{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,26]],"date-time":"2025-12-26T03:44:19Z","timestamp":1766720659974,"version":"build-2065373602"},"reference-count":52,"publisher":"MDPI AG","issue":"10","license":[{"start":{"date-parts":[[2025,5,12]],"date-time":"2025-05-12T00:00:00Z","timestamp":1747008000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Natural Science Foundation of Guangxi Province","award":["2024GXNSFAA010178","2020GXNSFAA297192","GXKL06240108","GXKL06200215"],"award-info":[{"award-number":["2024GXNSFAA010178","2020GXNSFAA297192","GXKL06240108","GXKL06200215"]}]},{"name":"Guangxi Key Laboratory of Wireless Broadband Communication and Signal Processing","award":["2024GXNSFAA010178","2020GXNSFAA297192","GXKL06240108","GXKL06200215"],"award-info":[{"award-number":["2024GXNSFAA010178","2020GXNSFAA297192","GXKL06240108","GXKL06200215"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Materials"],"abstract":"<jats:p>This study proposes and numerically demonstrates a novel nonreciprocal electromagnetic metasurface by integrating a highly nonlinear liquid metamaterial (LMM) with a simple two-dimensional silicon dielectric grating. The transmission characteristics of the proposed structure were investigated using a full-vector finite-element method. We demonstrated that the proposed subwavelength-thickness metasurface achieves a transmission coefficient contrast of up to 0.96 between forward and backward propagation. Highly nonlinear LMMs, when employed as nonreciprocal media, significantly lower the radiation power needed to induce a nonlinear response compared to natural materials. Furthermore, we numerically analyzed the effects of the grating\u2019s structural parameters, LMM thickness, and packing fraction on transmittance. The proposed design holds promise for applications in optical isolators.<\/jats:p>","DOI":"10.3390\/ma18102241","type":"journal-article","created":{"date-parts":[[2025,5,12]],"date-time":"2025-05-12T10:58:07Z","timestamp":1747047487000},"page":"2241","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Numerical Study of Optical Nonreciprocal Transmission via Liquid Metamaterial Nonlinearity"],"prefix":"10.3390","volume":"18","author":[{"given":"Tiesheng","family":"Wu","sequence":"first","affiliation":[{"name":"Guangxi Key Laboratory of Wireless Broadband Communication and Signal Processing, School of Information and Communication, Guilin University of Electronic Technology, Guilin 541004, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xin","family":"Cheng","sequence":"additional","affiliation":[{"name":"Guangxi Key Laboratory of Wireless Broadband Communication and Signal Processing, School of Information and Communication, Guilin University of Electronic Technology, Guilin 541004, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yujing","family":"Lan","sequence":"additional","affiliation":[{"name":"Guangxi Key Laboratory of Wireless Broadband Communication and Signal Processing, School of Information and Communication, Guilin University of Electronic Technology, Guilin 541004, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0009-0004-8127-2194","authenticated-orcid":false,"given":"Zhenyu","family":"Li","sequence":"additional","affiliation":[{"name":"Guangxi Key Laboratory of Wireless Broadband Communication and Signal Processing, School of Information and Communication, Guilin University of Electronic Technology, Guilin 541004, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Changpeng","family":"Feng","sequence":"additional","affiliation":[{"name":"Guangxi Key Laboratory of Wireless Broadband Communication and Signal Processing, School of Information and Communication, Guilin University of Electronic Technology, Guilin 541004, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yingshuang","family":"Huang","sequence":"additional","affiliation":[{"name":"Guangxi Key Laboratory of Wireless Broadband Communication and Signal Processing, School of Information and Communication, Guilin University of Electronic Technology, Guilin 541004, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yingtao","family":"Tang","sequence":"additional","affiliation":[{"name":"Guangxi Key Laboratory of Wireless Broadband Communication and Signal Processing, School of Information and Communication, Guilin University of Electronic Technology, Guilin 541004, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Hongyun","family":"Li","sequence":"additional","affiliation":[{"name":"Guangxi Key Laboratory of Wireless Broadband Communication and Signal Processing, School of Information and Communication, Guilin University of Electronic Technology, Guilin 541004, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yiwei","family":"Peng","sequence":"additional","affiliation":[{"name":"The Electronic Fifth Institute of the Ministry of Industry and Information Technology, Guangzhou 511370, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2025,5,12]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"076401","DOI":"10.1088\/0034-4885\/79\/7\/076401","article-title":"A review of metasurfaces: Physics and applications","volume":"79","author":"Chen","year":"2016","journal-title":"Rep. Prog. Phys."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"2638","DOI":"10.1021\/acsphotonics.7b01038","article-title":"Functional meta-optics and nanophotonics governed by Mie resonances","volume":"4","author":"Kruk","year":"2017","journal-title":"ACS Photonics"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"10","DOI":"10.1109\/MAP.2012.6230714","article-title":"An overview of the theory and applications of metasurfaces: The two-dimensional equivalents of metamaterials","volume":"54","author":"Holloway","year":"2012","journal-title":"IEEE Antennas Propag. Mag."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"1232009","DOI":"10.1126\/science.1232009","article-title":"Planar photonics with metasurfaces","volume":"339","author":"Kildishev","year":"2013","journal-title":"Science"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"024401","DOI":"10.1088\/0034-4885\/78\/2\/024401","article-title":"Holographic optical metasurfaces: A review of current progress","volume":"78","author":"Genevet","year":"2015","journal-title":"Rep. Prog. Phys."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"4370","DOI":"10.1109\/TAP.2024.3378388","article-title":"Virtual polarizer: Coherent perfect ultrawideband polarization control of chiral electromagnetic waves","volume":"72","author":"Wu","year":"2024","journal-title":"IEEE Trans. Antennas Propag."},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Hu, J., Bandyopadhyay, S., Liu, Y.-h., and Shao, L.-Y. (2021). A review on metasurface: From principle to smart metadevices. Front. Phys., 8.","DOI":"10.3389\/fphy.2020.586087"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"9765089","DOI":"10.34133\/2022\/9765089","article-title":"Review on metasurfaces: An alternative approach to advanced devices and instruments","volume":"2022","author":"Zhao","year":"2022","journal-title":"Adv. Devices Instrum."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"13518","DOI":"10.1364\/OE.488700","article-title":"Broadband electrically controlled reflective metasurface for reconfigurable circularly polarized wavefront manipulation","volume":"31","author":"Xin","year":"2023","journal-title":"Opt. Express"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"758","DOI":"10.1038\/nphoton.2011.270","article-title":"On-chip optical isolation in monolithically integrated non-reciprocal optical resonators","volume":"5","author":"Bi","year":"2011","journal-title":"Nat. Photon."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"91","DOI":"10.1038\/nphoton.2008.273","article-title":"Complete optical isolation created by indirect interband photonic transitions","volume":"3","author":"Yu","year":"2009","journal-title":"Nat. Photon."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"330","DOI":"10.1016\/S0030-4018(99)00027-9","article-title":"Nonreciprocal coupled waveguides for integrated optical isolators and circulators for tm-modes","volume":"161","author":"Bahlmann","year":"1999","journal-title":"Opt. Commun."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"729","DOI":"10.1126\/science.1206038","article-title":"Nonreciprocal light propagation in a silicon photonic circuit","volume":"333","author":"Feng","year":"2011","journal-title":"Science"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"126","DOI":"10.1016\/j.carbon.2020.10.076","article-title":"Optical nonlinearity and non-reciprocal transmission of graphene integrated metasurface","volume":"173","author":"Chen","year":"2021","journal-title":"Carbon"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"033901","DOI":"10.1103\/PhysRevLett.109.033901","article-title":"Electrically driven nonreciprocity induced by interband photonic transition on a silicon chip","volume":"109","author":"Lira","year":"2012","journal-title":"Phys. Rev. Lett."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"941","DOI":"10.1364\/OL.29.000941","article-title":"Magneto-optical nonreciprocal phase shift in garnet\/silicon-oninsulator waveguides","volume":"29","author":"Espinola","year":"2004","journal-title":"Opt. Lett."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"369","DOI":"10.1007\/s00340-005-1846-x","article-title":"Magneto-optical defects in two-dimensional photonic crystals","volume":"81","author":"Wang","year":"2005","journal-title":"Appl. Phys. B"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"18594","DOI":"10.1364\/OE.522109","article-title":"Omni-polarized Faraday isolator based on non-Hermitian Faraday system","volume":"32","author":"Hu","year":"2024","journal-title":"Opt. Express"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"101810","DOI":"10.1016\/j.jestch.2024.101810","article-title":"Broadband asymmetric absorption-transmission and double-band rasorber of electromagnetic waves based on superconductor ceramics metastructures-photonic crystals","volume":"57","author":"Lei","year":"2024","journal-title":"Eng. Sci. Technol. An Int. J."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"38023","DOI":"10.1364\/OE.536915","article-title":"Dual-channel asymmetric absorption-transmission properties based on plasma metastructures-photonic crystals","volume":"32","author":"Lei","year":"2024","journal-title":"Opt. Express"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"8359","DOI":"10.1038\/ncomms9359","article-title":"All-passive nonreciprocal metastructure","volume":"6","author":"Mahmoud","year":"2015","journal-title":"Nat. Commun."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"279","DOI":"10.1364\/OPTICA.5.000279","article-title":"Microresonator isolators and circulators based on the intrinsic nonreciprocity of the Kerr effect","volume":"5","author":"Silver","year":"2018","journal-title":"Optica"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"113","DOI":"10.1038\/s41928-018-0025-0","article-title":"Broadband passive isolators based on coupled nonlinear resonances","volume":"1","author":"Sounas","year":"2018","journal-title":"Nat. Electron."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"561","DOI":"10.1038\/s41566-022-01018-7","article-title":"Asymmetric parametric generation of images with nonlinear dielectric metasurfaces","volume":"16","author":"Kruk","year":"2022","journal-title":"Nat. Photon."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"81","DOI":"10.1038\/s41566-023-01333-7","article-title":"Passive bias-free non-reciprocal metasurfaces based on thermally nonlinear quasi-bound states in the continuum","volume":"18","author":"Cotrufo","year":"2024","journal-title":"Nat. Photon."},{"key":"ref_26","first-page":"1367628","article-title":"Nonlinear optics in metamaterials","volume":"3","author":"Litchinitser","year":"2018","journal-title":"Adv. Phys. X"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"833","DOI":"10.1038\/ncomms1805","article-title":"Giant nonlinear optical activity in a plasmonic metamaterial","volume":"3","author":"Ren","year":"2012","journal-title":"Nat. Commun."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"1371","DOI":"10.1364\/OE.16.001371","article-title":"Spatial solitons and light-induced instabilities in colloidal media","volume":"16","author":"Matuszewski","year":"2008","journal-title":"Opt. Express"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"14129","DOI":"10.1364\/OE.15.014129","article-title":"Plasmonic nanoclusters: A path towards negative-index metafluids","volume":"15","author":"Urzhumov","year":"2007","journal-title":"Opt. Express"},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"559","DOI":"10.1364\/JOSAB.31.000559","article-title":"Liquid metacrystals","volume":"31","author":"Zharov","year":"2014","journal-title":"J. Opt. Soc. Am. B"},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"1553","DOI":"10.1002\/adma.201504924","article-title":"Tunable meta-liquid crystals","volume":"28","author":"Liu","year":"2016","journal-title":"Adv. Mater."},{"key":"ref_32","doi-asserted-by":"crossref","unstructured":"Zharov, A., Viskadourakis, Z., Kenanakis, G., Fierro, V., and Celzard, A. (2021). Control of light transmission in a plasmonic liquid metacrystal. Nanomaterials, 11.","DOI":"10.3390\/nano11020346"},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"1307","DOI":"10.1364\/JOSAB.453595","article-title":"Resonant absorption of electromagnetic waves by an induced inhomogeneity in a liquid metamaterial","volume":"39","author":"Zharov","year":"2022","journal-title":"J. Opt. Soc. Am. B"},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"013504","DOI":"10.1103\/PhysRevA.106.013504","article-title":"Resonant absorption in an inhomogeneous disordered metamaterial: First-principles simulation","volume":"106","author":"Zharov","year":"2022","journal-title":"Phys. Rev. A"},{"key":"ref_35","first-page":"2171","article-title":"Metamaterials and their applications: An overview","volume":"236","author":"Valipour","year":"2022","journal-title":"Proc. Inst. Mech. Eng. L"},{"key":"ref_36","first-page":"1417055","article-title":"Metafluidic metamaterial: A review","volume":"3","author":"Zhang","year":"2018","journal-title":"Adv. Phys. X"},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"32249","DOI":"10.1021\/acsami.4c04251","article-title":"Self-powered terahertz modulators based on metamaterials, liquid crystals, and triboelectric nanogenerators","volume":"16","author":"Hao","year":"2024","journal-title":"ACS Appl. Mater. Interfaces"},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"5033","DOI":"10.1364\/OL.500952","article-title":"Non-reciprocal electromagnetic metasurface based on the nonlinearity of a liquid metamaterial","volume":"48","author":"Zharov","year":"2023","journal-title":"Opt. Lett."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"1069","DOI":"10.1515\/nanoph-2017-0132","article-title":"Bianisotropic metasurfaces: Physics and applications","volume":"7","author":"Asadchy","year":"2018","journal-title":"Nanophotonics"},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"54","DOI":"10.1364\/OL.5.000054","article-title":"Nonlinear optics in aerosols","volume":"5","author":"Palmer","year":"1980","journal-title":"Opt. Lett."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"347","DOI":"10.1364\/OL.7.000347","article-title":"Use of a liquid suspension of dielectric spheres as an artificial Kerr medium","volume":"7","author":"Smith","year":"1982","journal-title":"Opt. Lett."},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"2444","DOI":"10.1364\/JOSAB.22.002444","article-title":"Nonlinear susceptibility of colloids consisting of silver nanoparticles in carbon disulfide","volume":"22","author":"Galembeck","year":"2005","journal-title":"J. Opt. Soc. Am. B"},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"2948","DOI":"10.1364\/JOSAB.24.002948","article-title":"High-order nonlinearities of aqueous colloids containing silver nanoparticles","volume":"24","author":"Rodrigues","year":"2007","journal-title":"J. Opt. Soc. Am. B"},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"1614","DOI":"10.1103\/PhysRevA.46.1614","article-title":"Nonlinear susceptibility of composite optical materials in the Maxwell Garnett model","volume":"46","author":"Sipe","year":"1992","journal-title":"Phys. Rev. A"},{"key":"ref_45","unstructured":"Hansen, J., and McDonald, I. (2006). Theory of Simple Liquids, Elsevier Science."},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"055801","DOI":"10.1103\/PhysRevA.75.055801","article-title":"Particle-optical self-trapping","volume":"75","author":"Gordon","year":"2007","journal-title":"Phys. Rev. A"},{"key":"ref_47","doi-asserted-by":"crossref","first-page":"10207","DOI":"10.1364\/OE.15.010207","article-title":"Soliton dynamics and self-induced transparency in nonlinear nanosuspensions","volume":"15","author":"Christodoulides","year":"2007","journal-title":"Opt. Exp."},{"key":"ref_48","doi-asserted-by":"crossref","first-page":"811","DOI":"10.1038\/416811a","article-title":"Insights into phase transition kinetics from colloid science","volume":"416","author":"Anderson","year":"2002","journal-title":"Nature"},{"key":"ref_49","doi-asserted-by":"crossref","first-page":"143","DOI":"10.1038\/s41566-022-01110-y","article-title":"Integrated passive nonlinear optical isolators","volume":"17","author":"White","year":"2023","journal-title":"Nat. Photon."},{"key":"ref_50","unstructured":"Polyanskiy, M. (2008). \u2018Refractive Index Database\u2019, Refractive Index. Info, Available online: https:\/\/refractiveindex.info\/."},{"key":"ref_51","doi-asserted-by":"crossref","first-page":"369","DOI":"10.1038\/s41566-020-0606-0","article-title":"Inverse-designed non-reciprocal pulse router for chip-based LIDAR","volume":"14","author":"Yang","year":"2020","journal-title":"Nat. Photon."},{"key":"ref_52","doi-asserted-by":"crossref","first-page":"388","DOI":"10.1038\/nphoton.2015.79","article-title":"Limitations of nonlinear optical isolators due to dynamic reciprocity","volume":"9","author":"Shi","year":"2015","journal-title":"Nat. Photon."}],"container-title":["Materials"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1996-1944\/18\/10\/2241\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,9]],"date-time":"2025-10-09T17:31:27Z","timestamp":1760031087000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1996-1944\/18\/10\/2241"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,5,12]]},"references-count":52,"journal-issue":{"issue":"10","published-online":{"date-parts":[[2025,5]]}},"alternative-id":["ma18102241"],"URL":"https:\/\/doi.org\/10.3390\/ma18102241","relation":{},"ISSN":["1996-1944"],"issn-type":[{"type":"electronic","value":"1996-1944"}],"subject":[],"published":{"date-parts":[[2025,5,12]]}}}