Spatially Dispersive Metasurfaces—Part III: Zero-Thickness Modeling of Periodic and Finite Nonuniform Surfaces
A zero-thickness model of nonuniform spatially dispersive (SD) metasurfaces is developed and demonstrated numerically for practical structures. This is an extension of Nizer Rahmeier et al. (2022) and Smy et al. (2022), which proposed a method of modeling uniform SD metasurfaces by expressing their...
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| Vydáno v: | IEEE transactions on antennas and propagation Ročník 71; číslo 7; s. 5935 - 5945 |
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| Jazyk: | angličtina |
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The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
01.07.2023
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| ISSN: | 0018-926X, 1558-2221 |
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| Abstract | A zero-thickness model of nonuniform spatially dispersive (SD) metasurfaces is developed and demonstrated numerically for practical structures. This is an extension of Nizer Rahmeier et al. (2022) and Smy et al. (2022), which proposed a method of modeling uniform SD metasurfaces by expressing their surface susceptibilities as rational polynomial functions in the spatial frequency domain. This led to the extended generalized sheet transition conditions (GSTCs) forming a set of differential equations relating the spatial derivatives of both difference and average fields around the surface that were then integrated into an integral equation (IE) solver. Here, the extended GSTCs are further developed to model nonuniform metasurfaces by approximating them as locally linear space-invariant (LSI). Using this model, a semianalytical Floquet method is derived to predict scattered fields from periodically varying metasurfaces. The extended GSTCs, Floquet method, and IE method are tested on several nonuniform surfaces consisting of short metal dipole cells of varying lengths exhibiting strong spatial dispersion. The physical surfaces are simulated in Ansys FEM-HFSS, while their zero-thickness equivalents, both dispersive and nondispersive, are simulated using the Floquet and IE methods. Excellent agreement is shown between the Floquet-SD and IE-GSTC-SD methods and HFSS, demonstrating the importance of spatial dispersion to model their scattered fields. |
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| AbstractList | A zero-thickness model of nonuniform spatially dispersive (SD) metasurfaces is developed and demonstrated numerically for practical structures. This is an extension of Nizer Rahmeier et al. (2022) and Smy et al. (2022), which proposed a method of modeling uniform SD metasurfaces by expressing their surface susceptibilities as rational polynomial functions in the spatial frequency domain. This led to the extended generalized sheet transition conditions (GSTCs) forming a set of differential equations relating the spatial derivatives of both difference and average fields around the surface that were then integrated into an integral equation (IE) solver. Here, the extended GSTCs are further developed to model nonuniform metasurfaces by approximating them as locally linear space-invariant (LSI). Using this model, a semianalytical Floquet method is derived to predict scattered fields from periodically varying metasurfaces. The extended GSTCs, Floquet method, and IE method are tested on several nonuniform surfaces consisting of short metal dipole cells of varying lengths exhibiting strong spatial dispersion. The physical surfaces are simulated in Ansys FEM-HFSS, while their zero-thickness equivalents, both dispersive and nondispersive, are simulated using the Floquet and IE methods. Excellent agreement is shown between the Floquet-SD and IE-GSTC-SD methods and HFSS, demonstrating the importance of spatial dispersion to model their scattered fields. |
| Author | Smy, Tom J. Dugan, Jordan Gupta, Shulabh Rahmeier, João Guilherme Nizer |
| Author_xml | – sequence: 1 givenname: Jordan orcidid: 0000-0001-7549-439X surname: Dugan fullname: Dugan, Jordan organization: Department of Electronics, Carleton University, Ottawa, Canada – sequence: 2 givenname: João Guilherme Nizer orcidid: 0000-0002-3858-7770 surname: Rahmeier fullname: Rahmeier, João Guilherme Nizer organization: Department of Electronics, Carleton University, Ottawa, Canada – sequence: 3 givenname: Tom J. orcidid: 0000-0001-5369-0082 surname: Smy fullname: Smy, Tom J. organization: Department of Electronics, Carleton University, Ottawa, Canada – sequence: 4 givenname: Shulabh orcidid: 0000-0002-0264-9474 surname: Gupta fullname: Gupta, Shulabh organization: Department of Electronics, Carleton University, Ottawa, Canada |
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| Cites_doi | 10.1109/TAP.2015.2423700 10.1109/TAP.2022.3209288 10.1109/ACCESS.2020.3045753 10.1109/MAP.2012.6230714 10.1103/PhysRevApplied.12.024026 10.1146/annurev-matsci-070616-124220 10.1038/nnano.2015.304 10.1088/0034-4885/79/7/076401 10.1002/andp.201600015 10.3390/app9091891 10.1109/AP-S/USNC-URSI47032.2022.9886401 10.1109/TAP.2019.2943423 10.1049/PBEW041E 10.1103/PhysRevB.94.140301 10.23919/EuCAP53622.2022.9769550 10.1002/9781118057926 10.1109/TAP.2022.3164125 10.23919/EuCAP48036.2020.9135486 10.22215/etd/2022-15239 10.1109/APUSNCURSINRSM.2017.8072898 10.1186/s13638-019-1438-9 10.1109/TAP.2021.3060901 10.23919/EuCAP53622.2022.9769601 10.1109/TAP.2003.817560 10.1109/TAP.2021.3070718 10.1103/PhysRevB.104.165426 10.1109/TAP.2020.3030972 10.1364/OE.22.026212 10.1002/adom.201400584 10.1109/TAP.2022.3164169 10.1103/PhysRevApplied.4.037001 |
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| SubjectTerms | CAD Computer aided design Differential equations Dipoles Dispersion Finite element method Functions (mathematics) Integral equations Mathematical analysis Metasurfaces Modelling Polynomials Thickness |
| Title | Spatially Dispersive Metasurfaces—Part III: Zero-Thickness Modeling of Periodic and Finite Nonuniform Surfaces |
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