{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,7]],"date-time":"2026-05-07T16:24:10Z","timestamp":1778171050866,"version":"3.51.4"},"reference-count":24,"publisher":"MDPI AG","issue":"10","license":[{"start":{"date-parts":[[2018,10,1]],"date-time":"2018-10-01T00:00:00Z","timestamp":1538352000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100004543","name":"China Scholarship Council","doi-asserted-by":"publisher","award":["201706830064"],"award-info":[{"award-number":["201706830064"]}],"id":[{"id":"10.13039\/501100004543","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["61501227,61071019"],"award-info":[{"award-number":["61501227,61071019"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100002858","name":"China Postdoctoral Science Foundation","doi-asserted-by":"publisher","award":["2015M581789"],"award-info":[{"award-number":["2015M581789"]}],"id":[{"id":"10.13039\/501100002858","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100004193","name":"Nanjing University of Aeronautics and Astronautics","doi-asserted-by":"publisher","award":["56YAH17032"],"award-info":[{"award-number":["56YAH17032"]}],"id":[{"id":"10.13039\/501100004193","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Jiangsu Innovation Program for Graduate Education","award":["KYLX16-0370"],"award-info":[{"award-number":["KYLX16-0370"]}]},{"DOI":"10.13039\/501100012226","name":"Fundamental Research Funds for the Central Universities","doi-asserted-by":"publisher","award":["NJ20160011"],"award-info":[{"award-number":["NJ20160011"]}],"id":[{"id":"10.13039\/501100012226","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100003329","name":"Ministerio de Econom\u00eda y Competitividad","doi-asserted-by":"publisher","award":["TEC2016-75650-R"],"award-info":[{"award-number":["TEC2016-75650-R"]}],"id":[{"id":"10.13039\/501100003329","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100002809","name":"Generalitat de Catalunya","doi-asserted-by":"publisher","award":["2017SGR-1159"],"award-info":[{"award-number":["2017SGR-1159"]}],"id":[{"id":"10.13039\/501100002809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Foundation of Graduate Innovation Center in NUAA","award":["kfjj20170414, kfjj20170411"],"award-info":[{"award-number":["kfjj20170414, kfjj20170411"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>The use of metasurfaces to increase the number of modes, lower the operating frequency, and improve the field uniformity in reverberation chambers (RCs) is investigated in this paper. The method used to improve the field uniformity and decrease the resonance frequencies is based on increasing the number of modes by using the concept of subwavelength cavities. The resonance frequencies of a RC with metasurface wall are derived and expressed analytically in terms of macroscopic characteristics. Simulation of the reflection phase of the unit cell is then given as a guideline to choose the required microscopic parameters of the designed metasurface. The mode density in such subwavelength RCs is then obtained using a numerical eigenmode solver. Compared to traditional RCs, a much higher modal density is obtained at low frequencies. The standard deviation of the field uniformity in the test volume of the RC corresponding to different types of metasurface walls is finally compared. It is shown that by increasing the number of modes in the RC at the lower band, the operating frequency decreases and the field uniformity of the RC is improved.<\/jats:p>","DOI":"10.3390\/s18103301","type":"journal-article","created":{"date-parts":[[2018,10,2]],"date-time":"2018-10-02T08:23:50Z","timestamp":1538468630000},"page":"3301","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":10,"title":["Enhancing the Number of Modes in Metasurfaced Reverberation Chambers for Field Uniformity Improvement"],"prefix":"10.3390","volume":"18","author":[{"given":"Hengyi","family":"Sun","sequence":"first","affiliation":[{"name":"Key Laboratory of Radar Imaging and Microwave Photonics, Ministry of Education, College of Electronic and Information Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing 211106, China"},{"name":"CIMITEC, Departament d\u2019Enginyeria Electr\u00f2nica, Universitat Aut\u00f2noma de Barcelona, 08193 Bellaterra, Barcelona, Spain"}]},{"given":"Changqing","family":"Gu","sequence":"additional","affiliation":[{"name":"Key Laboratory of Radar Imaging and Microwave Photonics, Ministry of Education, College of Electronic and Information Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing 211106, China"}]},{"given":"Zhuo","family":"Li","sequence":"additional","affiliation":[{"name":"Key Laboratory of Radar Imaging and Microwave Photonics, Ministry of Education, College of Electronic and Information Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing 211106, China"}]},{"given":"Qian","family":"Xu","sequence":"additional","affiliation":[{"name":"Key Laboratory of Radar Imaging and Microwave Photonics, Ministry of Education, College of Electronic and Information Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing 211106, China"}]},{"given":"Jiajia","family":"Song","sequence":"additional","affiliation":[{"name":"Key Laboratory of Radar Imaging and Microwave Photonics, Ministry of Education, College of Electronic and Information Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing 211106, China"}]},{"given":"Baijie","family":"Xu","sequence":"additional","affiliation":[{"name":"Key Laboratory of Radar Imaging and Microwave Photonics, Ministry of Education, College of Electronic and Information Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing 211106, China"}]},{"given":"Xiaohang","family":"Dong","sequence":"additional","affiliation":[{"name":"Key Laboratory of Radar Imaging and Microwave Photonics, Ministry of Education, College of Electronic and Information Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing 211106, China"}]},{"given":"Kuan","family":"Wang","sequence":"additional","affiliation":[{"name":"Key Laboratory of Radar Imaging and Microwave Photonics, Ministry of Education, College of Electronic and Information Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing 211106, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1494-9167","authenticated-orcid":false,"given":"Ferran","family":"Mart\u00edn","sequence":"additional","affiliation":[{"name":"CIMITEC, Departament d\u2019Enginyeria Electr\u00f2nica, Universitat Aut\u00f2noma de Barcelona, 08193 Bellaterra, Barcelona, Spain"}]}],"member":"1968","published-online":{"date-parts":[[2018,10,1]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Besnier, P., and D\u00e9moulin, B. (2011). Electromagnetic Reverberation Chambers, John Wiley & Sons, Inc.. [1st ed.].","DOI":"10.1002\/9781118602034"},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Wanderlinder, L.F., Lemaire, D., and Seetharamdoo, D. (2016, January 5\u20139). Experimental analysis for metamaterials used to lower the LUF of a reverberation chamber. Proceedings of the 2016 International Symposium on Electromagnetic Compatibility-EMC EUROPE, Wroclaw, Poland.","DOI":"10.1109\/EMCEurope.2016.7739279"},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Wanderlinder, L.F., Lemaire, D., Coccato, I., and Seetharamdoo, D. (2017, January 28\u201331). Practical implementation of metamaterials in a reverberation chamber to reduce the LUF. Proceedings of the 2017 IEEE 5th International Symposium on Electromagnetic Compatibility (EMC-Beijing), Beijing, China.","DOI":"10.1109\/EMC-B.2017.8260448"},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Song, J., Li, Z., Sun, H., Shi, J., Gu, C., and Wang, K. (2018, January 14\u201318). Field uniformity improvement at lower frequencies in a reverberation chamber using metasurfaces. Proceedings of the 2018 IEEE International Symposium on Electromagnetic Compatibility and 2018 IEEE Asia-Pacific Symposium on Electromagnetic Compatibility (EMC\/APEMC), Singapore.","DOI":"10.1109\/ISEMC.2018.8393969"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"442","DOI":"10.1109\/TEMC.2002.801757","article-title":"Compound exponential distributions for undermoded reverberation chambers","volume":"44","author":"Arnaut","year":"2002","journal-title":"IEEE Trans. Electromagn. Compat."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"745","DOI":"10.1109\/TEMC.2007.908290","article-title":"Investigation of reverberation chamber measurements through high-power goodness-of-fit tests","volume":"49","author":"Lemoine","year":"2007","journal-title":"IEEE Trans. Electromagn. Compat."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"104101","DOI":"10.1063\/1.2338795","article-title":"All-dimensional subwavelength cavities made with metamaterials","volume":"89","author":"Li","year":"2006","journal-title":"Appl. Phys. Lett."},{"key":"ref_8","unstructured":"Seetharamdoo, D., and Coccato, I.M. (2011, January 26\u201330). Investigation on the use of metamaterials to lower the operating frequency of reverberation chamber. Proceedings of the EMC Europe 2011 York, York, UK."},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Andries, M.I., Seetharamdoo, D., and Besnier, P. (2014, January 1\u20134). Analytical modal analysis to evaluate the contribution of metamaterials to the improvement of reverberation chambers. Proceedings of the 2014 International Symposium on Electromagnetic Compatibility (EMC Europe), Gothenburg, Sweden.","DOI":"10.1109\/EMCEurope.2014.6931028"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"10","DOI":"10.1109\/LAWP.2002.802576","article-title":"An idea for thin subwavelength cavity resonators using metamaterials with negative permittivity and permeability","volume":"1","author":"Engheta","year":"2002","journal-title":"IEEE Antennas Wirel. Propag. Lett."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"261","DOI":"10.1109\/LAWP.2004.836576","article-title":"A metamaterial surface for compact cavity resonators","volume":"3","author":"Caiazzo","year":"2004","journal-title":"IEEE Antennas Wirel. Propag. Lett."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"017701","DOI":"10.1103\/PhysRevLett.115.017701","article-title":"Wave-field shaping in cavities: Waves trapped in a box with controllable boundaries","volume":"115","author":"Fink","year":"2015","journal-title":"Phys. Rev. Lett."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"18881","DOI":"10.1364\/OE.22.018881","article-title":"Hybridized resonances to design tunable binary phase metasurface unit cells","volume":"22","author":"Kaina","year":"2014","journal-title":"Opt. Express"},{"key":"ref_14","first-page":"1","article-title":"Layer potential approach for fast eigenvalue characterization of the Helmholtz equation with mixed boundary conditions","volume":"37","author":"Fink","year":"2018","journal-title":"Comput. Appl. Math."},{"key":"ref_15","first-page":"4675","article-title":"Development and Validation of New Reverberation Chamber for Wireless Devices","volume":"37","author":"Sim","year":"2018","journal-title":"Wirel. Commun. Mob. Comput."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"296","DOI":"10.1109\/TEMC.2010.2081993","article-title":"The role of losses in the definition of the overmoded condition for reverberation chambers and their statistics","volume":"53","author":"Cozza","year":"2011","journal-title":"IEEE Trans. Electromagn. Compat."},{"key":"ref_17","unstructured":"CISPR, and Joint Task Force (2018, September 05). A\u2013IEC SC 77B: IEC 61000-4-21 Electromagnetic Compatibility (EMC)-Part 4-21: Testing and Measurement Techniques-Reverberation Chamber Test Methods. Available online: https:\/\/webstore.iec.ch\/publication\/4191#additionalinfo."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"248","DOI":"10.1109\/TEMC.2006.870705","article-title":"Statistical model of an undermoded reverberation chamber","volume":"48","author":"Orjubin","year":"2006","journal-title":"IEEE Trans. Electromagn. Compat."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"637","DOI":"10.1109\/15.974645","article-title":"Operation of electromagnetic reverberation chambers with wave diffractors at relatively low frequencies","volume":"43","author":"Arnaut","year":"2001","journal-title":"IEEE Trans. Electromagn. Compat."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"61","DOI":"10.1109\/TEMC.2002.808021","article-title":"Statistics of the quality factor of a rectangular reverberation chamber","volume":"45","author":"Arnaut","year":"2003","journal-title":"IEEE Trans. Electromagn. Compat."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"174902","DOI":"10.1063\/1.4982916","article-title":"Ultra-wideband and broad-angle linear polarization conversion metasurface","volume":"121","author":"Sun","year":"2017","journal-title":"J. Appl. Phys."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"40782","DOI":"10.1038\/srep40782","article-title":"Broadband and broad-angle polarization-independent metasurface for radar cross section reduction","volume":"7","author":"Sun","year":"2017","journal-title":"Sci. Rep."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"1577","DOI":"10.1038\/s41598-018-20066-0","article-title":"Metasurfaced Reverberation Chamber","volume":"8","author":"Sun","year":"2018","journal-title":"Sci. Rep."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"38","DOI":"10.7716\/aem.v4i2.271","article-title":"Statistics of the electromagnetic response of a chaotic reverberation chamber","volume":"44","author":"Gros","year":"2015","journal-title":"Adv. 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