Radiation Properties of Metamaterials in Millimeter Wavelength Region

G. Naumenko, A. Potylitsyn, M. Shevelev , V. Soboleva, V. Bleko Tomsk Polytechnic University, 30, Lenin Avenue, Tomsk, 634050, Russia

naumenko@tpu.ru

We propose and demonstrate a type of composite metamaterials, which is constructed by combining thin copper wires and split ring resonators on the same board. Using the optimized target parameters we had investigated the orientation-angular dependence of radiation refraction in metamaterial target. The measurements were performed in free space as well, as the spectral characteristics of refracted radiation in comparison with the initial spectra. The measured dependences show the formal correspondence of the radiation characteristics to the negative refraction index of the metamaterial structures. This correspondence is only formal one, which follows from the Snellius law, because really the permittivity and the permeability should be considered as macroscopic tensor characteristics of metamaterial.

Keywords-metamaterial; refraction; negative index;

I. INTRODUCTION Last years, the metamaterials have inspired a great interest

due to their unique physical properties and novel applications of these materials [1,2]. In usual materials the permittivity and magnetic permeability are positive. Nevertheless for some artificial structures both the permittivity and the magnetic permeability may be of negative values. This leads to the phenomenon, when the phase and group velocity of electromagnetic waves can be directed in opposite directions. Such metamaterials are named often “double negative materials” or “left-handed materials”. This leads to the number of interesting properties of such materials [3]. In 1968, Veselago proved the possibility of the existence of physical media with negative refractive index [4]. Later this idea was developed by other authors in frame of macroscopic electrodynamics [5-8].

The negative permittivity and the magnetic permeability for a frequency being close to the resonance may be realized by creation of the area of the circle resonators with gaps [9]. Using combination of these resonators with thin strips the properties of left-handed materials were demonstrated in [10,11]. Later, the analytical development of such materials, simulation and estimation of the scalar values of the refracting index were performed [12,13]. The experimental measurements were carried out using wavequid chamber with the metamaterial structure in the output [14]. The disadvantage of this approach is the problem of coupling of surface waves in a waveguide with the propagation of waves in the structure of the metamaterial. In [15] was considered the interaction of

radiation with meta materials in free space. This approach is free on the limitations on the size and orientation of the target in space. However, in this paper were considered only the coefficients of transmission of radiation through the structure and did not considered the refraction of radiation.

Let’s note, that in the interaction of radiation with metamaterials the principle of similarity is valid, when the similarity criterion is the relationship of geometric characteristics of the metamaterial structure to the radiation wavelength. Therefore, the results obtained in the optical range can be used, for example, in the millimeter wavelength range, and vice versa. On the other hand, the modification of the structure of metamaterials during the study is easier and cheaper to perform in the millimeter range. This determined the choice of the spectral range of our research.

II. EXPERIMENT From the available experimental results [9,10,11,16], the

effect of a negative refractive index is better seen when an array of double frames with gaps and narrow strips along these gaps are used [16]. These structures we had choose for a detailed investigation of their radiation characteristics (Fig. 1).

Figure 1. The unit cell of the metamaterial.

As follows from the theory of similarity [18], the main effect in the spectral dependence is observed when the ratio of wavelength to the size of the unit cell is of order unity. For the measurements the target was prepared in the form of a prism (Fig. 2), the base of which is a right triangle with acute angle of 42 degree and cells period is 12 mm. The above-mentioned structure was realized by a coating of a copper on the plastic

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substrate of thickness 0.5 mm with a geometric relations c = b = 0.05a, where a=12 mm (see Fig. 1). The period of alternation of flat structures is 10 mm.

Figure 2. The appearance of the target metamaterial

Using this target in the scheme presented in Fig. 3, the refractive indexes of the radiation in the plane of orientation angles of the target and observation angles were investigated.

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Figure 3. Scheme for measuring the angular and orientational characteristics of refracted radiation.

E used the parallel beam, formed by a parabolic mirror with the radiation source, placed in the focus of the mirror. To eliminate the effect of the wave zone, radiation was detected using a parabolic telescope, i.e. the registered angular distribution is similar to a distribution, registered at the infinite distance. The source of radiation ensures the generation of radiation with a wavelength of 9.2 mm. and 29 mm. with the possibility of changing the ratio of the intensities of these lines.

As a result of these investigations in the plane of , were found areas in which the refraction of radiation may be interpreted as a refraction with a positive refraction index, and the areas with the refraction with a negative refraction index.

Within these areas, we measured the interferograms using an interferometer with separation of the radiation flux at the two reflecting plates (see Fig. 4).

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Figure 4. Interferometer for spectra measurement.

Using the inverse Fourier transforms of interferograms (see [19]), the radiation spectra were calculated. In Fig. 5 and Fig. 6 the sample of interferogram of incident radiation and the spectrum recovered from this interferogram are shown.

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Figure 5. The sample of interferogram of incident radiation

Below we present three, in our opinion the most typical areas, with both the positive and the negative refractive index.

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Figure 6. The spectrum recovered from the interferogram shown in Fig. 5

The area with the positive index of refraction is observed in a geometry shown in Fig. 7.

Figure 7. The refraction geometry of number 1.

The distribution of radiation intensity in this area is shown in Fig. 8. It is clear that the dielectric constant and magnetic permeability, and, hence, the refractive index of metamaterial is not scalar. However, in a rough approximation, as is done in [20], we may to estimate the refractive index, assuming the applicability of Snell's law.

For this geometry the estimation gives the positive value of the refractive index n = 1.64 like for a conventional material. One can note that the intensity distribution in the plane of the angles , has a local character. For comparison, in Fig. 9 the intensity distribution of radiation, which is refracted in the similar Teflon target with a refractive index n = 1.34, is shown.

Figure 8. The distribution of radiation intensity in the plane of observation angle and orientation angle in

geometry of number 1.

Figure 9. The intensity distribution of radiation which is refracted in the Teflon target.

The spectrum of the incident radiation and the spectrum of refracted radiation from the target from metamaterial in geometry of number 1 is shown in Fig. 10.

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Figure 10. The spectrum of the incident radiation (gray line) and the spectrum of refracted radiation (black line) in geometry of number 1

It is noteworthy that in this geometry, the spectrum of the refracted radiation is not very different from that of the incident radiation.

Quite different behavior is observed in the geometry of number 2 shown in Fig. 11.

Figure 11. The refraction geometry of number 2

In this case, the correlation of the observation angle and the angle of the target is expressed more clearly (Fig.12), although it does not have the character of the specular reflection.

Figure 12. The distribution of radiation intensity in the plane of observation angle and orientation angle in geometry of

number 2.

It is noteworthy that in this range of angles the estimation of the refractive index has a negative value n = -0.5. In addition, by comparing the spectrum of the source (Fig. 13) and the refracted light (Fig. 14), we see that the line

29 mm is almost completely suppressed, and only the radiation with a wavelength smaller than the size of cells is refracted.

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Figure 13. The spectrum of the incident radiation (gray line) and the spectrum of refracted radiation (black line) in geometry of number 2.

The most interesting, in our opinion, is the geometry of the number 3, presented in Fig. 14.

Figure 14. The refraction geometry of number 3

In this geometry, the intensity distribution over the angles is multimodal (Fig.15), the refractive index is negative (n = -1.45) and the radiation is refracted in the backward half-sphere.

Figure 15. The distribution of radiation intensity in the plane of observation angle and orientation angle in geometry of

number 3.

It is noteworthy that the spectral characteristics of the refracted radiation are quite different from previous ones. Despite the fact, that for a contrast we have suppressed the intensity of the long-wavelength components ( 29 mm) of the radiation source, in the spectrum of the refracted radiation this line is basic, but the hard component is completely suppressed (see Fig. 16).

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Figure 16. The spectrum of the incident radiation (gray line) and the spectrum of refracted radiation (black line) in geometry of number 3.

Analysis of the results shows that the behavior of the radiation in the metamaterials is complex. This is due to the fact that the optical properties of metamaterials can no longer be considered in terms of scalar electrodynamics characteristics of the target material. On the other hand, although electrodynamics based on integral tensor parameters of the medium is well developed [21], a theory that relates the parameters of the structures of metamaterials with tensor permittivity and permeability, has not properly developed.

ACKNOWLEDGMENT This work was supported in part by the Ministry of

Education and Science under the Federal Program “Scientific and scientific-pedagogical personnel of innovative Russia'' and the Federal Target Scientific and Technical program number 0.326.2012.

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