{"paper_id":"0880d984-242b-42fa-aafc-ec64a0f8e19a","body_text":"License and Terms: This document is copyright 2025 the Author(s); licensee Beilstein-Institut.\nThis is an open access work under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0). Please note that the reuse,\nredistribution and reproduction in particular requires that the author(s) and source are credited and that individual graphics may be subject to special legal provisions.\nThe license is subject to the Beilstein Archives terms and conditions: https://www.beilstein-archives.org/xiv/terms.\nThe definitive version of this work can be found at https://doi.org/10.3762/bxiv.2025.58.v1\nThis open access document is posted as a preprint in the Beilstein Archives at https://doi.org/10.3762/bxiv.2025.58.v1 and is\nconsidered to be an early communication for feedback before peer review. Before citing this document, please check if a final,\npeer-reviewed version has been published.\nThis document is not formatted, has not undergone copyediting or typesetting, and may contain errors, unsubstantiated scientific\nclaims or preliminary data.\nPreprint Title Electromagnetic study of a split-ring resonator metamaterial with\nCold-Electron Bolometers\nAuthors Ekaterina A. Matrozova, Alexander V. Chiginev, Leonid S. Revin and\nAndrey L. Pankratov\nPublication Date 06 Okt. 2025\nArticle Type Full Research Paper\nORCID® iDs Ekaterina A. Matrozova - https://orcid.org/0000-0003-1013-1365;\nAlexander V. Chiginev - https://orcid.org/0000-0002-6676-9141;\nAndrey L. Pankratov - https://orcid.org/0000-0003-2661-2745\n\nElectromagnetic study of a split-ring resonator metamaterial with1\nCold-Electron Bolometers2\nEkaterina A. Matrozova1, Alexander V. Chiginev1,2, Leonid S. Revin1,2 and Andrey L.3\nPankratov1,2∗14\nAddress: 1Nizhny Novgorod State Technical University n.a. R.E. Alekseev, Minin Street, 24,5\nNizhny Novgorod, 603155, Russia6\n2Institute for Physics of Microstructures of the Russian Academy of Sciences, Akademicheskaya7\nStreet, 7, Nizhny Novgorod, 603950, Russia8\nEmail: Andrey L. Pankratov1,2 - alp@ipmras.ru9\n∗ Corresponding author10\nAbstract11\nWe present an electromagnetic study of a metamaterial receiver based on split-ring resonators with12\nintegrated cold-electron bolometers. We suggest a modified antenna design that allows one to sig-13\nnificantly increase the absorbed power and the bandwidth. The trade-off between the bandwidth14\nexpansion due to miniaturization and the reduction in absorption efficiency determined by the Airy15\nspot size of the coupling lens is investigated. To solve this issue, a simultaneous miniaturization of16\nthe size of the entire structure with an increase in the number of array elements is proposed. The17\ndesign with a 37-element array demonstrates an increase in power absorption by a factor of 1.418\ncompared to the original 19-element single-ring array, as well as an increase in operating band-19\nwidth from 160 to 820 GHz.20\nKeywords21\nMetamaterial, split-ring resonator, cold electron bolometer22\n1\n\nIntroduction23\nHighly sensitive receivers with broadband antennas are of significant interest for advanced spec-24\ntroscopic applications and various radioastronomy tasks [1-5]. In particular, broadband receiving25\nsystems are required for use with a Fourier Transform Spectrometer based on the Martin-Paplett in-26\nterferometer that is planned to be used in future missions, such as BISOU (Balloon Interferometer27\nfor Spectral Observations of the Universe) [3,4] and Millimetron [2,5]. The use of Cold-Electron28\nBolometers (CEBs) is particularly advantageous for such systems, enabling operation in a wide29\nfrequency range from GHz to X-ray [6-8] due to a normal-metal absorber. CEBs offer several ad-30\nvantages over other types of receiver, such as Transition Edge Sensors (TESs) [9-11]. These ad-31\nvantages include their micrometer scale size, which facilitates direct integration into antenna slots32\nwithout the need for microwave feed lines (e.g., microstrip or coplanar lines), thus simplifying the33\ndesign and preventing signal degradation at higher frequencies [12]. Furthermore, the natural elec-34\ntron cooling mechanism in CEBs [13-15] is highly suitable for operation with cryogenic systems35\nsuch as3He sorption fridges. Perhaps most critically, CEBs demonstrate exceptional immunity to36\ncosmic rays [16], a paramount requirement for balloon and space missions.37\nOur group has recently designed, fabricated and characterized a metamaterial receiver with inte-38\ngrated CEBs, operating in a broad frequency range [17]. In that work, each element represented a39\nring antenna with two embedded CEBs connected parallel in DC, whereas the antennas in the array40\nwere connected in series. In the present work, we propose and numerically investigate a new de-41\nsign of a CEB metamaterial receiver based on double split-ring resonators (SRRs) to increase both42\nthe magnitude of the absorbed signal and the working bandwidth. We consider various geometrical43\nmodifications of this design and perform a comparative analysis.44\nDesign and Simulation Approach45\nIn our previous work [17], a metamaterial comprising 19 ring antennas enabled the reception of46\nexternal electromagnetic signals in the broad band from 150 to 550 GHz, as well as in the band47\nfrom 900 to 1300 GHz. To further enhance signal absorption, we propose replacing simple ring48\n2\n\nFigure 1: Schematic layout of the investigated metamaterial arrays: a) 19-element array of single-\nring antennas; b) 19-element array of split-ring resonators; c) 37-element array of miniaturized\nSRRs. The Inset: a single unit cell with two embedded CEBs represented as an RC circuit.\nantennas with SRRs [18-21]. The SRR is a well-established magnetic metamaterial element whose49\nresonant properties are governed by its internal inductance and capacitance, allowing for a strong50\nmagnetic response and associated current loops at the designed resonance frequency.51\nThe simulated receiving structure is placed on a 500𝜇m-thick silicon substrate. A 4-mm-diameter52\nsilicon hyperhemispherical lens is placed on the back side of the substrate to efficiently couple the53\nincident radiation into the planar structure. The external signal is incident from a waveguide port54\nlocated behind the Si lens, simulating a realistic excitation source.55\nThe signal is received by an array of the proposed ring resonators. Two Cold-Electron Bolometers56\n3\n\nare embedded into the outer ring of each SRR element. In the simulation, each CEB is modeled57\nas an RC circuit (see inset in Fig. 1), where𝑅𝑎𝑏𝑠 = 75Ω represents the resistance of the CEB’s58\nnormal-metal absorber, and𝐶𝑆𝐼 𝑁 = 20 fF is the capacitance of the two SIN junctions of the CEB59\nconnected in series. The total absorbed power is calculated as the sum of the powers absorbed in60\nthese discrete ports representing the CEBs.61\nThe design of the previously studied metamaterial with CEBs and single-ring antennas is shown62\nin Fig. 1a. To increase the absorbed power and the working frequency band, we propose and ana-63\nlyze a new design based on SRR (Fig. 1b and c). The geometric parameters of the structures are as64\nfollows:65\n• Single ring: outer ring diameter𝑑𝑒𝑥𝑡 = 80𝜇m, inner ring diameter𝑑𝑖𝑛𝑡 = 70𝜇m. The lattice66\nconstant (period) of the metamaterial array is𝑃 = 86𝜇m. The total size of the structure is67\n424 𝜇m.68\n• SRR, large scale: the outer ring has an external diameter of𝑑𝑒𝑥𝑡, 1 = 80𝜇m and an internal69\ndiameter of𝑑𝑖𝑛𝑡, 1 = 70𝜇m. The inner ring has an external diameter of𝑑𝑒𝑥𝑡, 2 = 40𝜇m and an70\ninternal diameter of𝑑𝑖𝑛𝑡, 2 = 30𝜇m. The period of the metamaterial array is𝑃 = 86𝜇m. The71\ntotal size of the structure is 424𝜇m.72\n• SRR, small scale: A scaled-down version with𝑑𝑒𝑥𝑡, 1 = 40𝜇m, 𝑑𝑖𝑛𝑡, 1 = 35𝜇m; 𝑑𝑒𝑥𝑡, 2 = 2073\n𝜇m, 𝑑𝑖𝑛𝑡, 2 = 15𝜇m. The lattice period for this dense array is𝑃 = 43𝜇m. The total size of the74\nstructure is reduced to 298𝜇m.75\nThis scaling of the SRR geometry is intended to shift the central frequency of the metamaterial to a76\nhigher value while maintaining the increasing absorption of the double-ring design.77\nThe transition from a single-ring antenna to a double split-ring resonator design, while keeping78\nthe number of elements to be constant, resulted in a significant improvement in performance. The79\naddition of the inner ring, which increases the total capacitance of the resonant element, leads to80\na slight reduction of the central frequency [19]. More importantly, it yielded a 1.5-fold increase in81\nthe total absorbed power.82\n4\n\n0 5 001 0001 5002 0000,00\n,10\n,20\n,3Absorbed powerF\nrequency (GHz) \na) Single-ring antennas b) SRRsE\nxperimental response (a.u.)\nFigure 2: Amplitude-frequency characteristics of the metamaterial receiver: a) 19-element array\nof single-ring antennas with a lattice period of𝑃 = 86𝜇m (red curve); b) 19-element array of SRRs\nwith 𝑃 = 86𝜇m (blue curve). The dashed black curve shows the experimentally measured bolome-\nter response.\nThe amplitude-frequency characteristics (AFC) for the simulated single-ring and SRR designs83\nare presented in Fig. 2. For the single-ring array, the absorbed power in the first resonance maxi-84\nmum reached a value of 0.18 (normalized units, with 0.5 maximal total power) at half maximum85\n(FWHM) spanning from 100 to 545 GHz (Fig. 2, red curve). In contrast, the SRR array demon-86\nstrated a higher absorbed power of 0.27 within a bandwidth of 105 to 440 GHz (Fig. 2, blue curve).87\nAs an experimental reference for our simulations, Fig. 2 also shows the frequency response mea-88\nsured for a fabricated sample consisting of a 19-element single-ring metamaterial (black dashed89\ncurve). This sample had the design described in [17] and was characterized using the same exper-90\nimental setup described there. This setup employs a YBaCuO Josephson junction oscillator as a91\nbroadband source, with the signal delivered to the sample via an oversized waveguide. Therefore,92\nthe measured frequency response is the combined frequency response of the entire path (oscilla-93\ntor, waveguide-feeder, lens and the CEB metamaterial itself), with \"fingers\" due to the used log-94\nperiodic antenna of the Josephson oscillator, which was not fully matched to the antenna. Despite95\nthis convolution, the experimental data clearly confirm the calculated dual-band behavior of the96\nmetamaterial, showing two broad peaks centered at approximately 350 GHz and 1100 GHz. This97\nagreement validates our simulation model.98\n5\n\n0\n5 001 0001 5002 0000,000\n,150\n,300\n5 001 0001 5002 0000,000\n,150\n,301 9-element array of the SRRsA\nbsorbed power a) Period = 86 µm  b) Period = 68,8 µm  c) Period = 51,6 µm  d) Period = 34,4 µm A\nbsorbed powerF\nrequency (GHz) \na) Period = 86 µm  b) Period = 68,8 µm  c) Period = 51,6 µm  d) Period = 34,4 µm 1\n9-element array of the Ring Antennas\nFigure 3: The upper plot: AFC of the 19 single-ring antenna metamaterial for different geometric\nscaling factors: a) black curve: outer ring diameter𝑑𝑜𝑢𝑡 = 80𝜇m, inner ring diameter𝑑𝑖𝑛 = 70𝜇m,\nperiod 𝑃 = 86𝜇m; b) red curve:𝑑𝑜𝑢𝑡 = 64𝜇m, 𝑑𝑖𝑛 = 56𝜇m, 𝑃 = 68.8𝜇m; c) blue curve:𝑑𝑜𝑢𝑡 =\n48 𝜇m, 𝑑𝑖𝑛 = 42𝜇m, 𝑃 = 51.6𝜇m; d) purple curve:𝑑𝑜𝑢𝑡 = 32𝜇m, 𝑑𝑖𝑛 = 28𝜇m, 𝑃 = 34.4𝜇m. The\nbottom plot: AFC of the 19 SRR-based metamaterial for different geometric scaling factors. The\ndesign parameters and scaling factors (0%, 20%, 40%, 60%) correspond to the upper plot.\nThe amplitude-frequency characteristics (AFC) of the single-ring and SRR metamaterials with99\nvarious scaling factors are presented in Fig. 3. The optimal number and size of the resonators are100\ngoverned by the requirement to fill the Airy spot of the silicon lens. If the total array size is smaller101\nthan the Airy spot, a portion of the incident signal will not interact with the metamaterial, instead102\nscattering into the surrounding space. Our simulations confirm this principle: a reduction in the103\nSRR dimensions and the array period by 20% led to a broadening of the absorption bandwidth and104\na small shift of the first resonance maximum towards higher frequencies. A further reduction of105\ndimensions by 40%resulted in an even wider bandwidth; however, the peak absorbed power began106\nto decrease, indicating that the array size was becoming insufficient relative to the Airy spot. A107\ndrastic 60%size reduction caused a severe deterioration of absorption.108\nTo achieve the widest possible bandwidth using SRRs, our results shown in Fig. 3 suggest prior-109\nitizing somewhat smaller unit cell sizes. Simply scaling down a fixed 19-element array leads to110\nless efficient signal reception due to the array becoming smaller than the Airy spot. As an efficient111\nalternative, we propose to halve the SRR dimensions and array period while simultaneously in-112\n6\n\ncreasing the number of elements from 19 to 37 (Fig. 1c). This approach successfully increased113\nthe absorbed power to 0.25, which is by a factor of 1.4 higher than for the single-ring array, while114\nalso achieving an ultra-wide receiving band from 160 to 820 GHz (Fig. 4, black line). If the 37-115\nelement array structure occupies the same area as the original single-ring structure, larger absorp-116\ntion efficiency at the first peak can be achieved (Fig. 4, red line), but the working bandwidth will117\nbe narrower than for the structure with smaller rings. Thus, by selecting the overall structure size,118\na compromise can be found between the maximum absorption efficiency and the widest receiving119\nbandwidth.120\n0 5 001 0001 5002 0000,00\n,10\n,20\n,33 7-element array of SRRsA\nbsorbed PowerF\nrequency (GHz) \na) Period = 43 µm  b) Period = 62 µm  c) Period = 86 µm \nFigure 4: The amplitude-frequency characteristics of the 37-element array of SRR-based metama-\nterial for different periods of the lattice.\nIt is important to note that the choice of the number of receiving antennas should be in a proper121\nbalance. Although a larger array can better fill the Airy spot, it also increases the total number of122\nbolometers. This, in turn, increases the differential resistance of the structure at the operating point123\nand increases the current noise contribution of the readout amplifier [17,30]. Furthermore, a larger124\nnumber of elements increases the fabrication complexity. Crucially, nearly doubling the number of125\nelements (from 19 to 37) does not produce a proportional increase in the absorbed power (Fig. 5).126\nFigure 5 shows the AFC of the SRR metamaterial with a different number of elements. For the127\nlarge-scale design (period𝑃 = 86𝜇m, rings: 𝑑𝑜𝑢𝑡, 1/𝑑𝑖𝑛,1 = 80/70𝜇m, 𝑑𝑜𝑢𝑡, 2/𝑑𝑖𝑛,2 = 40/30𝜇m),128\ndoubling the number of elements increased the absorbed power by only about 7%, with a minor in-129\n7\n\n0 5 001 0001 5002 0000,00\n,10\n,20\n,3Absorbed powerF\nrequency (GHz) \na) 19 SRR, Period = 43 µm  b) 19 SRR, Period = 86 µm  c) 37 SRR, Period = 43 µm  d) 37 SRR, Period = 86 µm \nFigure 5: Dependence of the absorbed power on the number of elements in the SRR array.\ncrease in bandwidth. The same doubling for the miniaturized design (𝑃 = 43𝜇m, rings: 𝑑𝑜𝑢𝑡, 1/𝑑𝑖𝑛,1130\n= 40/35𝜇m, 𝑑𝑜𝑢𝑡, 2/𝑑𝑖𝑛,2 = 20/15𝜇m) is more efficient, leading to 17% increase in power. This131\nhigher efficiency is directly linked to the Airy spot coverage: adding elements to the smaller array132\nmore effectively increases its total area towards the optimal size. For the already-large array, new133\nelements are added at the periphery or outside the most intense part of the Airy spot, which do not134\nactually help.135\nDiscussion136\nSolving the problem of broadband high-sensitivity reception for terahertz applications naturally137\nentails comparing the metamaterial-based approach presented here with traditional broadband138\nantenna solutions such as the log-periodic [22-24] or spiral antennas [25,26]. These antennas are139\nindeed a well-established technology, providing wideband frequency response and high detec-140\ntion/radiation efficiency. However, their widespread use is subject to a fundamental limitation: the141\nactive receiving element is typically a single detector unit located at the antenna’s feed point. This142\nconfiguration can become a bottleneck when detecting ultra-low power signals in the presence of143\nhigh background radiation, as the single detector must handle the entire power load, potentially144\nlimiting the dynamic range and complicating the optimization of noise-equivalent power (NEP).145\n8\n\nThere have been proposals to integrate multiple sensing elements directly into the structure of a146\nlog-periodic antenna [27-29]. While promising, such designs face significant challenges in imple-147\nmentation. The complex geometry of the antenna makes it difficult to integrate a large number of148\ndetectors and to design complex series-parallel electrical networks necessary for optimal power dis-149\ntribution and impedance matching. In contrast, the metamaterial approach offers a fundamentally150\nmore flexible paradigm. A periodic array of resonators, such as our SRR-based design, inherently151\nfunctions as a multi-absorber system. This architecture allows for the precise engineering of the de-152\ntector network: the number of CEBs, their individual connection (series or parallel), and the overall153\narray configuration to achieve an optimal balance between power load, responsivity, and total noise154\n[17,30].155\nThis capability is particularly critical for applications like cosmic microwave background polarime-156\ntry or high-resolution spectroscopy, where the detector must operate photon-noise-limited under a157\nspecific background power load. For CEBs, we have previously demonstrated that the optimal con-158\nfiguration for minimizing the total NEP with a given readout amplifier involves a specific series-159\nparallel combination of bolometers. The metamaterial platform is ideal for implementing such an160\noptimized multi-absorber receiver. By adapting the array geometry and the electrical connection161\nscheme between CEBs, one can precisely control the power absorbed per bolometer and the re-162\nsulting differential resistance, thereby achieving photon-noise-limited performance across a wide163\nbandwidth. This level of design control is considerably more challenging to realize within the con-164\nstrained geometry of a single-feed log-periodic antenna.165\nConclusions166\nIn this work, we have presented a comprehensive electromagnetic study on the design and opti-167\nmization of a metamaterial receiver based on split-ring resonators integrated with cold-electron168\nbolometers. The transition from a conventional single-ring antenna design to a double SRR config-169\nuration has been demonstrated to be a highly efficient strategy to enhance the receiver performance.170\nThis design improvement resulted in a substantial 1.5-fold increase in the absorbed power, confirm-171\n9\n\ning the theoretical advantage of SRRs in providing a stronger magnetic resonance and greater field172\nconcentration within the capacitive gaps where the CEBs are located.173\nOur investigation of the scaling of the metamaterial array revealed a critical design trade-off. While174\nreducing the dimensions of the SRR unit cells effectively broadens the operational bandwidth, it175\nalso reduces the total absorbed power if the array’s physical size becomes smaller than the Airy176\nspot of the coupling lens. We successfully resolved this issue by implementing a strategy of simul-177\ntaneous miniaturization and increasing the array density. By halving the SRR dimensions and lat-178\ntice period while nearly doubling the number of elements (from 19 to 37), we achieved an optimal179\ncompromise. The resulting receiver exhibits both enhanced absorption (by a factor of 1.4 larger180\nthan the original single-ring design) and an ultra-wide bandwidth spanning from 160 to 820 GHz.181\nFurthermore, we quantified the non-linear relationship between the number of array elements and182\nthe absorbed power, showing that the benefit of adding elements is significantly higher for a minia-183\nturized array that initially underfills the Airy spot. This provides a crucial practical guideline for184\ndesigning efficient multi-absorber receivers, balancing performance gains against the increased185\ntechnological complexity and noise considerations associated with a larger number of bolometers.186\nThis work solidifies the position of CEB-based SRR metamaterials as a highly promising platform187\nfor constructing ultra-broadband, high-sensitivity receivers essential for next-generation spectro-188\nscopic and radioastronomical applications, particularly in demanding space and balloon-borne189\nenvironments. Future work will focus on the experimental fabrication and characterization of the190\nproposed miniaturized 37-element SRR array to validate these simulation results.191\nFunding192\nThe work is supported by Russian Science Foundation Grant No. 21-79-20227.193\nReferences194\n1. Ajito, K. et al., in Terahertz Spectroscopy Methods and Instrumentation, Encyclopedia of195\nSpectroscopy and Spectrometry (Third Edition) (Academic Press, 2017), p. 432.196\n10\n\n2. Likhachev, S.F.; Larchenkova, T.I. Phys. – Uspekhi2024, 67, 768. doi:197\n10.3367/UFNe.2024.03.039662198\n3. Maffei, B. et al., Proc. SPIE 13102, Millimeter, Submillimeter, and Far-Infrared Detectors and199\nInstrumentation for Astronomy XII, 131020N (2024).200\n4. Coulon, X.; Maffei, B.; Aghanim, N. EPJ Web of Conferences2024, 293, 00012.201\ndoi:10.1051/epjconf/202429300012202\n5. Novikov, D.I.; Doroshkevich, A.G.; Larchenkova, T.I.; Malinovsky, A.M.; Mihalchenko,203\nA.O.; Osipova, A.M.; Parfenov, K.O.; Pilipenko, S.V. Phys. Usp.,2025, 68, in press;204\ndoi:10.3367/UFNe.2025.08.040006205\n6. Anghel, D.V.; Kuzmin, L.S. Phys. Rev. Appl.2020, 13, 024028.206\ndoi:10.1103/PhysRevApplied.13.024028207\n7. Pimanov, D.A.; Pankratov, A.L.; Gordeeva, A.V.; Chiginev, A.V.; Blagodatkin, A.V.; Revin,208\nL.S.; Razov, S.A.; Safonova, V.Yu.; Fedotov, I.A.; Skorokhodov, E.V. Supercond. Sci. Tech-209\nnol. 2025, 38, 035026. doi:10.1088/1361-6668/adb942210\n8. Nahum, M; Martinis, J.M. Appl. Phys. Lett.1995, 66, 3203. doi:10.1063/1.113723211\n9. Irwin, K.D.; Hilton, G.C. Transition-edge sensor, in Cryogenic Particle Detection. Topics in212\nApplied Physics, vol. 99 (Springer, Berlin, 2008).213\n10. Withington, S. Contemporary Physics2022, 63, 116-137.214\ndoi:10.1080/00107514.2023.2180179215\n11. Safonova, V.Y. et al., Beilstein J. Nanotechnol.2024, 15, 1353–1361.216\ndoi:10.3762/bjnano.15.108217\n12. O’Brient, R. et al., Appl. Phys. Lett.2013, 102, 063506. doi:10.1063/1.4791692218\n11\n\n13. Gordeeva, A.V.; Pankratov, A.L.; Pugach, N.G. et al. Sci. Rep.2020, 10, 21961.219\ndoi:10.1038/s41598-020-78869-z220\n14. Pimanov, D.A.; Frost, V.A.; Blagodatkin, A.V.; Gordeeva, A.V.; Pankratov, A.L.; Kuzmin,221\nL.S. Beilstein J. Nanotechnol.2022, 13, 896–901. doi:10.3762/bjnano.13.80222\n15. Lemziakov, S.A.; Karimi, B.; Nakamura, S. et al. J. Low Temp. Phys.2024, 217, 54–81.223\ndoi:10.1007/s10909-024-03144-8224\n16. Salatino, M. et al., J. Low Temp. Phys.2014, 176, 323. doi:10.1007/s10909-013-1057-5225\n17. Revin, L.S. et al., Phys. Rev. Appl.2024, 22, 064040. doi:10.1103/PhysRevApplied.22.064040226\n18. Pendry, J.B. et al., IEEE Trans. Microw. Theory Tech.1999, 47, 2075. doi:10.1109/22.798002227\n19. Reddy, A.N.; Raghavan, S. in 2013 IEEE Int. Conf. on Emerging Trends in Computing, Com-228\nmunication and Nanotechnology (ICECCN) (2013), pp. 625-629.229\n20. Sydoruk, O.; et al., J. Appl. Phys.2009, 105, 014903. doi:10.1063/1.3056052230\n21. Marques, R. et al., Metamaterials with Negative Parameters: Theory, Design and Microwave231\nApplications (Wiley, 2008).232\n22. Tarasov, M.; Kuzmin, L.; Stepantsov, E.; Kidiyarova-Shevchenko, A. Quasioptical Tera-233\nhertz Spectrometer Based on a Josephson Oscillator and a Cold Electron Nanobolometer. In234\nNanoscale Devices—Fundamentals and Applications, NATO Science Series; Chapter: Ad-235\nvanced Sensors of Electromagnetic Radiation; Springer: Dordrecht, The Netherlands, 2006;236\nVolume 233.237\n23. Stepantsov, E.; Tarasov,M.; Kalabukhov, A.; Kuzmin, L.; Claeson, T.J. Appl. Phys.2004, 96,238\n3357. doi:10.1063/1.1782273239\n24. Gao, X.; Zhang, T.; Du„ J.; Weily, A.R.; Guo, Y.J.; Foley, C.P. Supercond. Sci. Technol.2017,240\n30, 095011. doi:10.1088/1361-6668/aa7cc1241\n12\n\n25. Tretyakov I.V. et al. IEEE Transactions on Terahertz Science and Technology202515, 2, 191-242\n199. doi:10.1109/TTHZ.2024.3505592.243\n26. Malnou, M.; Luo, A.; Wolf, T.; Wang, Y.; Feuillet-Palma, C.; Ulysse, C.; Faini, G.;244\nFebvre, P.; Sirena, M.; Lesueur, J.; Bergeal, N. Appl. Phys. Lett.2012, 101, 233505.245\ndoi:10.1063/1.4769441246\n27. Yu, M.; Geng, H.; Hua, T.; An, D.; Xu, W.; Chen, Z.N.; Chen, J.; Wang, H.; Wu, P. Super-247\ncond. Sci. Technol.2020, 33, 025001. doi:10.1088/1361-6668/ab5e13248\n28. Sharafiev, A.; Malnou, M.; Feuillet-Palma, C.; Ulysse, C.; Wolf, T.; Couëdo, F.; Febvre,249\nP.; Lesueur, J.; Bergeal, N. Supercond. Sci. Technol.2018, 31, 035003. doi:10.1088/1361-250\n6668/aa9d48251\n29. Glushkov, E.I.; Chiginev, A.V.; Kuzmin, L.S.;, Revin, L.S. Beilstein Journal of Nanotechnol-252\nogy 2022, 13, 325–333. doi:10.3762/bjnano.13.27253\n30. Kuzmin, L.S.; Pankratov, A.L.; Gordeeva, A.V.; Zbrozhek, V.O.;, Shamporov, V.A.; Revin,254\nL.S.; Blagodatkin, A.V.; Masi, S.; de Bernardis, P. Nature Communications Physics2019, 2,255\n104. doi:10.1038/s42005-019-0206-9256\n13","source_license":"CC-BY-4.0","license_restricted":false}