Abstract
The development of metamaterials has led to the search and selection of effective methods for radio wave nondestructive testing of their electrophysical parameters. The existing approaches to testing, based on the recovery of the effective electrophysical parameters of metamaterials from the reflection and transmission coefficients of an electromagnetic wave, have low reliability and do not provide the local inspection of the parameters. In this paper, we propose for the first time a radio-wave method for local inspection of complex dielectric and magnetic permeabilities, as well as the thickness of flat-layered samples of metamaterials on a metal substrate using surface electromagnetic waves of the microwave range. The method is based on solving the inverse problem of determining the effective electrophysical parameters of a metamaterial from the frequency dependence of the complex attenuation coefficient of the field of a surface electromagnetic wave excited in the sample under study. In this case, the electrophysical parameters of the metamaterial are represented in the form of parametric frequency functions in accordance with the Drude–Lorentz dispersion models, and the solution of the inverse problem is reduced to minimizing the objective function constructed from the discrepancy between the experimental and calculated theoretical values of the attenuation coefficients of the surface electromagnetic wave field on a grid of discrete frequencies. The structure of the measuring complex that implements the proposed inspection method is presented. A sample of a flat-layered metamaterial based on SRR elements with a region of negative refraction in the frequency range of 10.06–10.64 GHz was investigated for the numerical and experimental verification of the method. Experimental verification has shown that the local values of the effective electrophysical parameters of the studied metamaterial differ from the calculated ones by no more than 10%.
Similar content being viewed by others
REFERENCES
Veselago, V.G., Electrodynamics of substances with simultaneously negative values of ε and μ, Usp. Fiz. Nauk, 1967, vol. 92, p. 517.
Lagarkov, A.N., Kisel, V.N., Sarychev, A.K., and Semenenko, V.N., Electrophysics and electrodynamics of metamaterials, Teplofiz. Vys. Temp., 2010, vol. 48, no. 6, pp. 1031—1048.
Lagarkov, A.N., Kisel, V.N., Sarychev, A.K., and Semenenko, V.N., Electrophysics and electrodynamics of metamaterials. http://www.itae.ru/science/ topics/No.1%20(metamaterials).pdf. Accessed October 31, 2020.
Vendik, I.B. and Vendik, O.G., Metamaterials and their application in microwaves: A review, Tech. Phys., 2013, vol. 58, no. 1, pp. 1–24.
Gulyaev, Yu.V., Lagarkov, A.N., and Nikitov, S.A., Metamaterials: Fundamental research and application prospects, Herald Russ. Acad. Sci., 2008, vol. 78, no. 5, pp. 438–457.
Slyusar, V., Metamaterials in antenna technology: Basic principles and results, Pervaya Milya, 2010, nos. 3–4, pp. 44–60.
Balabukha, N.P., Bashirin, A.A., and Semenenko, V.N., The effect of backward radiation of electromagnetic waves by a waveguide structure made of metamaterial, JETP Lett., 2009, vol. 89, no. 10, pp. 593–598.
Ming Huang and Jingjing Yang, Microwave Sensor Using Metamaterials, Wave Propagation, Petrin A., Ed., IntechOpen, 2011, print on demand. https://doi.org/10.5772/14459
Mitrokhin, V.N., Ryzhenko, D.S., and Tyagunov, V.A., Experimental studies of microwave devices containing metamaterials, Phys. Wave Process. Radio Eng. Syst., 2011, vol. 14, no. 3, pp. 43–53.
Pendry, J.B., Holden, A.J., Robbins, D.J., and Stewart, W.J., Magnetism from conductors and enhanced nonlinear phenomena, IEEE Trans. Microwave Theory Tech., 1999, vol. 47, no. 11, pp. 2075–2084. https://doi.org/10.1109/22.798002
Ivanova, V.I., et al., Development of a broadband radio-absorbing coating with high performance properties, J. Radio Electron., 2016, no. 7, pp. 1–23.
Simovskiy, K.R., On material parameters of metamaterials (a review), Opt. Spektrosk., 2009, vol. 107, no. 5, pp. 766–793.
Hongsheng Chen, Jingjing Zhang, Yang Bai, Yu Luo, Lixin Ran, Qin Jiang, and Jin Au Kong, Experimental retrieval of the effective parameters of metamaterials based on a waveguide method, Opt. Express, 2006, vol. 14, no. 26, pp. 12944–12949. https://doi.org/10.1364/OE.14.012944
Krupka, J., Derzakowski, K., and Hartnett, J.G., Measurements of the complex permittivity and the complex permeability of low and medium loss isotropic and uniaxially anisotropic metamaterials at microwave frequencies, Meas. Sci. Technol., 2009, vol. 20, no. 10, article ID 105702. https://doi.org/10.1088/0957-0233/20/10/105702
Ran, L., Huangfu, J., Chen, H., Zhang, X., Chen, K., Grzegorczyk, T., and Kong, J., Experimental study on several left-handed metamaterials, Prog. Electromagn. Res., 2005, vol. 51, pp. 249–279. https://doi.org/10.2528/PIER04040502
Zhaofeng Li, Koray Aydin, and Ekmel Ozbay, Determination of the effective constitutive parameters of bianisotropic metamaterials from reflection and transmission coefficients, Phys. Rev. E, 2009, vol. 79, article ID 026610. https://doi.org/10.1103/PhysRevE.79.026610
Smith, D.R., Schultz, S., Markos, P., and Soukoulis, C.M., Determination of effective permittivity and permeability of metamaterials from reflection and transmission coefficients, Phys. Rev. B, 2002, vol. 65, article ID 195104. https://doi.org/10.1103/PhysRevB.65.195104
Smith, D.R., Vier, D.C., Koschny, T., and Soukoulis, C.M., Electromagnetic parameter retrieval from inhomogeneous metamaterials, Phys. Rev. E, 2005, vol. 71, article ID 036617. https://doi.org/10.1103/PhysRevE.71.036617
Shelby, R. A., Smith, D. R., and Schultz, S., Experimental Verification of a Negative Index of Refraction, Science, 2001, vol. 292, no. 5514, pp. 77–79. https://doi.org/10.1126/science.1058847
Ugur Cem Hasar, Joaquim J. Barroso, Cumali Sabah, Yunus Kaya, and Mehmet Ertugrul, Differential uncertainty analysis for evaluating the accuracy of S-parameter retrieval methods for electromagnetic properties of metamaterial slabs, Opt. Express, 2012, vol. 20, no. 27, pp. 29002–29022. https://doi.org/10.1364/OE.20.029002
Smith, D.R., Gollub, J., Mock, J.J., Padilla, W.J., and Schuring, D., Calculation and measurement of bianisotropy in a split ring resonator metamaterial, J. Appl. Phys., 2006, vol. 100, article ID 024507. https://doi.org/10.1063/1.2218033
Islam Sikder Sunbeam, Faruque Mohammad Rashed Iqbal, and Islam Mohammad Tariqul, The design and analysis of a novel split-H-shaped metamaterial for multi-band microwave applications, Materials, 2014, no. 7(7), pp. 4994–5011. https://doi.org/10.3390/ma7074994
Simovski, C., Belov, P.A., and He, S., Backward wave region and negative material parameters of a structure formed by lattices of wires and split-ring resonators, IEEE Trans. Antennas Propag., 2003, vol. 51, pp. 2582–2345. https://doi.org/10.1109/TAP.2003.817554
Nader, E. and Ziolokowski, R. W., Metamaterials. Physics and Engineering Explorations, Nader Engheta, Ed., New York: Wiley, 2006.
Lubkowski, G., Schuhmann, R., and Weiland, T., Extraction of effective metamaterial parameters by parameter fitting of dispersive models, Microwave Opt. Technol. Lett., 2007, vol. 49, no. 2, pp. 285–288. https://doi.org/10.1002/mop.22105
Lagarkov, A.N., Matytsin, S.M., Rozanov, K.N., and Sarychev, A.K., Dielectric properties of fiber-filled composites, J. Appl. Phys., 1998, vol. 84, no. 7, pp. 3806–3814. https://doi.org/10.1063/1.368559
Andreev, M.V., Borul’ko, V.F., and Drobakhin, O.O., On the implementation of the method of quasisolutions in determining the parameters of the layers of dielectric layered structures, Defektoskopiya, 1997, no. 3, pp. 39–53.
Andreev, M.V., Borul’ko, V.F., and Drobakhin, 0.0., Experimental studies of the method of quasisolutions in determining the parameters of the layers of dielectric layered structures, Defektoskopiya, 1997, no. 4, pp. 70–78.
Antropov, O.S. and Drobakhin, O.O., Increase in the resolution of the reflection coefficient Fourier-transform method by spectrum extrapolation based on the method of the minimum duration principle, Russ. J. Nondestr. Test., 2009, vol. 45, no. 5, pp. 347–354.
Walter, C.H., Traveling Wave Antennas, New York: McGraw-Hill, 1965.
Vaganov, R.B., Korshunov, I.P., Korshunova, E.N., and Oleinikov, A.D., Experimental study of the structure of a surface electromagnetic wave in an anisotropically conducting tape, Radiotekh. Elektron., 2013, vol. 58, no. 2, pp. 136–142.
Kaz’min, A.I. and Fedyunin, P.A., Reconstruction of the structure of electrophysical parameters of multilayer dielectric materials and coatings from the frequency dependence of the attenuation coefficient of the field of a surface electromagnetic wave, Izmer. Tekh., 2019, no. 9, pp. 39–45. https://doi.org/10.32446/0368-1025it.2019-9-39-45.
Kaz’min, A.I. and Fedyunin, P.A., Testing for defects in multilayer dielectric materials by the microwave method, Zavod. Lab. Diagn. Mater., 2020, vol. 86, no. 2, pp. 37–43. https://doi.org/10.26896/1028-6861-2020-86-2-37-43
Kaz’min, A.I. and Fedyunin, P.A., Estimating the extent of exfoliation of dielectric and magnetodielectric coatings with surface microwaves, Russ. J. Nondetsr. Test., 2020, vol. 56, no. 9, pp. 727–741. https://doi.org/10.31857/S0130308220090055
Ufimtsev, P.Ya. and Ling, R.T., New results for the properties of TE surface waves in absorbing layers, IEEE Trans. Antennas Propag., 2001, vol. 49, no. 10, pp. 1445–1452. https://doi.org/10.1109/8.954933
Shevchenko, V.V., Basic modes of a symmetric planar waveguide made of metamaterial, Radiotekh. Elektron., 2010, vol. 55, no. 9, pp. 1052–1055.
Manenkov, A.B., Dispersion characteristics of modes of a waveguide made of metamaterial, Radiotekh. Elektron., 2012, vol. 57, no. 9, pp. 968–977.
Mahmoud, S. F. and Viitanen, A. J., Surface wave character on a slab of metamaterial with negative permittivity and permeability, Prog. Electromagn. Res., 2005, vol. 51, pp. 127–137. https://doi.org/10.2528/PIER03102102
Baccarelli, P., Burghignoli, P., Frezza, F, Galli, A., Lampariello, P., Lovat, G., and Paulotto, S., Fundamental modal properties of surface waves on metamaterial grounded slabs, IEEE Trans. Microwave Theory Tech., 2005, vol. 53, no. 4, pp. 1431–1442. https://doi.org/10.1109/TMTT.2005.845208
Felsen, L. and Markowitz, N., Radiation and Scattering of Waves, New York: Wiley–IEEE Press, 1978.
Shu, W. and Song, J.-M., Complete mode spectrum of a grounded dielectric slab with double negative metamaterials, Prog. Electromagn. Res., 2006, vol. 65, pp. 103–123. https://doi.org/10.2528/PIER06081601
Kim Ki Young, Sno Young Ki, Tae Heung-Sik, and Lee Jeong-Hae, Guided mode propagations of grounded double-positive and double-negative metamaterial slabs with arbitrary material indexes, J. Korean Phys. Soc., 2006, vol. 49, no. 2, pp. 577–584.
Shabunin, S., Excitations of space and surface waves by patch and slot antennas, Proc. Eur. Conf. Antennas Propag., 2006. https://doi.org/10.1109/eucap.2006.4585090
Guido, V., Jackson, D.R., and Galli, A., Fundamental properties of surface waves in lossless stratified structures, Proc. R. Soc., 2010, vol. 466, pp. 2447–2469. https://doi.org/10.1098/rspa.2009.0664
Frezza, F. and Tedeschi, N., Electromagnetic inhomogeneous waves at planar boundaries: Tutorial, J. Opt. Soc. Am. A, 2015, vol. 32, no. 8, pp. 1485–1501. https://doi.org/10.1364/JOSAA.32.001485
Brekhovskikh, L.M., Volny v sloistykh sredakh (Waves in Layered Media), Moscow: Nauka, 1973.
Chen Zhuozhu and Shen Zhongxiang, Surface waves propagating on grounded anisotropic dielectric slab, Appl. Sci., 2018, no. 8(1), p. 102. https://doi.rog/10.3390/app8010102
Author information
Authors and Affiliations
Corresponding authors
Rights and permissions
About this article
Cite this article
Kaz’min, A.I., Fedyunin, P.A. Testing Electrophysical Parameters of Metamaterials by the Method of Surface Electromagnetic Waves. Russ J Nondestruct Test 57, 320–336 (2021). https://doi.org/10.1134/S1061830921040070
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S1061830921040070