Extraction of the Electromagnetic Parameters of a Metamaterial Using the Nicolson–Ross–Weir Method: An Analysis Based on Global Analytic Functions and Riemann Surfaces
Source abstract
Abstract
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.
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Research context
OpenAlex topics: Metamaterials and Metasurfaces Applications · Advanced Antenna and Metasurface Technologies · Electromagnetic Scattering and Analysis
SciVX discovery tags are terminology-based. OpenAlex topics are source-provided classifications.
Affiliations
Department of Information Engineering, Infrastructures and Sustainable Energy, Mediterranea University, 89124 Reggio Calabria, Italy
Department of Civil, Energetic, Environmental and Material Engineering, Mediterranea University, 89124 Reggio Calabria, Italy
References (41)
Show source-provided references
1. Recent progress on metamaterials: From effective medium model to real-time information processing system10.1016/j.pquantelec.2019.05.001 ↗
2. Imaging with metamaterials10.1038/s42254-021-00394-3 ↗
3. Cui, T.J., Smith, D.R., and Liu, R. (2010). Metamaterials, Springer.10.1007/978-1-4419-0573-4 ↗
4. Cui, T.J., Tang, W.X., Yang, X.M., Mei, Z.L., and Jiang, W.X. (2017). Metamaterials: Beyond Crystals, Noncrystals, and Quasicrystals, CRC Press.10.1201/9781315373614 ↗
5. Homogenization of metamaterials by field averaging10.1364/JOSAB.23.000391 ↗
6. First-principles homogenization theory for periodic metamaterials10.1103/PhysRevB.84.075153 ↗
7. Chen, L.F., Ong, C.K., Neo, C.P., Varadan, V.V., and Varadan, V.K. (2004). Microwave Electronics: Measurement and Materials Characterization, John Wiley & Sons.10.1002/0470020466 ↗
8. Facile synthesis of novel fluorescent thiazole coumarinyl compounds: Electrochemical, time resolve fluorescence, and solvatochromic study10.1016/j.molstruc.2020.129422 ↗
9. Effect of organic solvents on solvatochromic, fluorescence, and electrochemical properties of synthesized thiazolylcoumarin derivatives10.1002/bio.4044 ↗
10. Hakim, M.L., Alam, T., Islam, M.T., Baharuddin, M.H., Alzamil, A., and Islam, M.S. (2022). Quad-Band Polarization-Insensitive Square Split-Ring Resonator (SSRR) with an Inner Jerusalem Cross Metamaterial Absorber for Ku-and K-Band Sensing Applications. Sensors, 22.10.3390/s22124489 ↗
11. Idrus, I.N., Faruque, M.R.I., Abdullah, S., Khandaker, M.U., Tamam, N., and Sulieman, A.A. (2022). An Oval-Square Shaped Split Ring Resonator Based Left-Handed Metamaterial for Satellite Communications and Radar Applications. Micromachines, 13.10.3390/mi13040578 ↗
12. Sgró, A., De Carlo, D., Angiulli, G., Morabito, F.C., and Versaci, M. (2018). Accurate computation of Drude-Lorentz model coefficients of single negative magnetic metamaterials using a micro-genetic algorithm approach. Multidisciplinary Approaches to Neural Computing, Springer.10.1007/978-3-319-56904-8_5 ↗
13. Wide bandwidth angle-and polarization-insensitive symmetric metamaterial absorber for X and Ku band applications10.1038/s41598-020-67262-5 ↗
14. Ajewole, B., Kumar, P., and Afullo, T. (2022). I-Shaped Metamaterial Using SRR for Multi-Band Wireless Communication. Crystals, 12.10.3390/cryst12040559 ↗
15. Square enclosed circle split ring resonator enabled epsilon negative (ENG) near zero index (NZI) metamaterial for gain enhancement of multiband satellite and radar antenna applications10.1016/j.rinp.2020.103556 ↗
16. On electromagnetic characterization and homogenization of nanostructured metamaterials10.1088/2040-8978/13/1/013001 ↗
17. Material parameters of metamaterials (a review)10.1134/S0030400X09110101 ↗
18. A review of the scattering-parameter extraction method with clarification of ambiguity issues in relation to metamaterial homogenization10.1109/MAP.2013.6529320 ↗
19. Robust method to retrieve the constitutive effective parameters of metamaterials10.1103/PhysRevE.70.016608 ↗
20. A unique extraction of metamaterial parameters based on Kramers–Kronig relationship10.1109/TMTT.2010.2065310 ↗
21. Unique retrieval of complex permittivity and permeability of dispersive materials from reflection and transmitted fields by enforcing causality10.1109/TMTT.2007.906473 ↗
22. Angiulli, G., Versaci, M., Calcagno, S., and Di Barba, P. (2019, January 29–31). Metamaterial unit cell characterization by using a multi-fidelity surrogate modelling approach. Proceedings of the 19th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering (ISEF), Nancy, France.10.1109/ISEF45929.2019.9097033 ↗
23. Quick retrieval of effective electromagnetic metamaterial parameters by using a Multi-fidelity Surrogate Modelling approach10.1051/epjap/2020200014 ↗
24. Causal homogenization of metamaterials10.1515/nanoph-2019-0069 ↗
25. An automated phase correction algorithm for retrieving permittivity and permeability of electromagnetic metamaterials10.1063/1.4882155 ↗
26. An electromagnetic parameters extraction method for metamaterials based on phase unwrapping technique10.1080/17455030.2016.1165899 ↗
27. Angiulli, G., and Versaci, M. (2021, January 21–25). An Analytic Continuation Algorithm for Recovering the Electromagnetic Parameters of Metamaterials. Proceedings of the 2021 Photonics & Electromagnetics Research Symposium (PIERS), Hangzhou, China.10.1109/PIERS53385.2021.9694694 ↗
28. Effective constitutive parameters retrieval method for bianisotropic metamaterials using waveguide measurements10.1109/TMTT.2016.2644639 ↗
29. Peiponen, K.E., Vartiainen, E.M., and Asakura, T. (1998). Dispersion, Complex Analysis and Optical Spectroscopy: Classical Theory, Springer Science & Business Media.
30. Retrieving the Effective Parameters of an Electromagnetic Metamaterial Using the Nicolson-Ross-Weir Method: An Analytic Continuation Problem along the Path Determined by Scattering Parameters10.1109/ACCESS.2021.3082261 ↗
31. Electromagnetic parameter retrieval from inhomogeneous metamaterials10.1103/PhysRevE.71.036617 ↗
32. Markushevich, A.I. (1985). Theory of Functions of a Complex Variable, Chelsea Publishing Company. [2nd ed.].
33. Kramers-Kronig relations and sum rules of negative refractive index media10.1140/epjb/e2004-00294-6 ↗
34. Numerical computation of the complex dielectric permittivity using Hilbert transform and FFT techniques10.1016/S0016-0032(98)00014-3 ↗
35. Palka, B.P. (1991). An Introduction to Complex Function Theory, Springer Science & Business Media.10.1007/978-1-4612-0975-1 ↗
36. Oppenheim, A., and Schafer, R.W. (2009). Discrete Time Signal Processing, Prentice Hall.
37. Wegert, E. (2012). Visual Complex Functions: An Introduction with Phase Portraits, Springer Science & Business Media.10.1007/978-3-0348-0180-5 ↗
38. Lucarini, V., Saarinen, J.J., Peiponen, K.E., and Vartiainen, E.M. (2005). Kramers-Kronig relations in Optical Materials Research, Springer Science & Business Media.
39. Superpositions of Lorentzians as the class of causal functions10.1103/PhysRevA.88.033834 ↗
40. Groetsch, C.W. (1980). Element of Applicable Functional Analysis, Marcel Dekker.
41. Chellappa, S., Franchetti, F., and Puschel, M. (2007). How to write fast numerical code: A small introduction. International Summer School on Generative and Transformational Techniques in Software Engineering, Springer.10.1007/978-3-540-88643-3_5 ↗