Analytical model of the fundamental mode of 3D square split ring resonators
An analytical model is developed for the charge and potential distributions of the fundamental mode of three-dimensional (3D) singly split ring resonators (SRRs) with square cross section, which nowadays can be conveniently fabricated by additive manufacturing techniques. This model allows the deriv...
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| Format: | Journal article |
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AIP Publishing
2019
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| _version_ | 1826303816567357440 |
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| author | Vallecchi, A Shamonina, E Stevens, C |
| author_facet | Vallecchi, A Shamonina, E Stevens, C |
| author_sort | Vallecchi, A |
| collection | OXFORD |
| description | An analytical model is developed for the charge and potential distributions of the fundamental mode of three-dimensional (3D) singly split ring resonators (SRRs) with square cross section, which nowadays can be conveniently fabricated by additive manufacturing techniques. This model allows the derivation of approximate formulas for the equivalent capacitance and the analysis of the resonant properties of this type of SRRs at any frequency. The total capacitance is expressed as the sum of the usual gap capacitance and a surface capacitance associated with the charges on the SRR walls, which are determined from the solution for the irrotational part of the electric field of a square split cylinder obtained by conformal mapping. The applicability of the proposed model for a broad range of SRR parameters is demonstrated by comparing the resonance frequency of sample SRR configurations found theoretically with the corresponding values obtained by numerical simulations and experiments. Furthermore, the functions describing the charge and current mode profiles provided in this work can be instrumental in estimating the near-field interaction and the coupling constants of an ensemble of resonant 3D square split rings and thus for tailoring the response of metamaterials and other devices formed by these elements. |
| first_indexed | 2024-03-07T06:08:26Z |
| format | Journal article |
| id | oxford-uuid:eea3c12c-8008-4c4b-a1b8-aa9ef7d70273 |
| institution | University of Oxford |
| last_indexed | 2024-03-07T06:08:26Z |
| publishDate | 2019 |
| publisher | AIP Publishing |
| record_format | dspace |
| spelling | oxford-uuid:eea3c12c-8008-4c4b-a1b8-aa9ef7d702732022-03-27T11:34:18ZAnalytical model of the fundamental mode of 3D square split ring resonatorsJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:eea3c12c-8008-4c4b-a1b8-aa9ef7d70273Symplectic Elements at OxfordAIP Publishing2019Vallecchi, AShamonina, EStevens, CAn analytical model is developed for the charge and potential distributions of the fundamental mode of three-dimensional (3D) singly split ring resonators (SRRs) with square cross section, which nowadays can be conveniently fabricated by additive manufacturing techniques. This model allows the derivation of approximate formulas for the equivalent capacitance and the analysis of the resonant properties of this type of SRRs at any frequency. The total capacitance is expressed as the sum of the usual gap capacitance and a surface capacitance associated with the charges on the SRR walls, which are determined from the solution for the irrotational part of the electric field of a square split cylinder obtained by conformal mapping. The applicability of the proposed model for a broad range of SRR parameters is demonstrated by comparing the resonance frequency of sample SRR configurations found theoretically with the corresponding values obtained by numerical simulations and experiments. Furthermore, the functions describing the charge and current mode profiles provided in this work can be instrumental in estimating the near-field interaction and the coupling constants of an ensemble of resonant 3D square split rings and thus for tailoring the response of metamaterials and other devices formed by these elements. |
| spellingShingle | Vallecchi, A Shamonina, E Stevens, C Analytical model of the fundamental mode of 3D square split ring resonators |
| title | Analytical model of the fundamental mode of 3D square split ring resonators |
| title_full | Analytical model of the fundamental mode of 3D square split ring resonators |
| title_fullStr | Analytical model of the fundamental mode of 3D square split ring resonators |
| title_full_unstemmed | Analytical model of the fundamental mode of 3D square split ring resonators |
| title_short | Analytical model of the fundamental mode of 3D square split ring resonators |
| title_sort | analytical model of the fundamental mode of 3d square split ring resonators |
| work_keys_str_mv | AT vallecchia analyticalmodelofthefundamentalmodeof3dsquaresplitringresonators AT shamoninae analyticalmodelofthefundamentalmodeof3dsquaresplitringresonators AT stevensc analyticalmodelofthefundamentalmodeof3dsquaresplitringresonators |