Analytic Continuation, Phase Unwrapping, and Retrieval of the Refractive Index of Metamaterials from S-Parameters
The heuristic homogenization approach is intensively employed to characterize electromagnetic metamaterials (MMs). The effective parameters are extracted within this framework using the Nicolson–Ross–Weir (NRW) method. Special attention must be devoted to handling this procedure because of the branc...
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MDPI AG
2024-01-01
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| author | Giovanni Angiulli Mario Versaci Salvatore Calcagno Paolo Di Barba |
| author_facet | Giovanni Angiulli Mario Versaci Salvatore Calcagno Paolo Di Barba |
| author_sort | Giovanni Angiulli |
| collection | DOAJ |
| description | The heuristic homogenization approach is intensively employed to characterize electromagnetic metamaterials (MMs). The effective parameters are extracted within this framework using the Nicolson–Ross–Weir (NRW) method. Special attention must be devoted to handling this procedure because of the branch ambiguity issue affecting it, i.e., the lack of uniqueness in the evaluation of the effective refractive index <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>n</mi><mrow><mi>e</mi><mi>f</mi><mi>f</mi></mrow></msub><mrow></mrow></mrow></semantics></math></inline-formula> rooted in the use of the multivalued complex logarithm to invert the Airy–Fresnel relation. Over the years, several techniques based on the phase-unwrapping approach have been introduced, but without any theoretical justification. In this paper, we aim to clarify the theoretical connection between the phase unwrapping method and the analytic continuation theory framework. Furthermore, three-phase-unwrapping approaches, which descend directly from the theory we discussed, are compared to identify which approach is best suited to reconstruct the complex refractive index of metamaterials when the NRW method is applicable. |
| first_indexed | 2024-03-08T03:49:03Z |
| format | Article |
| id | doaj.art-b0ce22aa7fa1416ea97bea84194d166a |
| institution | Directory Open Access Journal |
| issn | 1424-8220 |
| language | English |
| last_indexed | 2024-03-08T03:49:03Z |
| publishDate | 2024-01-01 |
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| spelling | doaj.art-b0ce22aa7fa1416ea97bea84194d166a2024-02-09T15:22:14ZengMDPI AGSensors1424-82202024-01-0124391210.3390/s24030912Analytic Continuation, Phase Unwrapping, and Retrieval of the Refractive Index of Metamaterials from S-ParametersGiovanni Angiulli0Mario Versaci1Salvatore Calcagno2Paolo Di Barba3Department 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, ItalyDepartment of Civil, Energetic, Environmental and Material Engineering, Mediterranea University, 89124 Reggio Calabria, ItalyDipartimento di Ingegneria Industriale e dell’Informazione, University of Pavia, 27100 Pavia, ItalyThe heuristic homogenization approach is intensively employed to characterize electromagnetic metamaterials (MMs). The effective parameters are extracted within this framework using the Nicolson–Ross–Weir (NRW) method. Special attention must be devoted to handling this procedure because of the branch ambiguity issue affecting it, i.e., the lack of uniqueness in the evaluation of the effective refractive index <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>n</mi><mrow><mi>e</mi><mi>f</mi><mi>f</mi></mrow></msub><mrow></mrow></mrow></semantics></math></inline-formula> rooted in the use of the multivalued complex logarithm to invert the Airy–Fresnel relation. Over the years, several techniques based on the phase-unwrapping approach have been introduced, but without any theoretical justification. In this paper, we aim to clarify the theoretical connection between the phase unwrapping method and the analytic continuation theory framework. Furthermore, three-phase-unwrapping approaches, which descend directly from the theory we discussed, are compared to identify which approach is best suited to reconstruct the complex refractive index of metamaterials when the NRW method is applicable.https://www.mdpi.com/1424-8220/24/3/912phase unwrappingscattering parametersmetamaterials |
| spellingShingle | Giovanni Angiulli Mario Versaci Salvatore Calcagno Paolo Di Barba Analytic Continuation, Phase Unwrapping, and Retrieval of the Refractive Index of Metamaterials from S-Parameters Sensors phase unwrapping scattering parameters metamaterials |
| title | Analytic Continuation, Phase Unwrapping, and Retrieval of the Refractive Index of Metamaterials from S-Parameters |
| title_full | Analytic Continuation, Phase Unwrapping, and Retrieval of the Refractive Index of Metamaterials from S-Parameters |
| title_fullStr | Analytic Continuation, Phase Unwrapping, and Retrieval of the Refractive Index of Metamaterials from S-Parameters |
| title_full_unstemmed | Analytic Continuation, Phase Unwrapping, and Retrieval of the Refractive Index of Metamaterials from S-Parameters |
| title_short | Analytic Continuation, Phase Unwrapping, and Retrieval of the Refractive Index of Metamaterials from S-Parameters |
| title_sort | analytic continuation phase unwrapping and retrieval of the refractive index of metamaterials from s parameters |
| topic | phase unwrapping scattering parameters metamaterials |
| url | https://www.mdpi.com/1424-8220/24/3/912 |
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