much energy the materials wasted (called the "loss tangent"), the Silver PLA and Black Resin were the most wasteful, losing more energy as heat, especially at the higher end of the frequency range. On the other hand, the Transparent, Green, and Red PLA were the most efficient, wasting the least amount of energy, making them potentially better choices for devices that need to be very efficient at high speeds.

The team found that for most of these materials, their "personality" stayed pretty consistent across the 70 to 110 GHz range, meaning they didn't have any weird resonances or sudden changes in behavior in this specific band. However, they noted that measuring how much energy was lost (the imaginary part of permittivity) was a bit trickier for the materials that lost very little energy, as tiny measurement errors could lead to bigger uncertainties in those calculations. Ultimately, the study confirms that while 3D-printed materials are promising for building future antennas and lenses, you can't just assume all plastics are the same. Even a simple change in color or the type of printer used can change how the material handles the high-speed waves of tomorrow's internet. This work provides a reliable map for engineers to navigate these materials, ensuring that the 3D-printed gadgets of the future are built with the right ingredients for the job.

Technical Summary: Permittivity Characterization of 3D-Printed Materials at Millimeter Waves

Problem Statement
The rapid advancement of additive manufacturing has introduced a new class of dielectric materials for electromagnetic applications, including antennas, lenses, and metasurfaces. While conventional materials possess well-documented permittivity across wide frequency ranges, the electromagnetic properties of commercially available 3D-printed materials remain insufficiently characterized, particularly in the millimeter-wave (mmWave) spectrum. Existing literature has extensively covered the GHz and THz ranges using resonant or free-space transmission-line methods. However, a significant measurement gap exists between 50 GHz and 200 GHz. This specific range (70–110 GHz) is critical for emerging 6G and beyond wireless communication technologies, yet reliable permittivity data for 3D-printed polymers and resins within this band is largely unavailable. Furthermore, traditional closed-waveguide methods face challenges at these frequencies due to the difficulty of achieving a perfect fit for samples within the small waveguide apertures.

Methodology
To address this gap, the authors employed an open-waveguide extraction method to characterize the complex permittivity of various 3D-printed materials between 70 GHz and 110 GHz. The experimental setup involved placing a material sample of thickness $d$ between two waveguide flanges (WR10 waveguide, 2.54 mm × 1.27 mm aperture), creating a discontinuity modeled as an equivalent $\pi$ -circuit.

Key methodological steps included:

Measurement: S-parameters were measured using an E8361C PNA Network Analyzer equipped with submillimeter-wave extenders. Thru-Reflect-Line (TRL) calibration was applied to remove systematic errors and define the phase reference plane.
Extraction: For samples with thickness $d \leq \lambda_d/10$ , an analytical formula was used to extract the shunt admittance ( $Y_p$ ) and subsequently the relative permittivity ( $\varepsilon_r$ ). For the thicker samples used in this study ( $\lambda_d/10 < d < \lambda_d/2$ ), numerical optimization was performed using ANSYS HFSS. The simulated shunt admittance, parametrized by permittivity, was fitted to the measured values to extract the real and imaginary parts of the permittivity.
Sample Preparation: The study utilized seven types of Ultimaker PLA (Green, Blue, Red, Silver, White, Black, Transparent) and two Formlabs resins (Black, White). To ensure measurement accuracy, the authors addressed challenges related to 3D printing non-uniformity. Thickness variations were mitigated by averaging micrometer measurements at multiple points. Holes for flange screws were manually drilled for PLA samples to avoid edge thickening inherent to the printing process, whereas resin samples maintained homogeneity even with printed holes.
Experimental Control: A torque meter was utilized to tighten the flanges, ensuring uniform pressure and preventing non-physical results (such as negative loss tangents) caused by excessive or inconsistent tightening.

Key Contributions

Data Generation: The paper provides experimentally measured complex permittivity data (real part $\varepsilon'_r$ and loss tangent $\tan \delta$ ) for nine distinct 3D-printed materials across the 70–110 GHz band.
Methodological Validation: The study demonstrates the efficacy of the open-waveguide method for mmWave characterization of 3D-printed slabs, highlighting its robustness against minor variations in sample shape and positioning.
Material Differentiation: The research reveals that materials from the same manufacturer, differing only in color additives (e.g., various PLA types), exhibit significantly distinct electromagnetic properties.

Results
The characterization yielded the following findings:

Permittivity Range: The frequency-averaged real part of the permittivity ranged from approximately 2.45 (Blue PLA) to 2.75 (Silver PLA and Black Resin).
Frequency Dispersion: All materials exhibited relatively stable permittivity values across the frequency band with minor fluctuations, indicating low normal frequency dispersion and the absence of material resonances within the 70–110 GHz range.
Loss Characteristics: Loss tangent values generally increased with frequency. Silver PLA and Black Resin demonstrated the highest loss tangents, exceeding 0.02 at higher frequencies. Conversely, Transparent, Green, and Red PLA showed the lowest loss tangents, suggesting suitability for applications requiring minimal dissipation.
Measurement Uncertainty: The authors noted that for low-loss materials, the extraction of the loss tangent is more susceptible to inaccuracies due to insufficient attenuation accumulation, leading to stronger deviations from the mean value compared to the real part of the permittivity.

Significance and Claims
The authors assert that their findings support the development of 6G and future wireless communication technologies, where 3D-printed materials are expected to play a pivotal role in fabricating new antennas and metasurfaces. The study claims that the presented methodology is readily applicable to other similar 3D-printable materials and can be extended to higher frequency ranges (e.g., 110–200 GHz) with appropriate adjustments to sample thickness. The paper modestly concludes that while the characterization of the 70–110 GHz range is challenging due to conventional measurement limitations, the open-waveguide approach offers a viable, rapid, and robust solution for identifying low-loss, cost-effective materials for mmWave device construction. The authors emphasize that despite belonging to the same brand, the specific formulation of 3D printing materials (including colorants) significantly impacts their electromagnetic performance, necessitating individual characterization for precise engineering applications.

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