3D Printed Alumina as a Millimeter-Wave Optical Element

TL;DR

The paper addresses the need for high-index, low-loss millimeter-wave optics by characterizing 3D-printed alumina discs with and without sub-wavelength ARCs. It combines transmission and reflection measurements from 158 to 700 GHz with transfer-matrix modeling to extract $n \\approx 3.107$ and $\\tan \\delta \\sim 10^{-3}$, noting thickness-driven uncertainty. A one-sided SWS-ARC is shown to suppress fringes and matches finite-element predictions based on the measured unit-cell geometry, validating the approach. The results indicate 3D-printed alumina can enable scalable, larger-diameter millimeter-wave optical elements for astrophysical instrumentation, with planned improvements including two-sided printing and broader material-property tuning.

Abstract

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 - 700~GHz we find an index of refraction consistent with $n= 3.107 \pm 0.007$. The loss over the entire frequency band between 158~GHz and 700~GHz 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 158~GHz 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.

Figures (5)

• Figure 1: Schematic of a 1D cross section in $x$ of the patterned disc. The schematic is not-to-scale.
• Figure 2: A photograph of the 3D printed sample (left), a confocal microscope images of a section of the sample (middle), and definitions of the shape parameters (right). In the right panel, the ${\rm w}$ and ${\rm p}$ quantities give width and pitch, respectively, and the ${\rm d}$ quantities give depth measured from the tip in the directions shown.
• Figure 3: Experimental configurations for transmission (left panel) and reflection measurements (right panel). The 'Transmitter' and 'Receiver' functions are provided by a vector network analyzer. The sketches are not to-scale.
• Figure 4: Transmittance $T$ and reflectance $R$ data (upper panels, blue and green points, respectively) as a function of frequency for the flat disc, the best fit models (solid blue and green, respectively), and the residuals from the best fits (lower panels). The expanded view of a low frequency band (right panel) also gives the sum of the measured transmittance and reflectance (black).
• Figure 5: Top and a perspective view of the unit cell used for FEA calculations (left), and measured transmittance and reflectance of the patterned disc (right, blue and orange data, respectively) together with FEA generated predictions (right, cyan and red solid). For the FEA predictions we use the unit cell (left), which is constructed from the average pyramid. We also include FEA predictions of performance if both sides of the sample would have been patterned (cyan and red dash).