Hierarchical sinuous-antenna phased array for millimeter wavelengths

Hierarchical sinuous-antenna phased array for millimeter wavelengths


We present the design, fabrication and measured performance of a hierarchical sinuous-antenna phased array coupled to superconducting transition-edge-sensor (TES) bolometers for millimeter wavelengths. The architecture allows for dual-polarization wideband sensitivity with a beam width that is approximately frequency-independent. We report on measurements of a prototype device, which uses three levels of triangular phased arrays to synthesize beams that are approximately constant in width across three frequency bands covering a 3:1 bandwidth. The array element is a lens-coupled sinuous antenna. The device consists of an array of hemispherical lenses coupled to a lithographed wafer, which integrates TESs, planar sinuous antennas and microwave circuitry including band-defining filters. The approximately frequency-independent beam widths improve coupling to telescope optics and keep the the sensitivity of an experiment close to optimal across a broad frequency range. The design can be straightforwardly modified for use with non-TES lithographed cryogenic detectors such as kinetic inductance detectors (KIDs). Additionally, we report on the design and measurements of a broadband hybrid that can simplify the design of future multichroic focal planes including but not limited to hierarchical phased arrays.


Lithographed superconducting detectors have found many applications in millimeter and submillimeter astronomy including measurements of the cosmic microwave background (CMB), galactic dust emission and star and planet formation.Zmuidzinas and Richards (2004) A major goal of modern cosmology is to make precise measurements of the polarized fluctuations in the CMB with science goals such as a measurement of the sum of neutrino masses and a detection of primordial -modes, which would be considered direct evidence for an inflationary epoch in the early universe.Seljak and Zaldarriaga (1997); Abazajian et al. (2016) The signals of interest are at the level of - on a - background, which motivates the development of increasingly sensitive instruments.Benson et al. (2014); Suzuki et al. (2016); Matsumura et al. (2016); Grayson et al. (2016); Thornton et al. (2016); Essinger-Hileman et al. (2014); Abitbol et al. (2017) In this letter, we propose an efficient method for improving the sensitivity of such experiments.

The noise-equivalent temperature (), often given in units of , is a measure of the instantaneous sensitivity of an experiment to a sky signal such as the CMB. The noise in an experiment’s maps of the sky can be reduced by integrating for longer lengths of time. The mapping speed , often given in units of , is a measure of the rate at which the map noise is reduced. An experiment with twice the mapping speed can achieve the same map noise in half the time.

The dependence of the mapping speed on pixel size is well known in the CMB community.Griffin, Bock, and Gear (2002) Here we consider the common case of single-moded detectors and a cryogenic aperture stop with the angular size of the telescope’s field of view held constant. A smaller pixel size allows for more pixels, which tends to increase the mapping speed. However, a smaller pixel has a wider beam and, therefore, receives a smaller fraction of power from the sky and a larger fraction from the aperture stop in the telescope optics, which contributes only noise. There are, therefore, two competing concerns in choosing a pixel size. A plot of mapping speed vs. pixel size for an example experiment is shown in Fig. 1, which shows a clear peak indicating an optimal pixel diameter.

Figure 1: Mapping speed vs. pixel diameter (solid) in units of f-number () of the detector-aperture system times wavelength () for an example multichroic focal plane for a space-based telescopeMatsumura et al. (2016): - sky with a - aperture stop and bands centered on , , , , and . A more precise treatment would yield slightly different curves for different frequencies, but the optimal diameter typically varies by less than in units of . Square markers indicate where the frequency bands of a conventional multichroic pixel would fall on this curve when the pixel diameter is optimized for ; circular markers indicate the same for a hierarchical focal plane based on triangular arrays for which the array-element diameter is optimized for . The hierarchical array allows near-optimal mapping speed in all frequency bands.

The pixel can be treated roughly as a diffraction aperture, so the diameter-to-wavelength ratio sets the beam width. As a result, the optimal pixel diameter is approximately proportional to wavelength.

A common problem with a conventional multichroic pixel, which is sensitive to multiple frequency bands but has a single fixed pixel diameter, is that the beam width and, therefore, the optimal pixel diameter are frequency-dependent. It is usually impossible, then, to choose a pixel diameter that is optimal in every frequency band. A multiscale focal plane solves this problem by creating pixels whose effective diameters scale with wavelength.

A multiscale focal plane can be realized through the use of a hierarchical phased array, which consists of superimposed antenna arrays operating in different frequency bands and increasing in size approximately inversely with frequency. An example topology is shown in Fig. 2 for a three-level hierarchy based on triangular arrays.

Figure 2: (Left) Example topology of a three-level hierarchical phased array. The highest frequencies (green) dissipate power to bolometers in a conventional way. The middle frequencies (red) sum three antennas coherently before dissipating power. The lowest frequencies (blue) sum six antennas. (Right) Effective pixels for a three-level hierarchy based on triangular arrays. Black circles represent individual antennas. The small green circles represent the effective pixels for the highest frequencies, small red triangles the middle frequencies and large blue triangles the lowest frequencies. The triangular hierarchy naturally creates a second hierarchy of rhombi, which can be used to tile the wafer.

The antennas couple free-space radiation to transmission lines, at which point the power is split into frequency bands via the filter banks. Transmission-line signals from neighboring antennas are then summed coherently before dissipating the power on a bolometer. The summing network includes a different number of antenna elements for each frequency band. The estimated improvement to mapping speed is shown in Fig. 1.

An additional benefit of a hierarchical focal plane is that the detector count per unit area may be reduced relative to a conventional design, even though the sensitivity may be improved. This is possible when the conventional design is optimized for high frequencies. In this case, the hierarchical design simply combines antennas at lower frequencies, which reduces the number of detectors per antenna. Whereas the conventional design would have a detector count that increases approximately linearly with the number of frequency bands, the hierarchical design has a detector count that increases approximately logarithmically. Under these conditions, a three-band experiment could reduce its detector count by half.

This paradigm is particularly attractive for satellite- and balloon-based experiments, for which increased weight and power are expensive. Additionally, the mapping speed tends to have a narrower optimum due to the larger optical loading from the aperture stop relative to the sky in the absence of atmospheric loading. For ground-based experiments, the reduction in system complexity, coming, e.g., from decreased power consumption and wire count for readout electronics, is also attractive.

A hierarchical focal plane can also mitigate systematic errors related to beam shape and polarization purity. The far-field beam is the product of the array factor and the beam of the individual antenna element. Beam non-idealities can be compensated for by choosing an appropriate array configuration. Some antennas, including the sinuous antenna discussed below, have a polarization response that varies or “wobbles” with frequency. By constructing an array consisting partially of mirror-imaged versions of the antenna element, the polarization wobble can be reduced or even cancelled completely.

We have developed a multiscale architecture based on hierarchical phased arrays that allows for dual-polarized wideband sensitivity at millimeter wavelengths. As the unit cell of these arrays, we choose the lenslet-coupled sinuous antenna on account of its broad bandwidth, frequency-independent beam waist and dual-polarized capability.Edwards et al. (2012); O’Brient et al. (2013); Westbrook et al. (2016) Since the beam waist is determined mainly by the lens diameter, the on-chip planar antenna need only occupy a fraction of the total pixel area, which makes space for microwave circuitry and detectors. The on-chip components of the unit cell is shown in Fig. 3.

Figure 3: Unit cell of the hierarchical array: a sinuous antenna coupled to out-of-phase microstrip lines, triplexing bandpass filters (middle, left and right) and double-ring hybrids (top and bottom). The - signal is sent directly to a bolometer (bottom center). For simplicity of fabrication, only one polarization is active in this prototype.

We find that the beam forming of the antenna arrays compensates for beam non-idealities in the unit cell, so the sinuous antenna can be substantially undersized relative to the case of a conventional multichroic pixel; here we use a - diameter (cf. 3-mm for a conventional pixel operating at the same frequenciesBenson et al. (2014)).

To simplify and accelerate the fabrication process for this prototype, we chose to avoid microstrip crossovers, since this would have added extra layers. This prototype is, consequently, a single-polarization device, although the architecture can be extended, by adding well-proven microstrip crossovers, to two polarizations. Separately, we have been developing microstrip crossunders, which perform the same function as crossovers but without requiring additional layers. We plan to make use of these crossunders in future hierarchical devices.

The sinuous antenna is coupled to two out-of-phase microstrip lines that route the signal to triplexing lumped-element bandpass filters, which split the signal into bands centered on , and with bandwidths of approximately . The - signal is brought directly to a bolometer, where the microstrip lines are terminated differentially on a lumped resistor (second-from-right image in Fig. 5). The out-of-phase lines for and are combined in double-ring hybrids to form single microstrip lines, which enter the summing networks.

An overview of the summing networks is shown in Fig. 4.

Figure 4: Fabricated prototype chip with overlaid hierarchical structure: - pixels (green), - array (blue) and - array (red). A conventional trichroic pixel (yellow) is included as a control. The other features on the chip are for test pixels that were included in the same mask design but are electrically independent of the hierarchical array.

The signals from neighboring antennas are combined with the Wilkinson power splitters shown in Fig. 5.

Figure 5: (Left) A Wilkinson divider consisting of superconducting microstrip lines and a resistor (connecting the output lines near the top). (Second from left) A planarized Wilkinson “trivider”. (Second from right) A bolometer island featuring an TES (left middle) and microstrip lines terminating differentially on a resistor (right middle). (Right) A bolometer island featuring a single microstrip line terminating in a single-ended resistor that is connected through a via in the insulating to the ground plane.

An advantage of these splitters is that the output ports are well-isolated from each other, which suppresses unwanted reflections between antennas. To increase their bandwidths, these Wilkinson splitters include additional segments ahead of the splitting node (only partially shown in Fig. 5). To planarize the Wilkinson “trivider”, we removed the resistor that would have connected the outermost output lines and then retuned the circuit parameters in simulation. The 3-antenna - array is formed using a single trivider. The 6-antenna - array is formed using three dividers followed by a single trivider. The microstrip lengths between the antennas and the splitters are identical within each frequency band to avoid phase delays that steer the beam off-zenith.

The summed signal is terminated on a lumped resistor on a bolometer island (rightmost image in Fig. 5), where the signal is detected by an TES with a critical temperature of approximately . The fabrication process and bolometer design are similar to those developed for the POLARBEAR-2 (PB-2) detector wafers.Westbrook et al. (2016); Suzuki et al. (2016)

For the microstrip ground plane and strip layer, we use superconducting . As a microstrip dielectric, we used for this prototype, but we intend to use for future devices, since it shows times lower loss and has been successfully implemented in the wafers recently fabricated for PB-2.

The wafer was mated with a lenslet arrayQuealy (2012) and installed in a test cryostat, which cools the detector wafer to . The bolometers are read out with DC superconducting quantum interference devices (SQUIDs).

The frequency response was measured with a Fourier-transform spectrometer. The results (Fig. 6) are similar for the conventional and hierarchical pixels, showing that the hierarchical design is not introducing a spurious frequency response.

Figure 6: The frequency response shows bands centered at , and for both the conventional trichroic pixel (dashed) and the hierarchical array (solid).

The beams were measured using a chopped liquid-nitrogen source on an XY stage. The results are shown in Fig. 7 for and .

Figure 7: Beam maps for (left column) and (right column). The conventional trichroic pixel (upper row) shows frequency-dependent beam widths. The hierarchical array (bottom row) shows roughly constant beam widths.

The array has created round beams of approximately the same size at both frequencies with widths that are consistent with expectations from EM simulations. The faint hexagonal pattern is expected from the array factor of triangular antenna arrays. The beam profiles are shown in Fig. 8, where we see that the hierarchical design has created approximately constant beam widths across the , and - bands.

Figure 8: Beam profiles for the conventional trichroic pixel (top) and the hierarchical array (bottom). The different markers correspond to different azimuthal angles, i.e., , , and . To guide the eye, the vertical dashed lines indicate the half maxima for the conventional pixel.

We were unable to measure the optical efficiency, since the optical loading from the room-temperature equipment exceeded the saturation power of the TESs. The measurements were performed, therefore, above the superconducting transition. Non-linearities in the detector response were removed in post-processing. We place conservative lower bounds on the optical efficiency relative to top-hat bands of fractional width centered on , and . We estimate optical efficiency at , at and at .

Looking forward to future hierarchical designs, we have been developing the lenslet-coupled sinuous antenna to cover a broad frequency range from to Westbrook et al. (2016) as well as testing new microwave components such as a broadband hybrid. As a potential replacement for the relatively narrowband double-ring hybrids (Fig. 3), we designed a hybrid that operates across a 4:1 bandwidth. This component saves space, simplifies the design and reduces the number of microstrip cross-overs. Our design (Fig. 9) relies on a microstrip-slotline-microstrip coupling.

Figure 9: A broadband hybrid relying on a microstrip-slotline-microstrip coupling.

Measurements of the bands (Fig. 10) show some degradation relative to those of Fig. 6 but are correctly placed.

Figure 10: Measurements of a prototype broadband hybrid. (Left) Spectra showing -, - and - bands. (Right) Beam profiles.

The beams are all co-centered to better than . The lack of frequency-dependent beam steering indicates that the hybrid splits power evenly with a phase difference over the entire frequency range.

We have demonstrated the essential features of a hierarchical sinuous phased array, which has the potential to substantially improve the mapping speed of multichroic focal planes. The architecture does not depend on detector type and can be straightforwardly adapted for non-TES lithographed cryogenic detectors such as kinetic inductance detectors (KIDs). We envision this technology as an integral part of future wideband millimeter-wave telescopes.

This work was supported by NASA grant NNX17AH13G. The devices were fabricated in the Marvell Nanolab at UC Berkeley.


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