IEEE JOURNAL OF SELECTED TOPICS IN QUANTUM ELECTRONICS, VOL. 21, NO. 4, JULY/AUGUST 2015 4700211 Reference-Plane-Invariant Effective Thickness and Electromagnetic Property Determination of Isotropic Metamaterials Involving Boundary Effects Ugur Cem Hasar, Joaquim Jos´ e Barroso, Member, IEEE, Gul Buldu, Musa Bute, Student Member, IEEE, Yunus Kaya, Tevhit Karacali, and Mehmet Ertugrul Abstract—It is well recognized that near-field effects become dominant when the metamaterial (MM) is in resonance. In ad- dition, any inaccurate information of the location of reference planes, and the effective length can seriously affect the accuracy of retrieved electromagnetic properties of MMs. By considering all these issues, in this research paper, we propose a retrieval method for reference-plane invariant and thickness-independent determination of electromagnetic parameters of MM slabs involv- ing boundary effects. Our method first accomplishes determina- tion of effective length of MMs and calibration-plane factors using scattering parameter measurements, aside the resonance region, of two identical MMs with different lengths. Our method then incor- porates near-field effects in accurate retrieval of electromagnetic properties of MMs. The method is verified by scattering param- eters simulated for a homogeneous conventional material and a weakly or negligibly coupled inhomogeneous MM slab made by two metallic concentric split-ring-resonators. Consequences of an inaccurate information of reference-plane transformation factors and the value of effective lengths and of noninclusion of near field effects on the retrieved electromagnetic properties are thoroughly discussed by way of few examples to substantiate the accuracy of the proposed method. Index Terms—Reference-plane invariant, thickness- independent, boundary effects, metamaterials. I. INTRODUCTION E LECTROMAGNETIC characterization of materials is a paramount need in analyses of various components, Manuscript received May 12, 2014; revised August 2, 2014; accepted Septem- ber 11, 2014. This work was supported by the Scientific and Technological Research Council of Turkey (TUBITAK) under Project Grant 112R032. U. C. Hasar is with the Department of Electrical and Electronics Engineering, University of Gaziantep, 27310 Gaziantep, Turkey, and also with the Center for Research and Application of Nanoscience and Nanoengineering, Ataturk University, 25240 Erzurum, Turkey (e-mail: uchasar@gantep.edu.tr). J. J. Barroso is with the Associated Plasma Laboratory, National Institute for Space Research, 12227-010 S˜ ao Jos´ e dos Campos, Brazil (e-mail: barroso@ plasma.inpe.br). G. Buldu and M. Bute are with the Department of Electrical and Electron- ics Engineering, University of Gaziantep, 27310 Gaziantep, Turkey (e-mail: gulbuldu@gmail.com; mbute@gantep.edu.tr). Y. Kaya is with the Department of Electricity and Energy, Bayburt University, 69000 Bayburt, Turkey (e-mail: ykaya@bayburt.edu.tr). T. Karacali and M. Ertugrul are with the Department of Electrical and Elec- tronics Engineering, Center for Research and Application of Nanoscience and Nanoengineering, Ataturk University, 25240 Erzurum, Turkey (e-mail: tevhit@ atauni.edu.tr; ertugrul@atauni.edu.tr). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/JSTQE.2014.2358565 structures, and applications. In recent years, artificial electro- magnetic materials, coined metamaterials (MMs), have attracted a huge interest due to their promising and conventionally- unattainable applications including perfect lenses [1], invisi- bility cloaks [2], sensors [3], absorbers [4], [5], tunable devices [6], [7], and antenna directivity enhancement [8], [9]. Accurate extraction of electromagnetic properties of MM slabs is very important because it allows the potential features of MMs to be incorporated into a design [10]. There are few differ- ent techniques for characterization of electromagnetic properties of MMs such as the qualitative effective medium theory [11], the technique using averaging of fields [12], the homogenization technique [13], and the technique based on measured/simulated scattering (S-) parameters [14]–[21]. Among these techniques, the latter one is suitable for both a numerical analysis and measurements as well as for an investigation of complex MM structures. Electromagnetic properties of MM slabs are generally de- scribed by effective electromagnetic properties [impedance (z), refractive index (n), relative permittivity (ε r ), and relative per- meability (μ r )] from S-parameters as a consequence of homoge- nization process (continuous medium) when both the size of the composite particles and the period of lattices are made smaller than the wavelength at the particle resonance. However, these properties do not completely reflect the behavior of homoge- nized MM slabs [22]. First, retrieved parameters can be depen- dent upon material thickness and surrounding environment [23]. Second, these parameters are not compatible with passivity and causality principles of MM slabs [24]. Finally, imaginary parts of these parameters are non-zero in the absence of a real dis- sipation [22]. All these discrepancies come from the effect of near fields both inside and at the boundaries of MM slabs due to higher-order Bloch modes and localized fields (microstruc- tures of MM slabs) [22]. They can be remedied by introduction of transition layers [25] or additional bulk effective parameters [26]. These approaches can both be equivalently analyzed by excess surface currents over MM slab boundaries [10], [22]. In particular, Dr. Kuester and Dr. Baker-Jarvis pointed out that near the resonance region of MM slabs, macroscopic proper- ties of MM slabs cannot be anymore directly related to electric and magnetic fields, but their averaged values through electric and magnetic susceptibilities [10], [27], [28]. They also demon- strated that due to these susceptibilities, (semi-infinite) reflection 1077-260X © 2014 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. 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