{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,6]],"date-time":"2026-04-06T14:42:57Z","timestamp":1775486577294,"version":"3.50.1"},"reference-count":39,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2022,9,18]],"date-time":"2022-09-18T00:00:00Z","timestamp":1663459200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Hunan Provincial Natural Science Foundation of China","award":["2020JJ4555"],"award-info":[{"award-number":["2020JJ4555"]}]},{"name":"Hunan Provincial Natural Science Foundation of China","award":["2022jj50180"],"award-info":[{"award-number":["2022jj50180"]}]},{"name":"Natural Science Foundation of Hunan Province of China","award":["2020JJ4555"],"award-info":[{"award-number":["2020JJ4555"]}]},{"name":"Natural Science Foundation of Hunan Province of China","award":["2022jj50180"],"award-info":[{"award-number":["2022jj50180"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>We designed magneto-electro-elastic piezoelectric, electromagnetic (EM) metamaterials (MEEPEM) by using a square lattice of the periodic arrays of conducting wires, piezoelectric photonic crystal (PPC), and split-ring resonators (SRRs). We analyzed the mechanism for multi-field coupling in MEEPEM. The magnetic field of the EM wave excites an attractive Amp\u00e8re force in SRRs, which periodically compress MEEPEM, and this can create electric polarization due to the piezoelectric effect. The electric field of the EM wave can excite a longitudinal superlattice vibration in the PPC, which can also create electric polarization. The electric polarization can couple to the electric field of the periodic arrays of conducting wires. The coupled electric field will couple to the EM wave. These interactions result in multi-field coupling in MEEPEM. The coupling creates a type of polariton, called multi-field coupling polaritons, corresponding to a photonic band gap, namely, the multi-field coupling photonic band gap. We calculated the dielectric functions, the reflection coefficients, and the effective magnetic permeability of MEEPEM. By using them, we analyzed the transmission properties of EM waves in the MEEPEM. We analyzed the possibility of MEEPEM as left-handed metamaterials and zero refractive index material.<\/jats:p>","DOI":"10.3390\/sym14091942","type":"journal-article","created":{"date-parts":[[2022,9,20]],"date-time":"2022-09-20T04:28:55Z","timestamp":1663648135000},"page":"1942","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Transmission Properties of Electromagnetic Waves in Magneto-Electro-Elastic Piezoelectric Electromagnetic Metamaterials"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-0460-3493","authenticated-orcid":false,"given":"Wen-Chao","family":"Bai","sequence":"first","affiliation":[{"name":"Department of Physics, Shaoyang University, Shaoyang 422001, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Hui","family":"Hu","sequence":"additional","affiliation":[{"name":"Department of Physics, Shaoyang University, Shaoyang 422001, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ben-Hu","family":"Zhou","sequence":"additional","affiliation":[{"name":"Department of Physics, Shaoyang University, Shaoyang 422001, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Gui-Xiang","family":"Liu","sequence":"additional","affiliation":[{"name":"Department of Physics, Shaoyang University, Shaoyang 422001, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ge","family":"Tang","sequence":"additional","affiliation":[{"name":"Department of Physics, Shaoyang University, Shaoyang 422001, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yang-Yu","family":"Huang","sequence":"additional","affiliation":[{"name":"Department of Physics, Shaoyang University, Shaoyang 422001, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yan","family":"Cao","sequence":"additional","affiliation":[{"name":"Department of Physics, Shaoyang University, Shaoyang 422001, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Han","family":"Zhang","sequence":"additional","affiliation":[{"name":"Department of Physics, Jilin University, Changchun 130012, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Han-Zhuang","family":"Zhang","sequence":"additional","affiliation":[{"name":"Department of Physics, Jilin University, Changchun 130012, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2022,9,18]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"2075","DOI":"10.1109\/22.798002","article-title":"Magnetism from conductors and enhanced nonlinear phenomena","volume":"47","author":"Pendry","year":"1999","journal-title":"IEEE Trans. Microw. Theory Tech."},{"key":"ref_2","first-page":"4773","article-title":"Extremely low frequency plasmons in metallic meso-structures","volume":"87","author":"Pendry","year":"2001","journal-title":"Phys. Rev. Lett."},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Abdulkarim, Y.I., \u00d6zkan Alkurt, F., Awl, H.N., Alt\u0131nta\u015f, O., Muhammadsharif, F.F., Appasani, B., Bak\u0131r, M., Karaaslan, M., Taouzari, M., and Dong, J. (2022). A Symmetrical Terahertz Triple-Band Metamaterial Absorber Using a Four-Capacitance Loaded Complementary Circular Split Ring Resonator and an Ultra-Thin ZnSe Substrate. Symmetry, 14.","DOI":"10.3390\/sym14071477"},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Lv, Z., Li, Z., Han, Y., Cao, Y., and Yang, L. (2022). A Wideband and Ultra-Thin Metamaterial Absorber Based on Resistive FSS. Symmetry, 14.","DOI":"10.3390\/sym14061148"},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Liu, N., Lei, X., Lai, F., and Xue, X. (2022). Longitudinal Wave Locally Resonant Band Gaps in Metamaterial-Based Elastic Rods Comprising Multi-Degree-of-Freedom DAVI Resonators. Symmetry, 14.","DOI":"10.3390\/sym14051030"},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Kim, Y., and Lee, J.-H. (2021). Design of Broadband and Wide-Angle Hexagonal Metamaterial Absorber Based on Optimal Tiling of Rhombus Carbon Pixels and Implantation of Copper Cylinders. Symmetry, 13.","DOI":"10.3390\/sym13112045"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"726","DOI":"10.1063\/1.3559532","article-title":"Magnetoelectric memory using orthogonal magnetization states and magnetoelastic switching","volume":"109","author":"Tiercelin","year":"2011","journal-title":"J. Appl. Phys."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"123","DOI":"10.1088\/0022-3727\/38\/8\/R01","article-title":"Revival of the magnetoelectric effect","volume":"38","author":"Fiebig","year":"2005","journal-title":"J. Phys. D Appl. Phys."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"13","DOI":"10.1016\/S0020-7683(99)00074-8","article-title":"Quantitative nondestructive evaluation","volume":"37","author":"Achenbach","year":"2000","journal-title":"Int. J. Solids Struct."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"83","DOI":"10.1016\/j.ultras.2016.03.006","article-title":"Love waves propagation in a transversely isotropic piezoelectric layer on a piezomagnetic half-space","volume":"69","author":"Ezzin","year":"2016","journal-title":"Ultrasonics"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"701","DOI":"10.1016\/j.compstruct.2018.09.031","article-title":"Guided wave propagation in a multilayered magneto-electro-elastic curved panel by Chebyshev spectral elements method","volume":"207","author":"Xiao","year":"2019","journal-title":"Compos. Struct."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"416","DOI":"10.1016\/j.ijmecsci.2019.02.017","article-title":"In-plane elastic wave propagation in nanoscale periodic piezoelectric\/piezomagnetic laminates","volume":"153","author":"Chen","year":"2019","journal-title":"Int. J. Mech. Sci."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"479","DOI":"10.1080\/00150197608236646","article-title":"Piezoelectric study of poling mechanism in lithium niobate crystals at temperature close to the curie point","volume":"13","author":"Tasson","year":"1976","journal-title":"Ferroelectrics"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"108","DOI":"10.1063\/1.103276","article-title":"Quasi-phase-matched second-harmonic generation of blue light in periodically poled LiNbO3","volume":"56","author":"Magel","year":"1990","journal-title":"Appl. Phys. Lett."},{"key":"ref_15","first-page":"160","article-title":"Study of periodically poled Czochralski-grown Nd:Mg:LiNbO3 by chemical etching and X-ray microanalysis","volume":"181","author":"Evlanova","year":"1991","journal-title":"J. Cryst. Growth"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"1967","DOI":"10.1016\/j.ssc.2009.07.035","article-title":"Site spectroscopy of Hf doping in Hf-doped LiNbO3 crystals","volume":"149","author":"Hammoum","year":"2009","journal-title":"Solid State Commun."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"3735","DOI":"10.1063\/1.115366","article-title":"Lattice location of rare-earth ions in LiNbO3","volume":"67","author":"Lorenzo","year":"1995","journal-title":"Appl. Phys. Lett."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"4877","DOI":"10.1103\/PhysRevB.44.4877","article-title":"Computer-simulation studies of extrinsic defects in LiNbO3 crystals","volume":"44","author":"Donnerberg","year":"1991","journal-title":"Phys. Rev. B"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"4184","DOI":"10.1103\/PhysRevLett.84.4184","article-title":"Composite medium with simultaneously negative permeability and permittivity","volume":"84","author":"Smith","year":"2000","journal-title":"Phys. Rev. Lett."},{"key":"ref_20","doi-asserted-by":"crossref","unstructured":"Landau, L.D., and Lifschitz, E.M. (1984). Electrodynamics of Continuous Media, Pergamon Press.","DOI":"10.1016\/B978-0-08-030275-1.50007-2"},{"key":"ref_21","unstructured":"Auld, B.A. (1973). Acoustic Fields and Waves in Solids, Wiley."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"167","DOI":"10.1016\/j.spmi.2016.06.026","article-title":"Theoretical investigation of the phonon-polaritonmode in Czochralski grown piezoelectric superlattice","volume":"97","author":"Bai","year":"2016","journal-title":"Superlattices Microstruct."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"1261","DOI":"10.1016\/j.ssc.2011.05.042","article-title":"Theoretical investigation of phonon-polariton modes in undoped and ion-doped PPLN crystals","volume":"151","author":"Bai","year":"2011","journal-title":"Solid State Commun."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"1573","DOI":"10.1364\/OL.23.001573","article-title":"Omnidirectional reflection from a one-dimensional photonic crystal","volume":"23","author":"Winn","year":"1998","journal-title":"Opt. Lett."},{"key":"ref_25","first-page":"12","article-title":"Theoretical investigation of transmission and dispersion properties of one dimensional photonic crystal","volume":"3","author":"Brakat","year":"2015","journal-title":"J. Electr. Electron. Eng."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"2772","DOI":"10.1103\/PhysRevLett.69.2772","article-title":"Calculation of photon dispersion","volume":"69","author":"Pendry","year":"1992","journal-title":"Phys. Rev. Lett."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"037401","DOI":"10.1103\/PhysRevLett.91.037401","article-title":"Nonlinear properties of left-handed metamaterials","volume":"91","author":"Zharov","year":"2003","journal-title":"Phys. Rev. Lett."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"1567","DOI":"10.1016\/j.physb.2011.01.071","article-title":"Influence of Mg doping on the dielectric properties of MgO-doped lithium niobate","volume":"406","author":"Bai","year":"2011","journal-title":"Phys. B"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"2164","DOI":"10.1063\/1.108282","article-title":"Elastic properties of 5 mol% MgO doped LiNbO3 crystals measured by line focus beam acoustic microscopy","volume":"61","author":"Kushibiki","year":"1992","journal-title":"Appl. Phys. Lett."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"064113","DOI":"10.1103\/PhysRevB.73.064113","article-title":"Dopant occupancy and structural stability of doped lithium niobate crystals","volume":"73","author":"Xue","year":"2006","journal-title":"Phys. Rev. B"},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"7863","DOI":"10.1063\/1.370597","article-title":"Surface-acoustic-wave properties of MgO-doped LiNbO3 single crystals measured by line-focus-beam acoustic microscopy","volume":"85","author":"Kushibiki","year":"1999","journal-title":"J. Appl. Phys."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"537","DOI":"10.1016\/S0038-1098(02)00180-1","article-title":"Dielectric characterization of the defect concentration in lithium niobate single crystals","volume":"122","author":"Xue","year":"2002","journal-title":"Solid State Commun."},{"key":"ref_33","first-page":"165","article-title":"Inequalities of the complete elliptic integrals","volume":"3","author":"Qi","year":"1995","journal-title":"Tamkang J. Math."},{"key":"ref_34","first-page":"197","article-title":"Lobatto type quadrature rules for functions with bounded derivative","volume":"3","author":"Cerone","year":"2003","journal-title":"Math. Inequal Appl."},{"key":"ref_35","first-page":"2787","article-title":"Some bounds for the complete elliptic integrals of the first and the second kinds","volume":"18","author":"Guo","year":"2009","journal-title":"Math. CA"},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"509","DOI":"10.1070\/PU1968v010n04ABEH003699","article-title":"The electrodynamics of substances with simultaneously negative values of \u03b5 and \u03bc","volume":"10","author":"Veselago","year":"1968","journal-title":"Sov. Phys. Usp."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"107401","DOI":"10.1103\/PhysRevLett.90.107401","article-title":"Experimental verification and simulation of negative index of refraction using Snell\u2019s law","volume":"90","author":"Parazzoli","year":"2003","journal-title":"Phys. Rev. Lett."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"1740","DOI":"10.1049\/iet-map.2015.0361","article-title":"Constitutive parameter analysis of left-handed dual-star split-ring resonator metamaterial for homogeneous infinite slab","volume":"9","author":"Ullah","year":"2015","journal-title":"IET Microw. Antennas Propag."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"36","DOI":"10.1002\/cta.2222","article-title":"Inversion response to optimize lumped-element circuits for metamaterial","volume":"45","author":"Uddin","year":"2017","journal-title":"Int. J. Circ. Theor. Appl."}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/14\/9\/1942\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T00:33:49Z","timestamp":1760142829000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/14\/9\/1942"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,9,18]]},"references-count":39,"journal-issue":{"issue":"9","published-online":{"date-parts":[[2022,9]]}},"alternative-id":["sym14091942"],"URL":"https:\/\/doi.org\/10.3390\/sym14091942","relation":{},"ISSN":["2073-8994"],"issn-type":[{"value":"2073-8994","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,9,18]]}}}