Extraction of the Electromagnetic Parameters of a Metamaterial Using the Nicolson–Ross–Weir Method: An Analysis Based on Global Analytic Functions and Riemann Surfaces
The characterization of electromagnetic metamaterials (MMs) plays a fundamental role in their engineering processes. To this end, the Nicolson–Ross–Weir (NRW) method is intensively used to recover the effective parameters of MMs, even though this is affected by the branch ambiguity problem. In this...
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| Format: | Article |
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MDPI AG
2022-11-01
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| Series: | Applied Sciences |
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| Online Access: | https://www.mdpi.com/2076-3417/12/21/11121 |
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| author | Giovanni Angiulli Mario Versaci |
| author_facet | Giovanni Angiulli Mario Versaci |
| author_sort | Giovanni Angiulli |
| collection | DOAJ |
| description | The characterization of electromagnetic metamaterials (MMs) plays a fundamental role in their engineering processes. To this end, the Nicolson–Ross–Weir (NRW) method is intensively used to recover the effective parameters of MMs, even though this is affected by the branch ambiguity problem. In this paper, we face this issue in the context of global analytic functions and Riemann surfaces. This point of view allows us to rigorously demonstrate the mathematical foundations of an algorithmic approach for avoiding the branch ambiguity problem, in which the phase unwrapping method is merged with K-K relations for recovering the effective parameters of an MM. In addition, exploiting the intimate relationship between the K-K relations and the Hilbert transform, a simple variant of the above algorithm is presented. |
| first_indexed | 2024-03-09T19:16:54Z |
| format | Article |
| id | doaj.art-30cdf2077e594477b6d8301501cd1b88 |
| institution | Directory Open Access Journal |
| issn | 2076-3417 |
| language | English |
| last_indexed | 2024-03-09T19:16:54Z |
| publishDate | 2022-11-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Applied Sciences |
| spelling | doaj.art-30cdf2077e594477b6d8301501cd1b882023-11-24T03:38:24ZengMDPI AGApplied Sciences2076-34172022-11-0112211112110.3390/app122111121Extraction of the Electromagnetic Parameters of a Metamaterial Using the Nicolson–Ross–Weir Method: An Analysis Based on Global Analytic Functions and Riemann SurfacesGiovanni Angiulli0Mario Versaci1Department of Information Engineering, Infrastructures and Sustainable Energy, Mediterranea University, 89124 Reggio Calabria, ItalyDepartment of Civil, Energetic, Environmental and Material Engineering, Mediterranea University, 89124 Reggio Calabria, ItalyThe characterization of electromagnetic metamaterials (MMs) plays a fundamental role in their engineering processes. To this end, the Nicolson–Ross–Weir (NRW) method is intensively used to recover the effective parameters of MMs, even though this is affected by the branch ambiguity problem. In this paper, we face this issue in the context of global analytic functions and Riemann surfaces. This point of view allows us to rigorously demonstrate the mathematical foundations of an algorithmic approach for avoiding the branch ambiguity problem, in which the phase unwrapping method is merged with K-K relations for recovering the effective parameters of an MM. In addition, exploiting the intimate relationship between the K-K relations and the Hilbert transform, a simple variant of the above algorithm is presented.https://www.mdpi.com/2076-3417/12/21/11121metamaterialNicolson–Ross–Weir methodphase unwrappingKramers–Kronig relationsanalytic continuationglobal analytic functions |
| spellingShingle | Giovanni Angiulli Mario Versaci Extraction of the Electromagnetic Parameters of a Metamaterial Using the Nicolson–Ross–Weir Method: An Analysis Based on Global Analytic Functions and Riemann Surfaces Applied Sciences metamaterial Nicolson–Ross–Weir method phase unwrapping Kramers–Kronig relations analytic continuation global analytic functions |
| title | Extraction of the Electromagnetic Parameters of a Metamaterial Using the Nicolson–Ross–Weir Method: An Analysis Based on Global Analytic Functions and Riemann Surfaces |
| title_full | Extraction of the Electromagnetic Parameters of a Metamaterial Using the Nicolson–Ross–Weir Method: An Analysis Based on Global Analytic Functions and Riemann Surfaces |
| title_fullStr | Extraction of the Electromagnetic Parameters of a Metamaterial Using the Nicolson–Ross–Weir Method: An Analysis Based on Global Analytic Functions and Riemann Surfaces |
| title_full_unstemmed | Extraction of the Electromagnetic Parameters of a Metamaterial Using the Nicolson–Ross–Weir Method: An Analysis Based on Global Analytic Functions and Riemann Surfaces |
| title_short | Extraction of the Electromagnetic Parameters of a Metamaterial Using the Nicolson–Ross–Weir Method: An Analysis Based on Global Analytic Functions and Riemann Surfaces |
| title_sort | extraction of the electromagnetic parameters of a metamaterial using the nicolson ross weir method an analysis based on global analytic functions and riemann surfaces |
| topic | metamaterial Nicolson–Ross–Weir method phase unwrapping Kramers–Kronig relations analytic continuation global analytic functions |
| url | https://www.mdpi.com/2076-3417/12/21/11121 |
| work_keys_str_mv | AT giovanniangiulli extractionoftheelectromagneticparametersofametamaterialusingthenicolsonrossweirmethodananalysisbasedonglobalanalyticfunctionsandriemannsurfaces AT marioversaci extractionoftheelectromagneticparametersofametamaterialusingthenicolsonrossweirmethodananalysisbasedonglobalanalyticfunctionsandriemannsurfaces |