"JOURNAL OF RADIO ELECTRONICS" (Zhurnal Radioelektroniki ISSN 1684-1719, N 9, 2017

contents             full textpdf   

Electromagnetic crystals with a negative refractive index

A. A. Fediy, D. A. Kalganov, I. V. Bychkov, A. V. Reshetov

Chelyabinsk State University, Faculty of Physics,  Br. Kashirinykh, 129, Chelyabinsk 454001, Russia


The paper is received on July 7, 2017


Abstract. Metamaterials with a negative refractive index contain, generally, two types of elements: long conductors (wires) and inductive–capacitive resonators (miniature split rings). The system of ring resonators causes a delay of propagation of electromagnetic waves in the metamaterial. This is due to the phase shift in the high frequency region of the amplitude-frequency characteristic (AFC) of the resonators. We used half-wave vibrators in our metamaterial samples instead of ring resonators. The measurements were carried out in a free-space using standard horn antennas in the frequency range 8 – 12 GHz. It has been shown experimentally that the vibrator array used in the metamaterial sample has a wide bandgap (9,3 – 11,0 GHz) located below the resonance frequency of individual vibrators (11,0 GHz). Consequently, for the investigated samples in the low-frequency region of the forbidden band for vibrators, the condition l/λ<0.5, where l is the length of the vibrator, and λ is the wavelength of the electromagnetic radiation, is valid. From the theory of vibrator antenna arrays, the characteristics of which  have been studied and described in detail in numerous monographs, it is known that in this case a parallel resonance is observed. The phase shift will be the same as for ring resonators in the high-frequency region of the AFC, and at these frequencies, the signal delay will lead to the negative value of the effective magnetic permeability. Angular dependence measurements of the electromagnetic waves transmission through the prism of the metamaterial with vibrators showed that negative refraction is observed at frequencies of 9,2 – 9,5 GHz, which corresponds to the low-frequency region of the frequency response of the vibrator array. Effective value of the refractive index for the studied metamaterial was n = - 1,37±0,06.

Keywords: metamaterials, electromagnetic crystal, negative refraction, vibrator.


1.   Veselago V.G. The electrodynamics of substances with simultaneously negative values ε and µ. Sov. Phys. Usp. 1967.  T. 92. No 3.  pp. 517-526

2.   Hardy, Whitehead. Resonator of the split ring type for the investigation of magnetic resonance in the range 200 ... 2000 MHz.  Scientific research instruments. 1981. No 2. pp. 64-68.

3.   D.R. Smith et.al. Composite medium with simultaneously negative permeability and permittivity.  Phys. Rev. Lett.  2000.  Vol. 84.  No. 18. pp. 4184-4187.

4    J.B. Pendry, A.J. Holden, D.J. Robbins, W.J. Stewart Magnetism from conductors and enhanced nonlinear phenomena. IEE Trans. Microwave Theory Tech.  1999.  Vol. 47.  No. 11. pp. 2075-2084.

5.   G. Dolling, C. Enkrich, M. Wegener, J. Zhou, C.M. Soukoulis, S. Linden Cut-wire pairs and plat pairs as magnetic atoms for optical metamaterials. Opt. Lett.  2005.  Vol. 30.  No. 23.  pp. 3198-3200.

6.   O.D. Volpyan, A.I. Kuzmichev. Otritsatel'noe prelomlenie voln. Vvedenie v fiziku i tekhnologiyu elektromagnitnykh materialov. [Negative refraction of waves. Introduction to the physics and technology of electromagnetic materials.]  Edited by G.M. Zverev.  Kiev-Moscow, Avers Publ., 2012.  360 p. (In Russian)

7.   D.I. Voskresensky, V.L. Gostyukhin, V.M. Maksimov, L.I. Ponomarev. Ustroistva SVCh i antenny.  [Microwave devices and antennas]. Edited by D.I. Voskresenskiy, 2-nd ext. ed., Moscow, Radio engineering Publ, 2006. 376 p. (In Russian).

8.   G.S. Gorelik. Kolebaniya i volny. [Oscillations and waves]. Edited by S.M. Rytov. Moscow, Fizmatlit Publ., 2007.  656 p. (In Russian)

9.   P.A. Belov, S.A. Tretyakov, A.J., Viitanen. J. Dispersion and reflection properties of artificial media formed by regular lattices of ideally conducting wires,  Waves and Appl. 2003. Vol.16. ą 8, pp. 1153-1170.

10. S. E. Bankov. Elektromagnitnye kristally. [Electromagnetic crystals].  Moscow, Fizmatlit Publ., 2010. 352 p. (In Russian)


For citation:

A. A. Fediy, D. A. Kalganov, I. V. Bychkov, A. V. Reshetov. Electromagnetic crystals with a negative refractive index. Zhurnal Radioelektroniki - Journal of Radio Electronics, 2017, No. 9. Available at http://jre.cplire.ru/jre/sep17/4/text.pdf. (In Russian)