{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T01:43:45Z","timestamp":1760060625296,"version":"build-2065373602"},"reference-count":48,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2025,9,5]],"date-time":"2025-09-05T00:00:00Z","timestamp":1757030400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Young Talent Project of the Scientific and Technological Research Plan of the Educational Commission of Hubei Province","award":["Q20232808","BK202323","T2024025"],"award-info":[{"award-number":["Q20232808","BK202323","T2024025"]}]},{"name":"Scientific Research Project of Hubei University of Science and Technology","award":["Q20232808","BK202323","T2024025"],"award-info":[{"award-number":["Q20232808","BK202323","T2024025"]}]},{"name":"Hubei Provincial Outstanding Young and Middle-Aged Scientific and Technological Innovation Team Program for Higher Education Institutions","award":["Q20232808","BK202323","T2024025"],"award-info":[{"award-number":["Q20232808","BK202323","T2024025"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>The hyperbolic properties are demonstrated in Cantor photonic multilayers, which exhibit quasi-periodicity and consist of graphene and dielectric layers, forming a centrosymmetric structure. Different from the traditionally periodic hyperbolic metamaterials, here we introduce the concept of layer weight in quasi-periodic photonic multilayers; the equivalent permittivity tensor presents a hyperbolic dispersion with a specific weight of dielectric thickness. Subsequently, the dispersion relation transforming from hyperbolicity to ellipticity has been explored. The tunability of the hyperbolic properties can be enhanced by varying the Fermi energy of the graphene, the thickness of the dielectric, the relaxation time of graphene, and the number of graphene monolayers. The reflectance and transmittance of light waves in the quasi-periodic hyperbolic metamaterials depend on the hyperbolically dispersive speciality strongly as well. This research provides theoretical guidance for the design and optimization of photonic devices based on hyperbolic metamaterials.<\/jats:p>","DOI":"10.3390\/sym17091460","type":"journal-article","created":{"date-parts":[[2025,9,5]],"date-time":"2025-09-05T07:46:17Z","timestamp":1757058377000},"page":"1460","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Quasi-Periodic Hyperbolic Metamaterials Composed of Graphene and Dielectric"],"prefix":"10.3390","volume":"17","author":[{"ORCID":"https:\/\/orcid.org\/0009-0001-4010-7676","authenticated-orcid":false,"given":"Miaomiao","family":"Zhao","sequence":"first","affiliation":[{"name":"School of Electronic and Information Engineering, Hubei University of Science and Technology, Xianning 437100, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Junfu","family":"Yang","sequence":"additional","affiliation":[{"name":"College of Mechanical and Vehicle Engineering, Chongqing University, Chongqing 400044, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0874-1749","authenticated-orcid":false,"given":"Dong","family":"Zhao","sequence":"additional","affiliation":[{"name":"School of Electronic and Information Engineering, Hubei University of Science and Technology, Xianning 437100, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9281-2369","authenticated-orcid":false,"given":"Hao","family":"Ni","sequence":"additional","affiliation":[{"name":"School of Electronic and Information Engineering, Hubei University of Science and Technology, Xianning 437100, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xiaoling","family":"Chen","sequence":"additional","affiliation":[{"name":"School of Electronic and Information Engineering, Hubei University of Science and Technology, Xianning 437100, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zhongli","family":"Qin","sequence":"additional","affiliation":[{"name":"School of Electronic and Information Engineering, Hubei University of Science and Technology, Xianning 437100, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zhiyong","family":"Yu","sequence":"additional","affiliation":[{"name":"School of Electronic and Information Engineering, Hubei University of Science and Technology, Xianning 437100, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yingquan","family":"Ao","sequence":"additional","affiliation":[{"name":"College of Information Engineering, Henan University of Science and Technology, Luoyang 471023, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2025,9,5]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"014201","DOI":"10.1088\/0256-307X\/28\/1\/014201","article-title":"Dual-band terahertz left-handed metamaterial with fishnet structure","volume":"28","author":"Du","year":"2011","journal-title":"Chin. 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