Quasioptic, Calibrated, Full 2-port Measurements of Cryogenic Devices under Vacuum in the 220-330 GHz Band

TL;DR

This work presents a quasi-optical, cryogenic measurement platform for determining the full $2\times2$ S-parameter set of devices in the $220-330$ GHz band, with the reference plane located inside the cryostat and de-embedding achieved via an extended Line-Reflect-Match calibration. The setup keeps the VNA and optics at room temperature while placing the DUT inside a vacuum cryostat, enabling correction for optical-path and window effects. Demonstrations on high-resistivity Si, stainless FSS, and Nb superconducting FSS show temperature-dependent behavior consistent with theory, including permittivity reduction in Si and superconducting performance in Nb at $4.8$ K. The method achieves ~30 dB return loss for the empty holder and yields meaningful S-parameter measurements under cryogenic conditions, offering a path toward robust testing of mm-wave/THz devices for radio astronomy and quantum technologies.

Abstract

A quasi-optical (QO) test bench was designed, simulated, and calibrated for characterizing S-parameters of devices in the 220-330 GHz (WR-3.4) frequency range, from room temperature down to 4.8 K. The devices were measured through vacuum windows via focused beam radiation. A de-embedding method employing line-reflect-match (LRM) calibration was established to account for the effects of optical components and vacuum windows. The setup provides all four S-parameters with the reference plane located inside the cryostat, and achieves a return loss of 30 dB with an empty holder. System validation was performed with measurements of cryogenically cooled devices, such as bare silicon wafers and stainless-steel frequency-selective surface (FSS) bandpass filters, and superconducting bandpass FSS fabricated in niobium. A permittivity reduction of Si based on 4-GHz resonance shift was observed concomitant with a drop in temperature from 296 K to 4.8 K. The stainless steel FSS measurements revealed a relatively temperature invariant center frequency and return loss level of 263 GHz and 35 dB on average, respectively. Finally, a center frequency of 257 GHz was measured with the superconducting filters, with return loss improved by 7 dB on average at 4.8 K. To the best of our knowledge, this is the first reported attempt to scale LRM calibration to 330 GHz and use it to de-embed the impact of optics and cryostat from cryogenically cooled device S-parameters.

Figures (16)

• Figure 1: Design and simulation of the quasioptical setup: CAD model of the left part of the quasioptical setup (a) with a schematic image of the beam evolution (b); and physical optics simulations of the beam inside the cryostat at $f=$ 272 GHz (desired antenna central frequency), namely (c) co-polarized beam profile at $z=0$, (d) cross-polarized beam profile at $z=0$, and (e) phase distribution within the co-polarized beam, dashed lines correspond to the beam waist level in Gaussian-beams, i.e., $1/e$ power change. Since the cryostat is located on the translation stage, one can also independently use the setup for room-temperature measurements. The distance between each quasioptical element is $d=f=152.4$ mm, except the double focal distance $2f$ as the optical (not physical) path between $R_2$ and $R_3$. The system has a mirror symmetry with respect to $x-y$ plane, and the inter-grid space is 2 mm.
• Figure 2: Measured S-parameter amplitudes of the waveguide-flange calibrated quasioptical system.
• Figure 3: Near-field measurements system with a half of the quasioptical system: (a) WR 3.4 frequency extender with a Pickett-Potter horn antenna; (b) parabolic reflector $R_1$; (c) flat mirror $M_1$; (d) parabolic reflector $R_2$; (e) WR 3.4 extender with a waveguide probe.
• Figure 4: Near field measurements of the beam: (a) co-polarized beam pattern at 220 GHz, (b) co-polarized beam pattern at 275 GHz, (c) co-polarized beam pattern at 330 GHz, (d) cross-polarized beam pattern at 220 GHz; (e) cross-polarized beam pattern at 275 GHz, and (f) cross-polarized beam pattern at 330 GHz. Co-polarized phase distribution patterns for (g) 220 GHz, (h) 275 GHz, and (i) 330 GHz. Dashed green lines correspond to $1/e$ power change, and the intergrid line space is 2 mm. Cross-pol is normalized with respect to the corresponding Co-pol, for convenience.
• Figure 5: (a) Photo of the system with the cryostat (marked in red circle) and (b) Line-Relect-Line (LRM) calibration procedure (Not to scale): firstly, a 300 $\mu m$ line is measured, then a reflection standard of the same thickness, and, finally, a double-sided match. $R_2$ and $R_3$ are parabolic reflectors with respect to Fig. \ref{['fig:Simulation2']}.