3D Printed Alumina as a Millimeter-Wave Optical Element

We present millimeter and sub-millimeter room temperature transmission and loss measurements of 3D printed alumina disc and of a disc with one-sided 3D printed sub-wavelength structures anti-reflection coatings (SWS-ARC). For four bands spanning 158 - 700GHz we find an index of refraction consistent with $n= 3.107 \pm 0.007$. The loss over the entire frequency band between 158GHz and 700GHz spans $ 1 \cdot 10^{-3} \leq \tan δ\leq 2.49 \cdot 10^{-3}$ with 10%-30% uncertainty at the lower range of frequencies shrinking to $\sim!2%$ at the higher frequencies. As expected, constructive and destructive interference fringes that are apparent with the flat disc data are absent with the disc that has SWS-ARC. The measured data are consistent with finite element analysis predictions that are based on the measured shape of the SWS. At frequencies between 158GHz and 200~GHz, below the onset of diffraction effects, reflectance is reduced from a maximum of 64% to about 25%, closely matching predictions. These measurements of the index, loss, and SWS-ARC of 3D printed alumina suggest that the material and fabrication technique could be useful for astrophysical applications.

💡 Research Summary

This paper reports the first comprehensive room‑temperature characterization of 3‑dimensional (3D) printed alumina optical elements in the millimeter‑ and sub‑millimeter‑wave regime (158 GHz – 700 GHz). Two 50 mm‑diameter discs were fabricated by sintering 99.6 % pure alumina powder that had been shaped with a commercial additive‑manufacturing system. One disc is flat on both sides (“flat” sample), while the other carries a one‑sided sub‑wavelength structure (SWS) anti‑reflection coating (ARC) formed directly during the printing (“patterned” sample). The SWS consists of an array of pyramidal features with an average pitch of ≈0.5 mm, height ≈2 mm, and tip width ≈0.16 mm, dimensions chosen to target the ∼2 mm wavelength (≈150 GHz) region.

Transmission and reflection measurements were performed with a vector network analyzer (VNA) using four sub‑bands (158‑230 GHz, 222‑315 GHz, 312‑460 GHz, 470‑700 GHz). The flat disc was measured across the full band, whereas the patterned disc was limited to 158‑230 GHz because diffraction effects become dominant at higher frequencies for the chosen pitch. Normalized transmission (field amplitude) and reflectance (field amplitude relative to a gold mirror) were recorded, and data outliers were removed through a three‑step statistical filter (removing unphysical values >1.3 and points >3σ from a transfer‑matrix model residual).

For the flat disc, a combined transmission‑reflection fit using a transfer‑matrix method (TMM) yielded an average refractive index n = 3.107 ± 0.007 across all bands. The uncertainty is dominated by the ±0.007 mm thickness measurement rather than statistical noise. The loss tangent tan δ increases with frequency: 1.0 × 10⁻³ (158‑230 GHz), 1.1 × 10⁻³ (222‑315 GHz), 1.80 × 10⁻³ (312‑460 GHz), and 2.49 × 10⁻³ (470‑700 GHz). These values are consistent with previously reported room‑temperature alumina loss (≈0.6‑2.6 × 10⁻⁴) when accounting for measurement uncertainties and the higher frequency range.

The patterned disc’s transmission and reflectance were measured for two orthogonal polarizations; the results were statistically indistinguishable, confirming polarization‑independent behavior of the SWS. To interpret the data, a finite‑element analysis (FEA) model was built from the average pyramidal unit cell, applying periodic boundary conditions and using the n and tan δ derived from the flat disc. The simulated spectra (0.25 GHz resolution) match the measurements closely. Notably, the SWS eliminates the Fabry‑Pérot fringes seen in the flat disc, producing a relatively flat response between 160 GHz and 230 GHz. Reflectance drops from a maximum of ~64 % (bare alumina) to ~25 % with the one‑sided SWS, in line with the model prediction.

Above ~200 GHz, sharp dips appear in both measured and simulated spectra, arising from diffraction when the incident wavelength becomes comparable to the SWS pitch (ν ≈ c/(n p) ≈ 200 GHz). The authors therefore limited measurements to the sub‑diffraction regime. Simulations of a hypothetical double‑sided SWS show that reflectance could be reduced to <0.3 % while maintaining >96 % transmission, highlighting the potential benefit of patterning both faces.

The discussion emphasizes several key points. First, 3D‑printed alumina retains the high density (3.9 g cm⁻³) and purity of conventional sintered alumina, yet enables direct fabrication of complex micro‑structures without post‑processing steps such as laser ablation or dicing. Second, the measured loss tangent, though slightly higher than that of standard alumina, remains low enough for many astronomical instruments, especially considering that loss typically decreases at cryogenic temperatures. Third, the SWS geometry demonstrated here provides effective broadband ARC up to the onset of diffraction; the low‑frequency turn‑on is set by the feature height, while the high‑frequency cut‑off is set by the pitch. By increasing height or reducing pitch, the usable bandwidth could be extended toward 600 GHz, limited only by the printer’s resolution (≈80 µm tip size). Fourth, the additive‑manufacturing approach offers scalability: no tool wear, potential for large‑diameter (>30 cm) optics, and rapid iteration of design parameters.

Limitations identified include the current one‑sided coating, the lack of low‑temperature dielectric measurements, and the need for tighter control of SWS dimensions to push the diffraction limit higher. Future work should explore double‑sided SWS, characterize thermal conductivity and loss at cryogenic temperatures, and demonstrate larger‑area components suitable for telescope lenses or low‑pass filters.

In summary, the authors provide a thorough experimental validation that 3D‑printed alumina, combined with directly printed sub‑wavelength anti‑reflection structures, can deliver low‑loss, low‑reflectance performance across a broad millimeter‑wave band. The agreement between measurement and finite‑element modeling confirms that the printed geometry is accurately reproduced electromagnetically. This work opens a pathway toward additive‑manufactured, high‑performance millimeter‑wave optics for astrophysical applications, with the promise of rapid prototyping, design flexibility, and scalability to large apertures.