1 Introduction

Observing the cosmic microwave background (CMB) provides profound insights into the origins and evolution of the universe [1]. However, measuring its B-mode polarization pattern remains a challenge in millimeter astronomy, mainly due to detector limitations arising from photon noise [2,3,4]. This emphasizes the need for next-generation telescopes featuring a significantly increased number of detectors and enhanced focal plane efficiency. Additionally, to achieve B-mode reduction polarimetry, it is imperative to observe the sky across multiple frequency bands due to foreground emissions from both galactic and extra-galactic sources [5, 6]. Antenna-coupled detectors can be designed to capture multi-frequency bands and offer polarization-selective sensitivity, particularly when integrated with on-chip band-pass filters, resulting in a compact and efficient solution for multichroic CMB detectors [7].

The bowtie slot antenna, often referred to broadband dipole or tapered slot, is preferred to couple with cryogenic detectors due to its simplicity in fabrication and broadband capabilities [8, 9]. Its planar structure not only facilitates seamless integration into various devices but also ensures consistent impedance characteristics across a broad frequency range. This makes it a compact and efficient alternative to more conventional designs like horn or sinusoidal antennas. For applications involving millimeter and sub-millimeter wave frequencies, especially in CMB observation, performance enhancements are often needed due to its limitation in impedance bandwidth. One approach is to expand the flare angle to 90 degrees [10], broadening the bandwidth at the cost of reduced polarization selectivity. Another effective approach involves employing an array configuration, such as double or dual-slot designs [11,12,13]. While potentially increasing the physical size, this modification can enhance frequency response, quasi-optical coupling efficiency, and overall system directivity.

This paper explores an innovative design for a bowtie slot antenna featuring a second flare angle, hence termed the double-flare angle (DFA) bowtie antenna. This design is an adaptation of the printed dipole planar bowtie antenna [14] where the flare angle is used to increase the bandwidth in dual-band operation. Our design is specifically tailored to observe CMB in multiple bands within the 100–300 GHz range, aligning with two frequency bands targeted by the CMB-S4 project [15] that are centered at 150 and 220 GHz. Additionally, the antenna must maintain sensitive linear polarization capabilities which is essential for CMB polarimetry. A compromise between various antenna aspects must be carefully considered to meet all requirements. We have limited the flare angle to a maximum of 40 degrees to ensure polarization sensitivity. Concurrently, the antenna’s effective length also needs to be sufficiently compact to maintain a broad operational bandwidth while avoiding dimensions that significantly exceed the target wavelengths. Oversizing the antenna could lead to excessive standing waves, resulting in increased sidelobes, poor beam shaping, or diminished gain in the desired direction, all of which critically impact the optical coupling efficiency of the antenna.

Evaluations in this paper primarily utilize the 3D full-wave simulator—CST Studio Suite [16], complemented by Sonnet [17] for enhanced superconductor modeling accuracy.

2 Antenna design

2.1 Double-Flare Angle Bowtie

We employ a rounded-edge bowtie antenna as base geometry, originally known for its improved return loss and more stable radiation patterns [18, 19]. The conventional bowtie model is mainly defined by its length (L) and flare angle (A). The DFA configuration introduces an additional angle and length, denoted as A2 and L2 (with the geometry constraint \(L2 < L1\) and \(A2 > A1\)). The primary flare angle A and length L are then denoted as A1 and L1, as shown in Fig. 1a.

Our analysis commenced by examining the antenna input impedance (\(Z_{11}\)) using Transient solver in CST. The simulation model and result are depicted in Fig. 1. A lumped discrete port (depicted as a red cone) feeds the antenna at the center, with the port’s impedance (\(Z_{0}\)) arbitrarily chosen. The \(Z_{11}\) is the antenna’s inherent property driven by its geometry and is independent of the input port impedance \(Z_{0}\). The antenna return loss (\(S_{11}\)) response, however, can vary widely depending on \(Z_{0}\) and is easily obtained with the following relationship: \(S_{11} = \frac{{Z_{11}} - Z_{0}}{{Z_{11}} + Z_{0}}\).

Fig. 1
figure 1

a Parametric designs of traditional (T-Bowtie) and double-flare angle (DFA-Bowtie) antennas. b \(Z_{11}\) comparison illustrates the additional flare angle bringing the second resonant frequency point nearer to the first one, enabling the second resonant frequency tuning feature but also increasing the overall resistivity of the antenna

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The parametric simulations of the traditional bowtie, as shown in Fig. 2a, b, reveal that the angle A is the primary determinant of the antenna’s bandwidth. Increasing A maintains the first resonance point while flattening the real part of \(Z_{11}\), thus broadening the impedance bandwidth. On the other hand, the length L mainly influences the resonant frequency of the bowtie by shifting the entire \(Z_{11}\) curve. The simulated behaviors of A and L therefore are consistent with theoretical expectations [20].

In the case of the DFA bowtie, illustrated in Fig.2c, d, adjustments to length L2 result in minor shifts in the imaginary part of \(Z_{11}\) and a decrease in resistance at the second resonance point when L2 is increased. If L2 approaches L1, the DFA bowtie transitions back to a traditional configuration, contradicting the DFA’s geometric constraints. Expanding angle A2 predominantly impacts the second resonance frequency, pulling it closer and increasing the overall resistive component of the antenna.

In general, despite the impacts of these parameters on the impedance profile of the DFA as we tested, the characteristic shape of \(S_{11}\) remains unchanged, that is, there are always 2 points of resonant frequency and the real part (resistance) of these two points is always different. Therefore, unless being fed by two different impedances correspondingly, this antenna can never achieve multi-band operation because there will always be impedance mismatch in each sub-band.

Fig. 2
figure 2

Parametric study of antenna input impedance \(Z_{11}\). a, b: L and A of T-Bowtie; c, d: L2 and A2 of DFA-Bowtie

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2.2 Optimization

Our primary objective is to design the antenna for dual sub-band operation, specifically targeting 150 GHz and 220 GHz with a 20% bandwidth for each band. To ideally achieve this, we aim for \(Z_{11}\) to be purely resistive (zero reactance) at both frequencies, and their values must be equal to facilitate multi-band operation with a single-input impedance, i.e., one feedline. Essentially, the antenna must satisfy the following two conditions simultaneously:

$$\begin{aligned} \text {Re}\{Z_{11}\}|_{f = {150\,\textrm{GHz}}}&= \text {Re}\{Z_{11}\}|_{f = {220\,\textrm{GHz}}}, \end{aligned}$$
(1 )
$$\begin{aligned} \text {Im}\{Z_{11}\}|_{f = {150\,\textrm{GHz}}}&= \text {Im}\{Z_{11}\}|_{f = {220\,\textrm{GHz}}} = 0. \end{aligned}$$
(2 )

As studied in section , meeting these criteria at the same time is challenging for the DFA design due to its inherent planar physical limitations and the natural frequency-dependent behavior of reactance. Our strategy involves optimizing each condition independently and then finding an optimal balance between them. The final optimization is represented by the blue curves in Fig. 3, focusing on the adjustment of parameters A1, L1, A2, and L2.

Fig. 3
figure 3

a Optimization scheme for \(Z_{11}\) and b corresponding \(S_{11}\) obtained at \(Z_{0}\) chosen to be 48\(~\Omega\). The orange curve zeroes the imaginary part at 150 and 220 GHz; the brown curve aligns the real part with \(46 \, \Omega\) at both frequencies. The blue curve represents the average of these two, constituting the final optimization result. This result is adopted for our DFA-Bowtie configuration, with detailed values provided in Table 1

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2.3 Microstrip Feedline Integration

Fig. 4
figure 4

a Parametric design and model stratification in CST. b Antenna return loss (\(S_{11}\)) comparison between T-Bowtie, DFA-Bowtie, and DFA-Bowtie with feedline

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The finalized antenna model, depicted in Fig. 4a, features a slot antenna etched into a niobium ground plane on a silicon substrate. This antenna is fed via a microstrip feedline, separated by an 885-nm-thick SiO\(_x\) dielectric layer with a relative permittivity of \(\varepsilon _r=4.318\) ( [21, 22]). The feedline terminates by a radial stub that provides wideband impedance matching and exhibits a virtual short circuit to the ground [23, 24]. The radial stub’s dimensions, including radius (stubR), angle (stubA), and position (stubH), are finely tuned to facilitate complete broadband frequency transfer from the feedline to the antenna. The feedline, composed of niobium like the ground plane, exhibits a surface impedance of 0.2 pH/\(\square\) in cryogenic state. The simulations are conducted using the CST frequency domain solver, taking into account the niobium kinetic inductance effect. Notably, the use of CST is crucial to ensure alignment with Sonnet for precise 3D superconducting antenna simulations [25].

The microstrip line width (\(msW\)) is fine-tuned using Sonnet to achieve a characteristic impedance of approximately \(48~\Omega\). This impedance matches the port impedance \(Z_{0}\) that was employed in our previous optimization to yield the optimal \(S_{11}\). Realizing high impedances on a microstrip line is difficult, as it necessitates reducing the width of the trace to a point where it becomes highly sensitive to fabrication tolerances. The optimal value of \(msW\) is determined from simulation to be 2.5 \(\upmu \hbox {m}\), which is at the threshold of our current fabrication we have.

As shown in Fig. 4b, the \(S_{11}\) obtained from the feedline model aligns well with the optimized \(S_{11}\) achieved from Fig. 3b, thereby validating our design approach. It is remarkably revealed that a conventional bowtie antenna, defined by dimensions \(A=A1\) and \(L=L1\) and without the additional flare angles A2 and L2, can also attain an \(S_{11}<-10 dB\) across an octave band. This performance is merely achievable when the antenna operates at an appropriate impedance of \(Z_{0}=37~\Omega\) These comparisons underscore the marginally enhanced performance reliability of the DFA-Bowtie design compared to its traditional counterpart.

Table 1 Parametric values
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3 Antenna-Lens Coupling

3.1 Lens Design and Integration

The antenna is positioned at the second foci of a silicon elliptical lens, as shown in Fig. 5a, to improve its gain and directivity. Silicon (\(\varepsilon _r = 11.9\)) is the preferred lens material for its low-loss properties at millimeter and sub-millimeter wavelengths [26]. Following the designs in [27, 28], the simulated lens has a 6 mm diameter—approximately triple the wavelength of the central bandwidth—and features a rim angle of \(70^\circ\). The semi-major axis and semi-minor axis of the elliptical lens are \(a = 3.140~\)mm and \(b = 3.005~\)mm.

3.2 Performance and Results

Fig. 5
figure 5

a Silicon elliptical lens schematic with slot antenna positioned at its second focus. b, c Comparison of radiation pattern for both bowtie designs at 150 and 220 GHz

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We compared the radiation pattern of the DFA and the traditional bowie with CST at 150 and 220 GHz, as is shown in Fig. 5b, c. It can be seen that the radiation patterns are identical at 150 GHz due to the DFA and traditional bowtie sharing the same first flare angle and length. However, at 220 GHz, the DFA demonstrates a notable side-lobe reduction of several dB. This improvement suggests a potential for further side-lobe reduction by optimizing the shape of the dielectric lens.

Fig. 6
figure 6

Comparison of directivity and cross-polarization levels for both bowtie designs

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The cross-polarization across the operation bandwidth is shown in Fig. 6. It shows the lens-coupled DFA maintains a cross-polarization level below −15 dB across the band simulated and is comparable with the traditional bowtie, which means there is no degradation by introducing the second flare in the design. In general, the cross-polarization becomes higher as frequencies increase. This tendency is due to the current distribution on the antenna surface, which determines its radiation pattern and polarization characteristics [19]. As the antenna becomes electrically large relative to shorter wavelengths, the potential for multiple radiation modes increases, elevating cross-polarization levels.

4 Conclusion and Perspective

In this study, we have proposed an innovative bowtie slot antenna design that is specifically optimized for CMB B-mode detectors, which demonstrates a performance slightly superior to that of a conventional one. Our latest simulations indicate a \(S_{11} < -10\) dB and cross-polarization less than −15 dB across a wide range of frequencies from 100 to 300 GHz. Further optimization of the far-field performance, including aspects such as sidelobe and Gaussian coupling efficiency, is in progress. This antenna is intended to be used as the receiving element in a dual-color multichroic CMB detector employing MKIDs. Next step will be to fabricate and test this design by the end of the year, aiming to assess its effectiveness for CMB B-mode polarimetry and to guide further improvements.