Three‐dimensional single‐shell dielectric lens design using complex coordinates and local axis‐displaced confocal quadrics
Abstract This study proposes an analytical formulation in complex coordinates to synthesise three‐dimensional single‐shell dielectric lens surfaces. An exact formulation based on geometrical optics is developed, and the synthesis problem is modelled as a non‐linear second‐order partial differential...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Wiley
2023-06-01
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| Series: | IET Microwaves, Antennas & Propagation |
| Subjects: | |
| Online Access: | https://doi.org/10.1049/mia2.12365 |
| _version_ | 1797805521940512768 |
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| author | Aline Rocha deAssis José Ricardo Bergmann Fernando José daSilva Moreira |
| author_facet | Aline Rocha deAssis José Ricardo Bergmann Fernando José daSilva Moreira |
| author_sort | Aline Rocha deAssis |
| collection | DOAJ |
| description | Abstract This study proposes an analytical formulation in complex coordinates to synthesise three‐dimensional single‐shell dielectric lens surfaces. An exact formulation based on geometrical optics is developed, and the synthesis problem is modelled as a non‐linear second‐order partial differential equation of the Monge–Ampère (MA) type. An alternative numerical scheme based on axis‐displaced confocal quadrics is used to locally represent the surface of dielectric lens. The advantage of this approach is to analytically obtain the partial derivatives present in the MA equation. To validate the proposed methodology, numerical results are obtained by an iterative algorithm that allows the simultaneous control of the transmitted beam width and the power density amplitude in the far‐field region. To illustrate the synthesis effectiveness, two examples of lens antennas are simulated and analysed. |
| first_indexed | 2024-03-13T05:53:18Z |
| format | Article |
| id | doaj.art-d2aaacd28f2345e38c829c76a51267c7 |
| institution | Directory Open Access Journal |
| issn | 1751-8725 1751-8733 |
| language | English |
| last_indexed | 2024-03-13T05:53:18Z |
| publishDate | 2023-06-01 |
| publisher | Wiley |
| record_format | Article |
| series | IET Microwaves, Antennas & Propagation |
| spelling | doaj.art-d2aaacd28f2345e38c829c76a51267c72023-06-13T09:41:13ZengWileyIET Microwaves, Antennas & Propagation1751-87251751-87332023-06-0117754755710.1049/mia2.12365Three‐dimensional single‐shell dielectric lens design using complex coordinates and local axis‐displaced confocal quadricsAline Rocha deAssis0José Ricardo Bergmann1Fernando José daSilva Moreira2Departamento de Engenharia Elétrica Universidade Federal de Ouro Preto (UFOP) João Monlevade Minas Gerais BrazilCETUC Pontifícia Universidade Católica do Rio de Janeiro (PUC‐Rio) Rio de Janeiro BrazilDepartamento de Engenharia Elétrica Universidade Federal de Minas Gerias (UFMG) Belo Horizonte Minas Gerais BrazilAbstract This study proposes an analytical formulation in complex coordinates to synthesise three‐dimensional single‐shell dielectric lens surfaces. An exact formulation based on geometrical optics is developed, and the synthesis problem is modelled as a non‐linear second‐order partial differential equation of the Monge–Ampère (MA) type. An alternative numerical scheme based on axis‐displaced confocal quadrics is used to locally represent the surface of dielectric lens. The advantage of this approach is to analytically obtain the partial derivatives present in the MA equation. To validate the proposed methodology, numerical results are obtained by an iterative algorithm that allows the simultaneous control of the transmitted beam width and the power density amplitude in the far‐field region. To illustrate the synthesis effectiveness, two examples of lens antennas are simulated and analysed.https://doi.org/10.1049/mia2.12365lensesoptical design techniquesshaped beam antennas |
| spellingShingle | Aline Rocha deAssis José Ricardo Bergmann Fernando José daSilva Moreira Three‐dimensional single‐shell dielectric lens design using complex coordinates and local axis‐displaced confocal quadrics IET Microwaves, Antennas & Propagation lenses optical design techniques shaped beam antennas |
| title | Three‐dimensional single‐shell dielectric lens design using complex coordinates and local axis‐displaced confocal quadrics |
| title_full | Three‐dimensional single‐shell dielectric lens design using complex coordinates and local axis‐displaced confocal quadrics |
| title_fullStr | Three‐dimensional single‐shell dielectric lens design using complex coordinates and local axis‐displaced confocal quadrics |
| title_full_unstemmed | Three‐dimensional single‐shell dielectric lens design using complex coordinates and local axis‐displaced confocal quadrics |
| title_short | Three‐dimensional single‐shell dielectric lens design using complex coordinates and local axis‐displaced confocal quadrics |
| title_sort | three dimensional single shell dielectric lens design using complex coordinates and local axis displaced confocal quadrics |
| topic | lenses optical design techniques shaped beam antennas |
| url | https://doi.org/10.1049/mia2.12365 |
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