We present finite element simulations of the transition-edge sensor (TES) microcalorimeter behavior using COMSOL Multiphysics. The simulated detector has a large absorber with a size of 990 × 990 μ m2. The simulation calculates the TES response after x-ray impact for a single pixel with a known, realistic, current-dependent resistive transition R ( T , I ) . The simulation includes the full electrothermal feedback effects and heat conduction through the multiple contact points of the absorber to the TES thermometer and supporting membrane. The presented model, especially the 2D model, has been optimized for high accuracy, making it suitable for simulating the detector response when incident photons hit different positions on the absorber. We study the effects of position dependence using Principal Component Analysis with the aim of extracting correct photon energies from the pulses. The simulations show that the degradation, i.e., the FWHM broadening, due to the pulse variations will be less than 0.7 eV at below 2 keV, while it can be significant ( > 1 eV) at a higher energy band. The simulation result for position dependence can guide the design of large-absorber detectors for future x-ray missions, such as the Hot Universe Baryon Surveyor.

We have successfully demonstrated three 4×2 hot electron bolometer (HEB) mixer arrays, designed to operate between 4.2 and 5.5 K, with local oscillator (LO) frequencies of 1.4, 1.9, and 4.7 THz, respectively. These arrays consist of spiral antenna coupled NbN HEB mixers combined with elliptical lenses. These are to date the highest pixel count arrays using a quasi-optical coupling scheme at supra-THz frequencies. At 1.4 THz, we obtained an average double sideband mixer noise temperature of 330 K, a mixer conversion loss of 5.2 dB, and an optimum LO power of 210 nW. The array at 1.9 THz has an average mixer noise temperature of 425 K, a mixer conversion loss of 6.4 dB, and an optimum LO power of 190 nW. For the array at 4.7 THz, we obtained an average mixer noise temperature of 715 K, a mixer conversion loss of 8.9 dB, and an optimum LO power of 240 nW. We found the arrays to be uniform regarding the mixer noise temperature with a standard deviation of 3% to 4%, the conversion loss with a standard deviation of 8% to 11%, and optimum LO power with a standard deviation of 5% to 6%. The noise bandwidth was also measured, being 3.5 GHz for the three arrays. These performances are comparable to previously reported values in the literature for single pixels and also other detector arrays at similar frequencies. Our arrays met the instrument requirements and were employed in the Galactic/Extra-Galactic ULDB Spectroscopic Terahertz Observatory (GUSTO), a NASA balloon-borne observatory. GUSTO launched from Antarctica on the 31st of December 2023 having a successful flight of 57 days, the longest ever recorded by NASA for such a mission profile.

The X-ray Integral Field Unit (X-IFU) is an imaging spectrometer based on a large array of Transition Edge Sensors (TES) measured using Time Domain Multiplexing (TDM). For the development of a backup detector array, we have designed and realized a cryogenic test setup capable of measuring 9 detectors in a single cooldown under DC bias. We have used this setup to study a small selection of low aspect ratio TES designs, intended to have a low normal resistance suitable for TDM readout. In this work we show how the different designs are affected by magnetic fields. We do this by presenting the impact on the transition shape, detector integrated Noise Equivalent Power (NEP), and sensitivity of the energy scale calibration. We find, in agreement with previous studies, that reducing the width of the TES bilayer greatly improves the detector resilience to magnetic fields, potentially by several orders of magnitude.

We measured the double sideband (DSB) receiver noise temperature (TrecDSB) of an NbN hot electron bolometer (HEB) mixer at three local oscillator frequencies of 1.6, 2.5, and 5.3 THz. The HEB has cleaned contact interfaces with a 200 nm thick Au layer. The measuredTrecDSB values are 530 ± 11 K, 640 ±18 K, and 2190 ±150 K at 1.6, 2.5, and 5.3 THz, respectively, using an air setup with total optical losses of 2.60 ± 0.04, 2.63 ± 0.16, and 4.70 ± 0.24 dB, respectively. We derived low mixer noise temperatures (TmixerDSB) of 240 ± 6 K at 1.6 THz and 290 ± 13 K at 2.5 THz, achieving over 30% improvement compared to published NbN HEB mixers. This enhancement can reduce the integration time of a heterodyne instrument by roughly a factor of 2. At 5.3 THz,TmixerDSB is 620 ± 55 K, showing limited improvement due to non-optimized antenna geometry. These results also contribute to understanding the device physics of a wide HEB (4 μm) at high frequencies.

SRON (Netherlands Institute for Space Research) is developing the focal plane assembly (FPA) for Athena X-IFU, whose demonstration model (DM) will use for the first time a time domain multiplexing (TDM)-based readout system for the on-board transition-edge sensors (TES). We report on the characterization activities on a TDM setup provided by NASA goddard space flight center (GSFC) and national institute for standards and technology (NIST) and tested in SRON cryogenic test facilities. The goal of these activities is to study the impact of the longer harness, closer to X-IFU specs, in a different EMI environment and switching from a single-ended to a differential readout scheme. In this contribution we describe the advancement in the debugging of the system in the SRON cryostat, which led to the demonstration of the nominal spectral performance of 2.8 eV at 5.9 keV with 16-row multiplexing, as well as an outlook for the future endeavors for the TDM readout integration on X-IFU’s FPA-DM at SRON.

The X-ray Integral Field Unit (X-IFU) is an instrument of European Space Agency's future NewAthena space observatory, with the goal to provide high-energy resolution (<4 eV at X-ray energies up to 7 keV) and high-spatial resolution (9 in.) spectroscopic imaging over the X-ray energy range from 200 eV to 12 keV, by means of an array of ∼1500 transition-edge sensors (TESs) read out via superconducting quantum interference device time-division multiplexing (TDM). A TDM-based laboratory test bed has been assembled at Netherlands Institute for Space Research, hosting an array of 75×75 μm2 TESs that are read out via 2-column × 32-row TDM. A system component that is critical to high-performance operation is the wiring harness that connects the room-temperature electronics to the cryogenic readout componentry. We report here on our characterization of such a test bed, whose harness has a length close to what was envisioned for X-IFU, which allowed us to achieve a co-added energy resolution at a level of 2.7-eV full width half maximum at 6 keV via 32-row readout. In addition, we provide an outlook on the integration of TDM readout into the X-IFU focal plane assembly development model.

At SRON, we have been developing X-ray TES micro-calorimeters as backup technology for the X-ray Integral Field Unit (X-IFU) of the Athena mission, demonstrating excellent resolving powers both under DC and AC bias. We also developed a frequency-domain multiplexing (FDM) readout technology, where each TES is coupled to a superconducting band-pass LC resonator and AC biased at MHz frequencies through a common readout line. The TES signals are summed at the input of a superconducting quantum interference device (SQUID), which performs a first amplification at cryogenic stage. Custom analog front-end electronics and digital boards take care of further amplifying the signals at room temperature and of the modulation/demodulation of the TES signals and bias carrier, respectively. We report on the most recent developments on our FDM technology, which involves a two-channel demonstration with a total of 70 pixels with a summed energy resolution of 2.34 ± 0.02 eV at 5.9 keV without spectral performance degradation with respect to single-channel operation. Moreover, we discuss prospects towards the scaling-up to a larger multiplexing factor up to 78 pixels per channel in a 1–6 MHz readout bandwidth.

The High-Resolution Receiver (HiRX) is one of two instruments of the Single Aperture Large Telescope for Universe Studies (SALTUS), a mission proposed to NASA's 2023 Astrophysics Probe Explorer. SALTUS employs a 14 m aperture, leading to a 16-fold increase in collecting area and a factor of 4 increase in the angular resolution with respect to the Herschel Space Telescope. It will be radiatively cooled to ≤45 K and has a planned duration of >5 years. HiRX consists of four bands of cryogenic heterodyne receivers with a high sensitivity and high spectral resolution, being able to observe the gaseous components of objects across the far-IR. HiRX is going to detect water, HD, and other relevant astrophysical lines while resolving them in velocity. HiRX covers the following frequency ranges: Band 1 from 455 to 575 GHz, Band 2 from 1.1 to 2.1 THz, Band 3 from 2.475 to 2.875 THz, and Band 4 for both 4.744 and 5.35 THz. Bands 1 to 3 contain single, high-performance mixers. Band 4 consists of an array of seven hexagonally packed pixels, where the central pixel operates as a heterodyne mixer. Band 1 utilizes superconducting-insulator-superconducting mixers (SIS), whereas Bands 2 to 4 use superconducting hot electron bolometers (HEB) mixers. The local oscillator (LO) system uses frequency-multiplier chains for Bands 1 and 2, and quantum cascade lasers for Bands 3 and 4. Autocorrelator spectrometers are used to process the intermediate frequency (IF) signals from each science band, providing instantaneous frequency coverage of 4 to 8 GHz for Band 1 and 0.5 to 4 GHz for Bands 2 to 4. SALTUS will also fly a chirp transform spectrometer system for high spectral resolution observations in Band 1.

The terahertz frequency region of the electromagnetic spectrum is crucial for understanding the formation and evolution of galaxies and stars throughout the universe's history, as well as the process of planet formation. Detecting the unique spectral signatures of molecules and atoms requires terahertz spectrometers, which must be operated in space observatories due to water vapor absorption in the Earth's atmosphere. However, current terahertz spectrometers face challenges such as low resolution, limited bandwidth, large volume, and complexity. In this paper, the issues of size and weight are addressed by demonstrating a concept for a centimeter-sized, low-weight terahertz spectrometer using a metasurface. The design of the metasurface spectrometer is first discussed for the 1.85 to 2.4 THz range, followed by its fabrication. Next, an array of quantum cascade lasers operating at slightly different frequencies around 2.1 THz is utilized to characterize the spectrometer. Finally, a spectrum inversion method is applied to analyze the measured data, confirming a resolution R (λ/Δλ) of at least 273. This concept can be extended to other application areas, such as planetary observations and various wavelengths in the far-infrared (FIR) and near-infrared (NIR) ranges.

We have demonstrated three 4×2 hot electron bolometer (HEB) mixer arrays for operation at local oscillator (LO) frequencies of 1.4, 1.9 and 4.7 THz, respectively. These arrays consist of spiral antenna coupled NbN HEB mixers combined with elliptical lenses. These are to date the highest pixel count arrays using a quasi-optical coupling scheme at supra-THz frequencies. At 1.4 THz, we obtained an average double sideband mixer noise temperature of 330 K, a mixer conversion loss of 5.2 dB, and an optimum LO power of 210 nW. The array at 1.9 THz has an average mixer noise temperature of 425K, a mixer conversion loss of 6.4 dB, and an optimum LO power of 190 nW. For the array at 4.7 THz we obtained an average mixer noise temperature of 715 K, a mixer conversion loss of 8.9 dB, and an optimum LO power of 240 nW. We found the arrays to be uniform regarding the mixer noise temperature with a standard deviation of 3-4%, the conversion loss with a standard deviation of 8-11%, and optimum LO power with a standard deviation of 5-6%. The noise bandwidth was also measured, being 3.5 GHz for the three arrays. These performances are comparable to previously reported values in the literature for single pixels and also other detector arrays at similar frequencies. Our arrays met the requirements and were employed in the Galactic/Extra-Galactic ULDB Spectroscopic Terahertz Observatory (GUSTO), a NASA balloon borne observatory. GUSTO launched from Antarctica on the 31st December 2023 having a successful flight of 57 days, the longest ever recorded by NASA for such mission profile.

We have simulated and measured the beam properties of lens-antenna coupled hot electron bolometer mixers at a few supra-terahertz frequencies between 1.4 and 5.3 THz. The quasi-optical structures consist of an elliptical lens and a logarithmic spiral antenna. The model used for our simulations consists of a finite-element analysis to simulate the far-field radiation pattern of the antenna, geometrical optics to map the antenna radiation to the lens surface, and physical optics to calculate an arbitrary far field. We perform a thorough study of the beam properties, such as beam waist radius, phase center location and axial ratio by varying the diameter and extension of the lens, and misalignments of the antenna relative to the lens, at different operating frequencies. The simulation results are applied to the design and optimization of three different lenses for mixers to be operated at 1.4, 1.9, and 4.7 THz, respectively, which will be used in the heterodyne array receivers on board of NASA's balloon borne GUSTO observatory. The beam properties were verified experimentally by measuring the beam patterns in amplitude at multiple planes using a heterodyne technique. We found that the experimental results show good agreement with those from the simulations. Our work has delivered the mixers with the required beam characteristics for GUSTO.

As a two-dimensional planar material with low depth profile, a metasurface can generate non-classical phase distributions for the transmitted and reflected electromagnetic waves at its interface. Thus, it offers more flexibility to control the wave front. A traditional metasurface design process mainly adopts the forward prediction algorithm, such as Finite Difference Time Domain, combined with manual parameter optimization. However, such methods are time-consuming, and it is difficult to keep the practical meta-atom spectrum being consistent with the ideal one. In addition, since the periodic boundary condition is used in the meta-atom design process, while the aperiodic condition is used in the array simulation, the coupling between neighboring meta-atoms leads to inevitable inaccuracy. In this review, representative intelligent methods for metasurface design are introduced and discussed, including machine learning, physics-information neural network, and topology optimization method. We elaborate on the principle of each approach, analyze their advantages and limitations, and discuss their potential applications. We also summarize recent advances in enabled metasurfaces for quantum optics applications. In short, this paper highlights a promising direction for intelligent metasurface designs and applications for future quantum optics research and serves as an up-to-date reference for researchers in the metasurface and metamaterial fields.

We report on the x-ray background rate measured with transition-edge sensors (TES) micro-calorimeters under frequency-domain multiplexing (FDM) readout as a possible technology for future experiments aiming at a direct detection of axion-like particles. Future axion helioscopes will make use of large magnets to convert axions into photons in the keV range and x-ray detectors to observe them. To achieve this, a detector array with high spectral performance and extremely low background is necessary. TES are single-photon, non-dispersive, high-resolution micro-calorimeters and represent a possible candidate for this application. We have been developing x-ray TES micro-calorimeters and an FDM readout technology in the framework of the space-borne x-ray astronomical observatories. We show that the current generation of our detectors is already a promising technology for a possible axion search experiment, having measured an x-ray background rate of 2.2(2) × 10⁻⁴ cm⁻² s⁻¹ keV⁻¹ with a cryogenic demonstrator not optimized for this specific application. We then make a prospect to further improve the background rate down to the required value ( < 1 0 − 7 cm⁻² s⁻¹ keV⁻¹) for an axion-search experiment, identifying no fundamental limits to reach such a level.

Terahertz (THz) radiation encompasses a wide spectral range within the electromagnetic spectrum that extends from microwaves to the far infrared (100 GHz-∼30 THz). Within its frequency boundaries exist a broad variety of scientific disciplines that have presented, and continue to present, technical challenges to researchers. During the past 50 years, for instance, the demands of the scientific community have substantially evolved and with a need for advanced instrumentation to support radio astronomy, Earth observation, weather forecasting, security imaging, telecommunications, non-destructive device testing and much more. Furthermore, applications have required an emergence of technology from the laboratory environment to production-scale supply and in-the-field deployments ranging from harsh ground-based locations to deep space. In addressing these requirements, the research and development community has advanced related technology and bridged the transition between electronics and photonics that high frequency operation demands. The multidisciplinary nature of THz work was our stimulus for creating the 2017 THz Science and Technology Roadmap (Dhillon et al 2017 J. Phys. D: Appl. Phys. 50 043001). As one might envisage, though, there remains much to explore both scientifically and technically and the field has continued to develop and expand rapidly. It is timely, therefore, to revise our previous roadmap and in this 2023 version we both provide an update on key developments in established technical areas that have important scientific and public benefit, and highlight new and emerging areas that show particular promise. The developments that we describe thus span from fundamental scientific research, such as THz astronomy and the emergent area of THz quantum optics, to highly applied and commercially and societally impactful subjects that include 6G THz communications, medical imaging, and climate monitoring and prediction. Our Roadmap vision draws upon the expertise and perspective of multiple international specialists that together provide an overview of past developments and the likely challenges facing the field of THz science and technology in future decades. The document is written in a form that is accessible to policy makers who wish to gain an overview of the current state of the THz art, and for the non-specialist and curious who wish to understand available technology and challenges. A such, our experts deliver a ‘snapshot’ introduction to the current status of the field and provide suggestions for exciting future technical development directions. Ultimately, we intend the Roadmap to portray the advantages and benefits of the THz domain and to stimulate further exploration of the field in support of scientific research and commercial realisation.

We report our most recent progress and demonstration of a frequency domain multiplexing (FDM) readout technology for transition-edge sensor (TES) arrays, both of which we have been developing in the framework of the X-IFU instrument on board the future Athena X-ray telescope. Using Ti/Au TES micro-calorimeters, high-Q LC filters and analog/digital electronics developed at SRON and low-noise two-stage SQUID amplifiers from VTT Finland, we demonstrated the feasibility of our FDM readout technology, with the simultaneous readout of 37 pixels with an energy resolution of 2.23 eV at an energy of 6 keV. We finally outline our plans for further scaling up and improving our technology in the future.

We have studied THz heterodyne detection in sub-micrometer MgB2 hot electron bolometer (HEB) mixers based on superconducting MgB2 films of ∼ 5 nm (HEB-A), corresponding to a critical temperature (Tc) of 33.9 K, and ∼ 7 nm (HEB-B), corresponding to a T c of 38.4 K. We have measured a double sideband (DSB) receiver noise temperature of 2590 K for HEB-A and 2160 K for HEB-B at 1.6 THz and 5 K. By correcting for optical losses, both HEBs show receiver noise temperatures of ∼1600 K referenced to the front of anti-reflection (AR)-coated Si lenses. An intermediate frequency (IF) noise bandwidth of 11 GHz has been measured for both devices. The required local oscillator (LO) power is about 13 μW for both HEBs. We have also measured a DSB receiver noise temperature of 3290 K at 2.5 THz and 5 K but with an AR-coated lens optimized for 1.6 THz. Besides, we have observed a step-like structure in current voltage (IV) curves, which becomes weaker when the LO power increases and observable only in their differential resistance. Such a correlated structure appears also in the receiver output power as a function of voltage, which is likely due to electronic inhomogeneities intrinsic to the variations in the thickness of the MgB2 films. Different behavior in the IV curves around the low bias voltages, pumped with the same LO power at 1.6 and 5.3 THz, was observed for HEB-B, suggesting the presence of a high-energy σ-gap in the MgB2 film.

We report a high accuracy pointing technique for quasi-optical hot electron bolometer (HEB) mixers in focal-plane arrays designed to operate at 1.4, 1.9, and 4.7 THz. The high accuracy pointing is achieved by prealignment of a HEB chip to a lens, measuring the angular error of each mixer in an array assembly, and then realignment of the chip to the same lens to correct the error. The realigned mixers, using 5 mm diameter Si elliptical lenses designed for operation at 4.7 THz, show a final pointing error distribution with an average (μ) = 0.13° and standard deviation (σ) = 0.06°, with respect to the normal direction of the respective array plane. Those using 10 mm diameter lenses designed for operation either at 1.4 or 1.9 THz, show μ = 0.08° and σ = 0.03°. We demonstrated our pointing technique in five 4×2 HEB focal plane arrays developed for NASA's balloon borne GUSTO THz observatory. Our results corroborate the simulated beam steering factors used to calculate the realignment corrections. With the unprecedented pointing accuracy at the high frequencies, our technique can significantly facilitate the use of lens-antenna, quasi-optical mixers for future focal-plane arrays, which is able to compete with traditional feedhorn-waveguide mixer arrays, operated typically below 1 THz, for astronomical instrumentation.

Gal/Xgal U/LDB Spectroscopic/ Stratospheric THz Observatory (GUSTO) is a NASA Explorers Mission of Opportunity that will make large scale maps of the Milky Way and Large Magellanic Cloud in three important interstellar lines: [CII], [OI], and [NII] at 158, 63, and 205 μm, respectively. During its ~75 day stratospheric (~36 km) flight, GUSTO’s 0.9-meter balloon-borne telescope and THz heterodyne array receivers will provide the spectral and spatial resolution needed to untangle the complexities of the interstellar medium by probing all phases of its Life Cycle. The GUSTO payload consists of (1) a telescope; (2) three 8-pixel heterodyne array receivers; (3) autocorrelator spectrometers; (4) instrument control electronics; and (5) a cryostat. The GUSTO gondola is derived from successful APL designs. Much of the GUSTO instrument architecture and hardware is based on the experience gained in developing and flying the Stratospheric Terahertz Observatory (STO). GUSTO is currently undergoing integration and test and will launch from the NASA Long Duration Balloon (LDB) Facility near McMurdo, Antarctica in December 2023.

We present an analysis of the bandwidth of an asymmetric 8-beam Fourier grating as the beam multiplexer for a 4.7 THz local oscillator used in a heterodyne receiver. We take the grating designed for NASA GUSTO balloon observatory as an example to address the bandwidth question although it does not need to operate over a wide frequency range. By illuminating the grating at different frequencies from 4.445 to 5.045 THz, we simulated the changes of its performance in three aspects using COMSOL Multiphysics: diffraction efficiency, power uniformity, and the angular distribution of the output beams. These parameters can affect the coupling efficiency between the output beams of the grating and the beams of a mixer array. The bandwidth of the grating is found to be 230 GHz, corresponding to 4.9% of the operating frequency, which is sufficient for many applications.

Transition-edge-sensor (TES) microcalorimeters and bolometers are used for a variety of applications.The sensors are based on the steep temperature-dependent resistance of the normal-to-superconducting transition, and are thus intrinsically sensitive to magnetic fields. Conventionally the detectors are shielded from stray magnetic fields using external magnetic shields. However, in particular for applications with strict limits on the available space and mass of an instrument, external magnetic shields might not be enough to obtain the required shielding factors or field homogeneity. Additionally, these shields are only effective for magnetic fields generated external to the TES array, and are ineffective to mitigate the impact of internally generated magnetic fields. Here we present an alternative shielding method based on a super-conducting groundplane deposited directly on the backside of the silicon nitride membrane on which the TESs are located. We demonstrate that this local shielding for external magnetic fields has a shielding factor of at the least approximately 80, and is also effective at reducing internal self-induced magnetic fields, as demonstrated by measurements and simulation of the eddy current losses in our ac-biased detectors. Measurements of 5.9-keV x-ray photons show that our shielded detectors have a high resilience to external magnetic fields, showing no degradation of the energy resolution or shifts of the energy-scale calibration for fields of several microtesla, values higher than expected in typical real-world applications.