# Broadband-Transmissive, Frequency-Selective Rasorber Design Using Characteristic Mode Analysis

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## Abstract

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## 1. Introduction

## 2. Theory of Characteristic Mode

## 3. Design and Analysis of the FSR

## 4. Experimental Verification

## 5. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

- Can, S.; Karakaya, E.U.; Ylmaz, A.E. Design, fabrication, and measurement of textile-based frequency selective surfaces. Microw. Opt. Technol. Lett.
**2020**, 62, 3444–3450. [Google Scholar] [CrossRef] - Fahad, A.K.; Ruan, C.; Nazir, R.; Haq, T.U.; He, W. Dual-Band Ultrathin Meta-Array for Polarization Conversion in Ku/Ka-Band With Broadband Transmission. IEEE Antennas Wirel. Propag. Lett.
**2020**, 19, 856–860. [Google Scholar] [CrossRef] - Omar, A.A.; Kim, J.; Hong, W. A 3-D Lumped-Components-Free Absorptive Frequency-Selective Transmission Structure Featuring Very Wide Two-Sided Absorption Bandwidths. IEEE Antennas Wirel. Propag. Lett.
**2020**, 19, 761–765. [Google Scholar] [CrossRef] - Costa, F.; Monorchio, A. A Frequency Selective Radome With Wideband Absorbing Properties. IEEE Trans. Antennas Propag.
**2012**, 60, 2740–2747. [Google Scholar] [CrossRef] - Bakshi, S.C.; Mitra, D.; Ghosh, S. A Frequency Selective Surface Based Reconfigurable Rasorber With Switchable Transmission/Reflection Band. IEEE Antennas Wirel. Propag. Lett.
**2019**, 18, 29–33. [Google Scholar] [CrossRef] - Sheng, X.; Gao, X.; Liu, N. Design of frequency selective rasorber with high in-band transmission and wideband absorption properties. IEICE Electron. Express
**2019**, 16, 20190545. [Google Scholar] [CrossRef][Green Version] - Yu, S.; Kou, N.; Ding, Z.; Zhang, Z. Harmonic-Suppressed Frequency Selective Rasorber Using Resistive-Film Sheet and Square-Loops Resonator. IEEE Antennas Wirel. Propag. Lett.
**2020**, 19, 292–296. [Google Scholar] [CrossRef] - Chen, Q.; Guo, M.; Sun, Z.; Sang, D.; Fu, Y. Polarization-independent frequency-selective rasorber with a broadened absorption band. Aeu Int. J. Electron. Commun.
**2018**, 96, 178–183. [Google Scholar] [CrossRef] - Guo, Q.; Su, J.; Li, Z.; Yang, L.Y.; Song, J. Absorptive/Transmissive Frequency Selective Surface With Wide Absorption Band. IEEE Access
**2019**, 7, 92314–92321. [Google Scholar] [CrossRef] - Sharma, A.; Ghosh, S.; Srivastava, K.V. A polarization-insensitive band-notched absorber for Radar Cross Section reduction. IEEE Antennas Wirel. Propag. Lett.
**2020**, 20, 259–263. [Google Scholar] [CrossRef] - Shen, Z.; Jiang, W.; Bo, L. 3-D Frequency Selective Rasorber: Concept, Analysis, and Design. IEEE Trans. Microw. Theory Tech.
**2016**, 64, 3087–3096. [Google Scholar] [CrossRef] - Jin, C.; Lv, Q.; Wang, J.; Li, Y. Capped Dielectric Inserted Perforated Metallic Plate Bandpass Frequency Selective Surface. IEEE Trans. Antennas Propag.
**2017**, 65, 7129–7136. [Google Scholar] [CrossRef] - Chen, Q.; Sang, D.; Guo, M.; Fu, Y. Miniaturized Frequency-Selective Rasorber With a Wide Transmission Band Using Circular Spiral Resonator. IEEE Trans. Antennas Propag.
**2019**, 67, 1045–1052. [Google Scholar] [CrossRef] - Wang, Z.; Fu, J.; Zeng, Q.; Song, M.; Denidni, T.A. Wideband Transmissive Frequency-Selective Absorber. IEEE Antennas Wirel. Propag. Lett.
**2019**, 18, 1443–1447. [Google Scholar] [CrossRef] - Guo, M.; Chen, Q.; Bai, T.; Wei, K.; Fu, Y. Wide Transmission Band Frequency-Selective Rasorber Based on Convoluted Resonator. IEEE Antennas Wirel. Propag. Lett.
**2020**, 19, 846–850. [Google Scholar] [CrossRef] - Sheng, X.; Gao, X.; Liu, N. Design of frequency selective rasorber with wide transmission/absorption bands. J. Phys. D Appl. Phys.
**2020**, 53, 1–6. [Google Scholar] [CrossRef] - Yang, Z.; Jiang, W.; Huang, Q.; Hong, T. A 2.5-D Miniaturized Frequency-Selective Rasorber With a Wide High-Transmission Passband. IEEE Antennas Wirel. Propag. Lett.
**2021**, 20, 1140–1144. [Google Scholar] [CrossRef] - Lv, Q.; Jin, C.; Zhang, B.; Mittra, R. Wide-Passband Dual-Polarized Elliptic Frequency Selective Surface. IEEE Access
**2019**, 7, 55833–55840. [Google Scholar] [CrossRef] - Lin, H.; Wu, Y.; Xiong, J.; Zhou, R.; Li, Q.; Tang, R. Dual-polarized bidirectional three-dimensional metamaterial absorber with transmission windows. Opt. Express
**2021**, 29, 40770–40780. [Google Scholar] [CrossRef] - Zahra, H.; Abbas, S.M.; Hashmi, R.M.; Esselle, K.P. Switchable Frequency Selective Surface Based on Composite Flexible Substrate for Modern Communication Systems. In Proceedings of the URSI Asia-Pacific Radio Science Conference (AP-RASC 2019), Delhi, India, 9–15 March 2019; pp. 1–2. [Google Scholar]
- Zahra, H.; Abbas, S.M.; Hashmi, R.M.; Matekovits, L.; Esselle, K.P. Bending analysis of switchable frequency selective surface based on flexible composite substrate. In Proceedings of the 2019 IEEE International Symposium on Antennas and Propagation and USNC-URSI Radio Science Meeting, Atlanta, GA, USA, 7–12 July 2019; pp. 2033–2034. [Google Scholar] [CrossRef]
- Zahra, H.; Abbas, S.M.; Shafique, M.F.; Esselle, K.P. A switchable FSS based on modified Jerusalem-cross unit cell with extended top loading. In Proceedings of the 2015 International Symposium on Antennas and Propagation (ISAP), Hobart, TAS, Australia, 9–12 November 2015; pp. 1–2. [Google Scholar]
- Zahra, H.; Rafique, S.; Shafique, M.F.; Esselle, K.P. A switchable frequency selective surface based on a modified Jerusalem-cross unit cell. In Proceedings of the 2015 9th European Conference on Antennas and Propagation (EuCAP), Lisbon, Portugal, 13–17 April 2015; pp. 1–2. [Google Scholar]
- Omar, A.A.; Huang, H.; Shen, Z. Absorptive frequency-selective reflection/transmission structures: A review and future perspectives. IEEE Antennas Propag. Mag.
**2019**, 62, 62–74. [Google Scholar] [CrossRef] - Wang, Y.; Wang, M.; Shen, Z.; Wu, W. 3-D Single-and Dual-Polarized Frequency-Selective Rasorbers With Wide Absorption Bands Based on Stepped Impedance Resonator. IEEE Access
**2021**, 9, 22317–22327. [Google Scholar] [CrossRef] - Garbacz, R.J. Modal expansions for resonance scattering phenomena. Proc. IEEE
**1965**, 53, 856–864. [Google Scholar] [CrossRef] - Lin, F.H.; Chen, Z.N. Low-Profile Wideband Metasurface Antennas Using Characteristic Mode Analysis. IEEE Trans. Antennas Propag.
**2017**, 65, 1706–1713. [Google Scholar] [CrossRef] - Gao, G.; Zhang, R.; Geng, W.; Meng, H.; Hu, B. Characteristic Mode Analysis of a Nonuniform Metasurface Antenna for Wearable Applications. IEEE Antennas Wirel. Propag. Lett.
**2020**, 19, 1355–1359. [Google Scholar] [CrossRef] - Song, Z.; Zhu, J.; Yang, L.; Min, P.; Lin, F.H. Wideband metasurface absorber (metabsorber) using characteristic mode analysis. Opt. Express
**2021**, 29, 35387–35399. [Google Scholar] [CrossRef] - Wu, Y.; Lin, H.; Xiong, J.; Hou, J.; Zhou, R.; Deng, F.; Tang, R. A broadband metamaterial absorber design using characteristic modes analysis. J. Appl. Phys.
**2021**, 129, 134902–134928. [Google Scholar] [CrossRef] - Guo, Q.; Su, J.; Li, Z.; Song, J.; Guan, Y. Miniaturized-Element Frequency-Selective Rasorber Design Using Characteristic Modes Analysis. IEEE Trans. Antennas Propag.
**2020**, 68, 6683–6694. [Google Scholar] [CrossRef] - Guo, Q.; Su, J.; Li, Z. Design of circuit analog absorber using characteristic mode analysis. In Proceedings of the 2020 IEEE MTT-S International Microwave Workshop Series on Advanced Materials and Processes for RF and THz Applications (IMWS-AMP), Suzhou, China, 29–31 July 2020; pp. 1–3. [Google Scholar] [CrossRef]
- Jiao, W.H.; Chang, Y.M.; Wang, L.; Wu, W.J. A Dual-Polarized Frequency Selective Rasorber with Wide Transmission Band. Radio Sci.
**2021**, 56, 7129–7136. [Google Scholar] [CrossRef] - Xiu, X.; Che, W.; Han, Y.; Yang, W. Low-Profile Dual-Polarization Frequency Selective Rasorbers Based on Simple-Structure Lossy Cross-Frame Elements. IEEE Antennas Wirel. Propag. Lett.
**2018**, 1002–1005. [Google Scholar] [CrossRef] - Wang, X.; Wang, J.; Yan, M.; Yang, J.; Qu, S. A Frequency Selective Rasorber by Engineering Transverse Standing Waves of Surface Current. IEEE Access
**2021**, 9, 51703–51709. [Google Scholar] [CrossRef]

**Figure 1.**Topology and dimensions of the proposed FSR. (

**a**) Overall FSR diagram. (

**b**) Resistive layer. (

**c**) FSS I and FSS III layer. (

**d**) FSS II layer (h = 0.813 mm, t = 9 mm, h1 = 2 mm, l1 = 0.4 mm, l2 = 0.8 mm, l3 = 4.5 mm, l4 = 4.7 mm, l5 = 3.7 mm, l6 = 5.1 mm, w1 = 0.2 mm, w2 = 0.2 mm, w3 = 0.3 mm, w4 = 0.3 mm, g1 = 0.1 mm, lr = 4.8 mm, wr = 1 mm, r = 1.6 mm).

**Figure 2.**Characteristic mode analysis for the designed absorption structure. (

**a**) Modal significance without R. (

**b**) Modal radiation patterns. (

**c**) Mode current at 3.8 GHz; (

**d**) mode current at 10.2 GHz; (

**e**) mode current at 12.0 GHz.

**Figure 3.**Characteristic mode analysis for the designed absorption structure with R. (

**a**) Modal significance with different R. (

**b**) Modal radiation patterns with R. (

**c**) Mode current at 3.8 GHz; (

**d**) mode current at 10.2 GHz; (

**e**) mode current at 12.0 GHz.

**Figure 4.**Scattering parameters of resistive layer: (

**a**) absorption performance with a ground plane; (

**b**) transmission/reflection coefficients of resistive layer without a ground plane.

**Figure 5.**Comparison of transmission characteristics between different FSS. (

**a**) Transmission/reflection coefficients of the C-type FSS and coupled FSS. (

**b**) Transmission/reflection coefficients of the three-layer FSS.

**Figure 6.**Parameterization optimization of FSR: (

**a**) position of resistors (lr); (

**b**) lumped resistor (R1).

**Figure 7.**Reflection/transmission coefficients of proposed FSR for oblique incidence under (

**a**) TE polarization and (

**b**) TM polarization.

**Figure 8.**Photograph of the proposed FSR and measurement environment: (

**a**) FSR prototype; (

**b**) metallic patches and rotating aperture; (

**c**) measurement setup.

Ref. | Transmission Band (GHz)/FBW | Passband (${\mathit{f}}_{\mathit{m}}$)/IL | 10 dB Absorption Band (GHz)/FBW | Periodicity |
---|---|---|---|---|

[13] | 8.3–11.07/28.6%(1 dB) | N.A. ^{a} | 2.4–7.1/98.9% | 0.096${\lambda}_{L}$ ^{b} |

[14] | 4.8–7.3/41.3%(3 dB) | 6.7/0.31 dB | 1.6–4.3/91.5% | 0.16${\lambda}_{L}$ |

[15] | 9.0–12.62/33.5%(1 dB) | N.A. | 3.88–7.63/65.2% | 0.181${\lambda}_{L}$ |

[16] | 4.3–17.4/19.6%(1 dB) | N.A. | 3.2–10.7/107.9% | 0.117${\lambda}_{L}$ |

[33] | 9.0–12.0/28.5%(1.25 dB) | N.A. | 3.18–8.16/87.8% | 0.21${\lambda}_{L}$ |

[34] | 3.35–4.86/36.8%(3 dB) | 4.25/0.26 dB | 2.04–6.2/101% | 0.109${\lambda}_{L}$ |

[35] | 9.2–10.0/8.3%(1 dB) | N.A./0.19 dB | 5.8–7.8/29.4% 11.8–18/41.6% | 0.19${\lambda}_{L}$ |

ours | 9.3–13.45/36.4%(1 dB) | 11.3/0.16 dB | 2.35–6.78/97.0% | 0.118${\lambda}_{L}$ |

^{a}the data in the paper is not given;

^{b}free-space wavelength at lowest working frequency.

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**MDPI and ACS Style**

Xiong, J.; Yang, B.; Wu, Y.; Zeng, X.; Li, Q.; Tang, R.; Lin, H. Broadband-Transmissive, Frequency-Selective Rasorber Design Using Characteristic Mode Analysis. *Electronics* **2022**, *11*, 1418.
https://doi.org/10.3390/electronics11091418

**AMA Style**

Xiong J, Yang B, Wu Y, Zeng X, Li Q, Tang R, Lin H. Broadband-Transmissive, Frequency-Selective Rasorber Design Using Characteristic Mode Analysis. *Electronics*. 2022; 11(9):1418.
https://doi.org/10.3390/electronics11091418

**Chicago/Turabian Style**

Xiong, Jie, Baoping Yang, Yanjie Wu, Xiongwei Zeng, Qiuyu Li, Rongxin Tang, and Hai Lin. 2022. "Broadband-Transmissive, Frequency-Selective Rasorber Design Using Characteristic Mode Analysis" *Electronics* 11, no. 9: 1418.
https://doi.org/10.3390/electronics11091418