Spectral Characteristics of the Double-Folded Slot Antennas with Cold-Electron Bolometers for the 220/240 GHz Channels of the LSPE Instrument

the Double-Folded Slot Antennas with Cold-Electron Bolometers for the 220/240 GHz Channels Abstract: We present the results of the experimental and theoretical study of the resonant properties and noise of a single cell of a receiving system based on cold-electron bolometers (CEB) with a double-folded slot antenna and coplanar lines. The system was designed to receive signals at 220/240 GHz frequencies with a 5% bandwidth. In measurements, we used the samples of the double-folded slot antennas with slot lengths of 162 um and coplanar line lengths from 185 to 360 um. Measurements of the resonance properties of CEB located at 0.3 K cryostat plate were carried out using a generator based on a high-temperature YBCO Josephson junction located inside the same cryostat at 4 K plate. This arrangement made it possible to obtain smooth amplitude-frequency characteristics with a clearly deﬁned peak of a 15–21 GHz bandwidth at different frequencies. Based on these results, 2-D array of double-folded slot antennas with CEBs as 220/240 GHz LSPE channel prototype was calculated.The absorption efﬁciency of the array has reached 81% and 77% for 220 and 240 GHz channels, respectively.


Introduction
Current work is aimed at the creation of a bolometric system with an antenna and an on-chip filter as an application in ultra-sensitive balloon-borne receiving systems for the study of cosmic microwave background radiation (CMB)-one of the important and actual issues of modern astronomy and cosmology. The Large Scale Polarization Explorer (LSPE) [1] is an experiment of the Italian Space Agency for studying the polarization pattern of the B-mode of CMB. In this experiment, it is supposed to observe a signal at the central frequency of 145 GHz with a bandwidth of 30%, and at frequencies of 220 and 240 GHz (with a bandwidth of 5%). The channel of 145 GHz is the main one for measuring the CMB. The 220 GHz and 240 GHz bands are ancillary frequency channels. They are needed to eliminate the influence of cosmic dust radiation on the measurements of the CMB [2], giving the offset of the main channel. The main difficulty of this project is the creation of a two-channel system for frequencies of 220 GHz and 240 GHz with a small HPBW of 5%.
As sensitive radiation detectors for this project, we propose to use the cold-electron bolometers (CEBs) [3][4][5]. These detectors have several advantages: a wide dynamic range due to the presence of effective electron cooling [5,6], high sensitivity to the received useful signal [7], and low internal noise below the photon noise of incoming signal [7,8]. The CEBs are insensitive to cosmic rays because of the small absorber volume and weak coupling between the electron and phonon subsystems of the absorber at low temperatures [9]. Besides, CEBs have a compact size of the order of several microns, which allows them to be placed directly into the antenna slot or a cut of a coplanar line [10][11][12]. CEBs allow fabrication of the integrated on-chip filters, consisting of tunnel superconducting-insulatornormal metal (SIN) capacitances, antenna and coplanar reactances.

Electromagnetic Model
As a model of the antenna cell, we use a double slot antenna. These antennas have been tested with various sensors, such as bismuth bolometers [13], quasioptical SIS mixers [14], and so on. The concept of double slot antenna has also been applied in the seashell antenna [11,12,15,16] which has been designed for use with CEBs and suggested for COrE project [17]. To make a single cell of the antenna matrices, we actually take one frequency channel of the seashell antenna. This antenna cell represents double-folded slot antennas connected by a coplanar line [18,19]. We started with simple double-slot antennas but could not achieve the required bandwidth of 5%. Then we tried double-folded slot antennas and managed to approach this value of the bandwidth. The peculiarity of this antenna with the CEB is that we do not simply match the resistance of the bolometer but must first compensate for the capacitance of the SIN junction, and then match it with the resistance of the bolometer.
As a sensor, we use a CEB inserted into a cut in the middle of the coplanar line ( Figure 1a). This antenna cell is characterized by a narrow bandwidth, which is one of the critical requirements for the ancillary channels of the LSPE project. Since a single bolometer has rather low saturation power, to make the antenna system operating at a larger optical load, these cells are proposed to be combined into an array [20]. The cells can be connected by DC conductors either in series or in parallel, to provide either current or voltage bias to CEBs, respectively. The required radiation diagram of the receiving system will be provided by a special back-to-back horn.
We perform numerical simulations of a single antenna cell in the CST Microwave Studio software package. The method of calculation of frequency characteristics of the antenna cell is described in [15,16]. First, we calculate the S-parameter of the system, and then Z-parameter in 3D electromagnetic simulations using the frequency domain solver. We place the discrete port to the position of the CEB. As the proposed antenna operates near serial resonance, i.e., near frequency f res where ImZ(f res ) = 0 and d(ImZ)/df > 0, in the vicinity of this resonance, the impedance of the antenna can be represented as Z = ReZ e +2πfL e +1/(2πfC e ) (Figure 1b). Here L e and C e are the equivalent inductance and capacitance of the slot antennas and coplanar lines near f res, respectively. Then, for CEB modeling the RC-chain (Figure 1b) is used. Here R abs is the resistance of an absorber; C SIN is the two serial SIN junction capacitance of the bolometric system. We calculate R abs and C SIN values using these relations: C SIN = (2πf 0 ImZ(f 0 )) −1 , R abs = ReZ(f 0 ). Here Z(f) is the Z-matrix diagonal component calculated in the electrodynamic part. We select C SIN values in the way that total C SIN and C e capacitances form a series resonance with L e at frequencies of 220 and 240 GHz, respectively. The value of R abs is chosen such to achieve the maximal coupling efficiency of an antenna system and a CEB. This parameter selection method is applicable only if ImZ(f 0 ) > 0 and if |S mn (f 0 )| << 1. Here S mn are off-diagonal components in the S-parameter matrix, which we calculate in the electrodynamic part. These relations lead to resonance at the operating frequency f 0 . The numerical simulation takes into account the effect of direct current conductors on the antenna electrodynamics. We simulate DC conductors by lumped capacitances, which we connect between the central coplanar line ends and the ground plane. The value of these capacitances is 350 fF. DC conductors by lumped capacitances, which we connect between the central coplanar line ends and the ground plane. The value of these capacitances is 350 fF.

Figure 1.
(a) Double-slot antenna single cell design: 1-slots; 2-receiving port cold-electron bolometers (CEB); 3-metal layer. Here the slot length is 162 um and the length of the coplanar line is L = 2 · (L1 + L2 + L3), and is equal to 360 um, which corresponds to the sample photo in Figure 3. (b) CEB connected to a double-slot antenna, equivalent circuit.

Experimental Setup
Cold-electron bolometer represents double SIN (SIN-superconductor-insulatornormal metal) junctions Al/Al2O3/Fe-Al/Al2O3/Al with normal metal nanoabsorber made of aluminum, whose superconductivity is suppressed by a 1 nm thin underlayer of Fe. The radiation through the antenna comes to the superconducting leads of the bolometer, and through a tunnel junction capacitance heats electrons in the normal metal nanoabsorber. The 'hot' electrons then tunnel through the barrier, forming the response current. With this current, 'hot' electrons are removed from the absorber decreasing its electron temperature, thus improving sensitivity and dynamic range [7]. CEBs with antenna systems were fabricated at Chalmers University of Technology. The substrate is made of silicon, the dielectric layer is made of SiO2. Figure 2 shows a SEM image of a fragment of the chip, which consists of a cell with CEB and a two-slot antenna with coplanar lines. Here the slot length is 162 um and the length of the coplanar line is L = 2 · (L 1 + L 2 + L 3 ), and is equal to 360 um, which corresponds to the sample photo in Figure 3. (b) CEB connected to a double-slot antenna, equivalent circuit.

Experimental Setup
Cold-electron bolometer represents double SIN (SIN-superconductor-insulatornormal metal) junctions Al/Al 2 O 3 /Fe-Al/Al 2 O 3 /Al with normal metal nanoabsorber made of aluminum, whose superconductivity is suppressed by a 1 nm thin underlayer of Fe. The radiation through the antenna comes to the superconducting leads of the bolometer, and through a tunnel junction capacitance heats electrons in the normal metal nanoabsorber. The 'hot' electrons then tunnel through the barrier, forming the response current. With this current, 'hot' electrons are removed from the absorber decreasing its electron temperature, thus improving sensitivity and dynamic range [7]. CEBs with antenna systems were fabricated at Chalmers University of Technology. The substrate is made of silicon, the dielectric layer is made of SiO 2 . Figure 2 shows a SEM image of a fragment of the chip, which consists of a cell with CEB and a two-slot antenna with coplanar lines. Appl. Sci. 2021, 11, x FOR PEER REVIEW 4 of 11 . To investigate the resonance properties of CEBs we have used a cooled generator based on high-temperature Josephson junctions as it was done in [21][22][23]. Long Josephson junction samples based on YBa2Cu3O7─δ film (YBCO) on the surface of 24° [001]-tilt Zr1-xYxO2 bicrystal substrates were deposited by magnetron sputtering using preliminary topology mask method [24,25]. The preliminary CeO2 mask was applied to the substrate, and with further deposition of the superconducting film, an insulator grew in the modified regions and a superconducting film in the unmodified regions. Thus, a pattern of a planar structure of a superconducting generator on a substrate was formed. At the same time, the superconducting film did not grow on the bicrystal boundary resulting in the formation of a superconductor─weaklink─superconductor structure, which is a Josephson junction. Figure 3 (top left) shows a fragment of a chip that consists of a long Josephson junction with a dipole antenna. When a direct current is passed through such a structure, an alternating voltage (electromagnetic field) arises, and the frequency of this generation is strictly determined by the average voltage in the junction and is in the range of 50-800 GHz [23]. Thus, Josephson junctions are effective generators for studying the amplitude-frequency characteristics of bolometric and detector systems. To investigate the resonance properties of CEBs we have used a cooled generator based on high-temperature Josephson junctions as it was done in [21][22][23]. Long Josephson junction samples based on YBa 2 Cu 3 O 7-δ film (YBCO) on the surface of 24 • [001]-tilt Zr 1-x Y x O 2 bicrystal substrates were deposited by magnetron sputtering using preliminary topology mask method [24,25]. The preliminary CeO 2 mask was applied to the substrate, and with further deposition of the superconducting film, an insulator grew in the modified regions and a superconducting film in the unmodified regions. Thus, a pattern of a planar structure of a superconducting generator on a substrate was formed. At the same time, the superconducting film did not grow on the bicrystal boundary resulting in the formation of a superconductor-weaklink-superconductor structure, which is a Josephson junction. Figure 3 (top left) shows a fragment of a chip that consists of a long Josephson junction with a dipole antenna. When a direct current is passed through such a structure, an alternating voltage (electromagnetic field) arises, and the frequency of this generation is strictly determined by the average voltage in the junction and is in the range of 50-800 GHz [23]. Thus, Josephson junctions are effective generators for studying the amplitude-frequency characteristics of bolometric and detector systems. Figure 3 shows a schematic view of the experiment. The generator chip consisted of a Josephson junction integrated with dipole antennas was mounted on a holder with a Si hyperhemisphere lens (4 mm diameter) located on a 4 K cryostat plate. The control magnetic field, perpendicular to the Josephson junction boundary, was created by current flowing through a coil of a copper wire. A bolometric system with the lens on the backside of the silicon substrate was placed on a 300 mK plate. The copper shield, covered with a black body, was used to avoid signal reflections from the shield back to the generator. The distance between the detector and the source was 3 cm.
Varying the current through the Josephson junction, we measured the bolometric response (voltage difference dV CEB at a fixed bias current through the CEB) and the voltage on the YBCO generator (the Josephson radiation frequency f = 2 eV YBCO /h). The generator was calibrated independently by a broadband CEB receiver, studied in [23], and compared with the response of the backward wave oscillator (BWO). In addition, the oscillator antenna was investigated by measuring the Shapiro steps [25] using the same BWO. Substituting the Josephson relation between the frequency and the voltage on the generator, we obtained the amplitude-frequency characteristic of the receiving system. Appl. Sci. 2021, 11, x FOR PEER REVIEW 5 of 11 Figure 3. The experimental setup view, its schematic representation, and samples design. Figure 3 shows a schematic view of the experiment. The generator chip consisted of a Josephson junction integrated with dipole antennas was mounted on a holder with a Si hyperhemisphere lens (4 mm diameter) located on a 4 K cryostat plate. The control magnetic field, perpendicular to the Josephson junction boundary, was created by current flowing through a coil of a copper wire. A bolometric system with the lens on the backside of the silicon substrate was placed on a 300 mK plate. The copper shield, covered with a black body, was used to avoid signal reflections from the shield back to the generator. The distance between the detector and the source was 3 cm.
Varying the current through the Josephson junction, we measured the bolometric response (voltage difference dVCEB at a fixed bias current through the CEB) and the voltage on the YBCO generator (the Josephson radiation frequency f = 2 eVYBCO/ħ). The generator was calibrated independently by a broadband CEB receiver, studied in [23], and compared with the response of the backward wave oscillator (BWO). In addition, the oscillator antenna was investigated by measuring the Shapiro steps [25] using the same BWO. Substituting the Josephson relation between the frequency and the voltage on the generator, we obtained the amplitude-frequency characteristic of the receiving system. Figure 4 presents the results of an experimental study of the resonant properties of CEBs with a double-folded slot antenna and coplanar lines. To develop a resonant receiving system at given frequencies, it is necessary to adjust the elements of the system, in particular, the capacity of the SIN junction in CEB and the length L = 2 · (L1 + L2 + L3) of the central coplanar line (see Figure 1). During the experiments, the effect of changes in these system parameters on the operating frequency was tested (Figure 4). We have also analyzed various designs of coplanar lines with rectangular turns as in Figure 3 (solid curves) and with rounded turns (dashed curves). It can be seen that by selecting the capacitance and lengths of the coplanar lines, the system can be tuned to the specified frequency range. It is seen that all characteristics have a clearly defined peak at different  Figure 4 presents the results of an experimental study of the resonant properties of CEBs with a double-folded slot antenna and coplanar lines. To develop a resonant receiving system at given frequencies, it is necessary to adjust the elements of the system, in particular, the capacity of the SIN junction in CEB and the length L = 2 · (L 1 + L 2 + L 3 ) of the central coplanar line (see Figure 1). During the experiments, the effect of changes in these system parameters on the operating frequency was tested ( Figure 4). We have also analyzed various designs of coplanar lines with rectangular turns as in Figure 3 (solid curves) and with rounded turns (dashed curves). It can be seen that by selecting the capacitance and lengths of the coplanar lines, the system can be tuned to the specified frequency range. It is seen that all characteristics have a clearly defined peak at different frequencies with a bandwidth of around 15 GHz. So, the resulting bandwidth of 6-9% practically meets the requirements for the LSPE experiment receiving system. Out of band peaks can be attributed both to peaks of YBCO amplitude-frequency characteristic and to the methodic of CEB sample irradiation. Due to the necessity to test the first on-chip filter prototypes we have placed up to 6 samples with various antennas on one chip and certain receivers are shifted from the chip center and standing waves differently affect various antennas. These issues will be corrected in future designs of both YBCO sources with more suitable broadband antennas and new designs of CEBs with on-chip filters with only one antenna at the chip center. Nevertheless, our experimental setup where the generator lens was mounted close to the receiver lens separated by infrared filters, allowed significantly reducing spurious resonances, which inevitably arose in experiments with room temperature sources of GHz radiation outside the cryostat [15] due to additional reflections from cryostat shields and much larger power.

Measurement Results
antennas. These issues will be corrected in future designs of both YBCO sources with more suitable broadband antennas and new designs of CEBs with on-chip filters with only one antenna at the chip center. Nevertheless, our experimental setup where the generator lens was mounted close to the receiver lens separated by infrared filters, allowed significantly reducing spurious resonances, which inevitably arose in experiments with room temperature sources of GHz radiation outside the cryostat [15] due to additional reflections from cryostat shields and much larger power. Figure 4. The amplitude-frequency characteristics of cold-electron bolometers with different capacitance C and lengths L of coplanar lines. Solid curves-rectangular coplanars, dashed curvesrounded coplanars, crosses-theory for the parameters close to the experiment for green solid curve with diamonds.
The experimental center frequencies are in some cases shifted from the calculated values (see Figure 4, calculated center frequencies are given in the legend). This difference is most probably caused by the influence of the standing waves in a substrate, which were not taken into account in the initial simulations. Another possible reason for the frequency shift, found when designing the system [7], was the effect of dc wires, which will be precisely calculated in future designs. However, the most critical reason for the frequency shift is the fact that at low capacitance of the order of 10 fF, a small increase in capacitance due to overexposure of a tunnel junction may significantly shift the resonance to lower frequencies. Besides, at frequencies of several hundred GHz and at low temperatures it may be necessary to take into account the surface impedance of gold, which differs from the one at low frequencies and room temperature, and is known to be frequency-dependent. Also, as follows from the experimental results, the samples with rectangular coplanar lines demonstrate a stronger effect of standing waves leading to sharper satellite spikes. The simulation results, taking into account reflections from the substrate edges, are shown by crosses for the parameters close to the experiment for green solid curve with diamonds Figure 4. The amplitude-frequency characteristics of cold-electron bolometers with different capacitance C and lengths L of coplanar lines. Solid curves-rectangular coplanars, dashed curvesrounded coplanars, crosses-theory for the parameters close to the experiment for green solid curve with diamonds.
The experimental center frequencies are in some cases shifted from the calculated values (see Figure 4, calculated center frequencies are given in the legend). This difference is most probably caused by the influence of the standing waves in a substrate, which were not taken into account in the initial simulations. Another possible reason for the frequency shift, found when designing the system [7], was the effect of dc wires, which will be precisely calculated in future designs. However, the most critical reason for the frequency shift is the fact that at low capacitance of the order of 10 fF, a small increase in capacitance due to overexposure of a tunnel junction may significantly shift the resonance to lower frequencies. Besides, at frequencies of several hundred GHz and at low temperatures it may be necessary to take into account the surface impedance of gold, which differs from the one at low frequencies and room temperature, and is known to be frequency-dependent. Also, as follows from the experimental results, the samples with rectangular coplanar lines demonstrate a stronger effect of standing waves leading to sharper satellite spikes. The simulation results, taking into account reflections from the substrate edges, are shown by crosses for the parameters close to the experiment for green solid curve with diamonds and qualitative agreement with the experiment is observed. Finally, among all the data we have found a sample (black dashed curve), which has a smooth shape and is centered exactly at the required 240 GHz. These sample parameters will be scaled in future designs to form a pair of antennas for 220/240 GHz channel of LSPE. Figure 5 presents the comparison of CEB output voltage noise in the absence and in the presence of YBCO GHz signal. It can be seen that the noise level does not change due to rather weak external signal power (on the order of 1 pW, which was got from fitting as in [23]), received by the CEB, and narrow spectral linewidth of YBCO oscillator, operating at 4 K temperature. The total voltage noise of a bolometer δV tot consists of three components: the noise of the amplifier δV amp , the noise of the bolometer itself δV CEB and the noise of an external signal δV ex , thus δV tot 2 = δV amp 2 + δV CEB 2 + δV ex 2 . Measured total noise (pedestal level) in the absence of an external signal at the frequency of 120 Hz is 8.5 nV/sqrt(Hz) (see Figure 5). Taking into account that the amplifier noise δV amp = 5 nV/sqrt(Hz), this means that the intrinsic noise of the bolometer δV CEB = 6.9 nV/sqrt(Hz) is slightly larger than the amplifier noise δV amp . When an external high-frequency signal is applied, the total noise of the bolometer may increase due to the amplitude and phase noise of the external generator (as it was in our experiments with the backward wave oscillator [15]) or due to photon noise δV ph . The absence of changes in our case, Figure 5, indicates high stability of the source based on the high-temperature YBCO Josephson junction. On the other hand, we also do not observe the contribution of photon noise. It was shown [23] that for a power load of 5 pW the total noise-equivalent power of a single CEB with room temperature amplifiers AD745 equals 10 −16 W/sqrt(Hz) and is larger than photon NEP. That is why we did not see noise growth in our experiments.
to rather weak external signal power (on the order of 1 pW, which was got from fitting as in [23]), received by the CEB, and narrow spectral linewidth of YBCO oscillator, operating at 4 K temperature. The total voltage noise of a bolometer δVtot consists of three components: the noise of the amplifier δVamp, the noise of the bolometer itself δVCEB and the noise of an external signal δVex, thus δVtot 2 = δVamp 2 + δVCEB 2 + δVex 2 . Measured total noise (pedestal level) in the absence of an external signal at the frequency of 120 Hz is 8.5 nV/sqrt(Hz) (see Figure 5). Taking into account that the amplifier noise δVamp = 5 nV/sqrt(Hz), this means that the intrinsic noise of the bolometer δVCEB = 6.9 nV/sqrt(Hz) is slightly larger than the amplifier noise δVamp. When an external high-frequency signal is applied, the total noise of the bolometer may increase due to the amplitude and phase noise of the external generator (as it was in our experiments with the backward wave oscillator [15]) or due to photon noise δVph. The absence of changes in our case, Figure 5, indicates high stability of the source based on the high-temperature YBCO Josephson junction. On the other hand, we also do not observe the contribution of photon noise. It was shown [23] that for a power load of 5 pW the total noise-equivalent power of a single CEB with room temperature amplifiers AD745 equals 10 −16 W/sqrt(Hz) and is larger than photon NEP. That is why we did not see noise growth in our experiments. Finally, on the basis of this single cell, we are developing an array of resonant CEBs which are able to work in the photon noise limited regime for larger signal powers. Such regime was demonstrated in our previous works [7,8] for parallel-series arrays of coldelectron bolometers [26].

Multi-Cell Double-Folded Slot Antenna with Coplanar Lines and CEBs for Ancillary Frequency Channels of LSPE
In this section, we consider rounded arrays of double-folded slot antenna cells with resonant cold-electron bolometers for secondary frequency channels of SWIPE instrument, designed for the LSPE project. These frequency channels are set to 220 and 240 GHz Finally, on the basis of this single cell, we are developing an array of resonant CEBs which are able to work in the photon noise limited regime for larger signal powers. Such regime was demonstrated in our previous works [7,8] for parallel-series arrays of coldelectron bolometers [26].

Multi-Cell Double-Folded Slot Antenna with Coplanar Lines and CEBs for Ancillary Frequency Channels of LSPE
In this section, we consider rounded arrays of double-folded slot antenna cells with resonant cold-electron bolometers for secondary frequency channels of SWIPE instrument, designed for the LSPE project. These frequency channels are set to 220 and 240 GHz with the required bandwidths around 5% for both channels and intended for receiving signals from a horn.
It is quite a challenging task to create such a narrowband array of antenna cells for so high frequency. While there are works on antenna metasurfaces [27][28][29][30][31][32][33], normally the resulting bandwidths are much above 10%. In difference with standard metasurfaces, where the signal from all antennas is fed to a single receiver, due to the small size of CEBs of order 1 um, it is possible to place the bolometer inside each antenna in the array, so we deal with the antenna array with distributed receivers. Here we show that certain progress in narrowband arrays is possible with double-folded slot cells, where a coplanar line is used for better impedance matching.
Previously, similar design of a current-biased array of double-slot cells with coplanar lines showed rather good results for creating a narrowband amplitude-frequency characteristic, as shown in simulations [20]. Now these antenna cells, grouped into rounded array, are connected in parallel with DC wires to work in a voltage-biased mode. DC wires are connected to coplanar lines, and they are put under the ground plane, so the construction requires an insulating layer between DC wires and the ground plane. For this design, the insulator is SiO 2 , while DC wires are made of gold.
Totally, there are three technological stages. The first one is for golden DC connection lines under cells ground planes. The second one creates insulation for these lines, providing no connection between DC wires and ground planes. At the third stage, we make ground planes with double-slot design and coplanar lines. Major DC connection wires are also created at this stage. A quarter of the rounded array used for calculations is shown in Figure 6.
of order 1 um, it is possible to place the bolometer inside each antenna in the array, so we deal with the antenna array with distributed receivers. Here we show that certain progress in narrowband arrays is possible with double-folded slot cells, where a coplanar line is used for better impedance matching.
Previously, similar design of a current-biased array of double-slot cells with coplanar lines showed rather good results for creating a narrowband amplitude-frequency characteristic, as shown in simulations [20]. Now these antenna cells, grouped into rounded array, are connected in parallel with DC wires to work in a voltage-biased mode. DC wires are connected to coplanar lines, and they are put under the ground plane, so the construction requires an insulating layer between DC wires and the ground plane. For this design, the insulator is SiO2, while DC wires are made of gold.
Totally, there are three technological stages. The first one is for golden DC connection lines under cells ground planes. The second one creates insulation for these lines, providing no connection between DC wires and ground planes. At the third stage, we make ground planes with double-slot design and coplanar lines. Major DC connection wires are also created at this stage. A quarter of the rounded array used for calculations is shown in Figure 6.  The diameter of this rounded array should not exceed 4.5 mm. It is because of a predefined configuration of a back-to-back feedhorn, which will be used with this system. The optimal antenna cells number to fill this feedhorn configuration is 112.
The feedhorn is located on the opposite side of the substrate. In the numerical modeling, the feedhorn is simulated by a waveguide port as a source of radiation. Here we work only with the mode E 01 .
Calculation of such quite a large array will require a lot of computational resources, so we use symmetry planes to decrease the calculation time. For the mode E 01 it is electric (E t = 0) symmetry plane at YZ plane and magnetic (H t = 0) symmetry plane at XZ plane. Due to this, we have to perform calculations for 28 antenna cells and the mesh cells number is about 3.5 million only. Without symmetry planes, these numbers would have increased by a factor of four. Figure 7 shows the accepted power versus frequency curves for all CEBs of the array at 220 and 240 GHz frequency channels, respectively. The bandwidth for the 220 GHz channel at half of the accepted power is about 18 GHz or 8.2%, from 210 to 228 GHz. It is quite close to meet the requirements for LSPE. The deviation from the required bandwidth is mostly at the lower frequencies, so to decrease the bandwidth an additional external filter can be used. The 240 GHz channel bandwidth is very close to meet LSPE project requirements. At half of the accepted power, the bandwidth is about 14 GHz or 5.8%, from 232.5 to 246.5 GHz. The absorption efficiency of the array has reached 81% and 77% for 220 and 240 GHz channels, respectively. The work on optimization of frequency response for 220 and 240 GHz channels is being continued.
Due to this, we have to perform calculations for 28 antenna cells and the mesh cells number is about 3.5 million only. Without symmetry planes, these numbers would have increased by a factor of four. Figure 7 shows the accepted power versus frequency curves for all CEBs of the array at 220 and 240 GHz frequency channels, respectively. The bandwidth for the 220 GHz channel at half of the accepted power is about 18 GHz or 8.2%, from 210 to 228 GHz. It is quite close to meet the requirements for LSPE. The deviation from the required bandwidth is mostly at the lower frequencies, so to decrease the bandwidth an additional external filter can be used. The 240 GHz channel bandwidth is very close to meet LSPE project requirements. At half of the accepted power, the bandwidth is about 14 GHz or 5.8%, from 232.5 to 246.5 GHz. The absorption efficiency of the array has reached 81% and 77% for 220 and 240 GHz channels, respectively. The work on optimization of frequency response for 220 and 240 GHz channels is being continued. Figure 7. Frequency response curves of the receiving system for LSPE ancillary channels 220 GHz (blue curve) and 240 GHz (red curve).

Discussion
A prototype of a single detecting cell in the form of a double-folded slot narrow-band antenna for the LSPE experiment has been developed. During this stage, technological issues of fabrication of these antennas were investigated, the influence of the length of coplanar lines and capacitances of SIN junctions on the operating frequency of the receiving system was checked. This allowed selecting a double-folded slot receiving system with the coplanar line, having smooth amplitude-frequency characteristic centered at 240 GHz, which can be used for further design of double frequency 220/240 GHz receiver for LSPE mission. Based on these results, 2-D array of double-folded slot antennas with CEBs as 220/240 GHz LSPE channel prototype was calculated.
A double-folded slot antenna with coplanar lines represents a type of planar antenna, which is suitable for cosmology projects due to its compactness, flexibility of adjustment, Figure 7. Frequency response curves of the receiving system for LSPE ancillary channels 220 GHz (blue curve) and 240 GHz (red curve).

Discussion
A prototype of a single detecting cell in the form of a double-folded slot narrow-band antenna for the LSPE experiment has been developed. During this stage, technological issues of fabrication of these antennas were investigated, the influence of the length of coplanar lines and capacitances of SIN junctions on the operating frequency of the receiving system was checked. This allowed selecting a double-folded slot receiving system with the coplanar line, having smooth amplitude-frequency characteristic centered at 240 GHz, which can be used for further design of double frequency 220/240 GHz receiver for LSPE mission. Based on these results, 2-D array of double-folded slot antennas with CEBs as 220/240 GHz LSPE channel prototype was calculated.
A double-folded slot antenna with coplanar lines represents a type of planar antenna, which is suitable for cosmology projects due to its compactness, flexibility of adjustment, and ease of fabrication. This antenna can be used for a wide range of tasks with multifrequency systems.

Data Availability Statement:
The data that support the findings of this work are available from the corresponding author upon reasonable request.