Abnormal Radiation Pattern of Metamaterial Waveguide

PIERS ONLINE, VOL. 4, NO. 6, 2008 641

A. N. Lagarkov, V. N. Semenenko, A. A. Basharin, and N. P. Balabukha Institute for Theoretical and Applied Electromagnetics of Russian Academy of Sciences (ITAE RAS) Izhorskaya 13, Moscow 125412, Russia

Abstract— The idea to inverse the radiation pattern of the microwave antenna due to appli- cation of the isotropic metamaterial screen with negative refractive index in S band is demonstrated at the ﬁrst time in this investigation. The electromagnetic simulation of waveguide antenna patterns by moment’s methods demonstrates an agreement modeling antenna patterns with measured antenna diagrams for values of metamaterial eﬀective parameters (permittivity and permeability) extracted from measured S-parameters of metamaterial sheet sample.

1. INTRODUCTION The prediction of left handed materials (LHM) by V. G. Veselago in 1967 [1] can be considered as a new stage in the development of electromagnetics of continuous media. Recently a lot of papers [2, 3] related to the artificial magnetoelectric media with anomalous electromagnetic properties have been appeared. Among these papers there are ones on 2-D, 3-D media with the negative permittivity and permeability [4, 5] and, hence, negative refractive index. The abnormal antenna patterns of a rectangular open waveguide loaded by a rectangular cross-section magnetoelectric tube made of the metamaterial with the negative refractive index in S frequency band for different thicknesses of tube are demonstrated at first in this paper.

2. SCHEME OF WAVEGUIDE RADIATOR The geometry of open waveguide loaded by the metamaterial screen having a shape of a rectangular cross-section tube (modiﬁed open waveguide radiator) is shown in Figs. 1–2. A standard coaxial-waveguide adapter of the S-band with the waveguide window of 50 × 25 mm in sizes is used in the measurements of antenna patterns of modiﬁed waveguide radiator.

metamaterial

0 180 0 0

feedline

waveguide

Figure 1: Schematic diagram of the waveguide radi- Figure 2: A view of the waveguide radiator. ation structure.

The metamaterial under investigation is an isotropic 2D lattice made of nichrome spiral wires (helixes) positioned randomly on the polyurethane substrate with 0.2 mm in thickness. To exclude chiral properties of the metamaterial sample is used an identical combination of left- and right handed helixes. The helixes were wound of the 0.4 mm nichrome wire with the number of turns 3 and coil pitch 1 mm. The helix external diameter is 5 mm. In the experiments an isotropic metamaterial sheet sample named as LR-5I (see Fig. 3 — 1/3 part of helixes set is positioned along rectangular coordinate axes of x, y and z respectively) with 5.2 mm in thickness is used. PIERS ONLINE, VOL. 4, NO. 6, 2008 642

A peculiarity of the spiral elements of the metamaterial under investigation consists in revealing of the 3D-isotropic electric and magnetic properties in one and the same frequency band [4]. A helix with the non-zero coil pitch is magnetic and electric dipole simultaneously eﬀectively excited both by the electric and magnetic ﬁelds under the coincidence of their polarization with the helix axis.

30 LR-5I

-10

-20

-30 Phase of Transmission Coefficient, deg -40 2 2.5 3 3.5 4 Frequency, GHz

Figure 3: A view of the metamaterial planar sample Figure 4: Phase of the metamaterial transmission LR-5I. coeﬃcient in dependence on frequency.

The experimental dependence of the phase of metamaterial transmission coefficient in the dependence of frequency with the area of negative values of phase in the vicinity of frequency of 3 GHz corresponding to the negative refractive index is demonstrated in Fig. 4. Extracting values of effective material parameters of the metamaterial sheet sample recalculated by the Fresnel’s formulae from the S-parameters values (complex reflection and transmission coefficients) are presented in Fig. 5. The measurements of metamaterial S-parameters are performed on R&S Vector Network Analyzer ZVA-24 with the time domain option and special calibration procedure and using wide-band horn antenna.

9 4.0 8 ε' 3.5 7 ε'' 3.0 µ' 6 2.5 µ'' 5 2.0 4 1.5 3 1.0 2 0.5 1 0.0 0 -0.5 -1 -1.0 -2 -1.5

2.02.5 3.03.5 4.0 2.02.5 3.03.5 4.0 Frequency, GHz Frequency, GH z

Figure 5: The eﬀective permittivity and permeability of metamaterial LR-5I in dependence on frequency.

3. THE ANTENNA PATTERNS OF WAVEGUIDE RADIATOR LOADED BY METAMATERIAL Based upon the numerical estimations of antenna patterns by the Method of moments (thin red lines) and experimental antenna patterns (thick black lines) for the waveguide radiator obtained in the anechoic chamber are presented in Figs. 6–11. The antenna diagrams are performed at the PIERS ONLINE, VOL. 4, NO. 6, 2008 643 frequencies closed to the metamaterial resonance frequency which is equal to 3 GHz. An oppor- tunity of obtaining a reversed antenna patterns for waveguide antenna structure loaded by the metamaterial tube had been shown at these diagrams (in Figs. 6–11 normalized antenna patterns is represented).

0 0 0 0 330 30 330 30 -5 -5 -10 -10 300 60 300 60 -15

-15 -20 -25 -20 270 90 270 90 -25 -15 -20 -15 -10 240 120 240 120 -10 -5 -5 210 150 210 150 0 0 180 180

Figure 6: The antenna patterns of a waveguide ra- Figure 7: The antenna patterns of a waveguide radiator at the frequency 3.1 GHz. diator loaded by the metamaterial tube (d = 5 mm) at the frequency 3.1 GHz.

0 0 0 0 30 330 30 330 -5 -5 10 10 300 60 15 300 60 15 20 20 25 30 25 270 90 270 90 30 20 25 15 20 240 120 120 10 15 240 10 -5 -5 210 150 150 0 0 210 180 180

Figure 8: The antenna patterns of a waveguide radi- Figure 9: The antenna patterns of a waveguide radiator loaded by the metamaterial tube (d = 10 mm) ator loaded by the metamaterial tube (d = 20 mm) at the frequency 3.1 GHz. at the frequency 3.1 GHz.

For a waveguide radiator loaded by the LR-5I metamaterial tube with the wall thickness d = 5 mm and length L = 150 mm there is a growing of the backside antenna lobe in comparison with the main antenna lobe. The difference between levels of the main and back directional lobes is approximately equal to 2 dB. With the increasing of the tube wall thickness d, there is an abnormal antenna pattern diagram when the backside directional lobe exceeds the main one more than by 20 dB. In this case the waveguide structure radiates mainly in the backside direction of “180 deg”. This effectp is observed only in the case when the metamaterial reveals negative refractive index of n = (ε0 + iε00)(µ0 + iµ00). To prove this fact in Fig. 11 an antenna pattern of the waveguide structure with the metamaterial PIERS ONLINE, VOL. 4, NO. 6, 2008 644 tube screen at the frequency of 4 GHz is presented. At this frequency refractive index of metamaterial is n > 0. The antenna pattern at this frequency has an ordinary form of diagram where the main directional lobe exceeds the backside lobe and the radiation occurs mainly in the front direction “0 deg”. The physical nature of this effect may be explained by the refraction of the electromagnetic waves at the boundary (air/metamaterial tube) inside waveguide structure. At this boundary the surface waves are excited and propagated in an opposite direction towards the spatial wave propagation in the waveguide structure.

0 0 0 0 330 30 330 30 -5 -5 -10 -10 -15 60 60 -20 300 -15 300 -25 -20 -30 -35 -25 -40 270 90 -30 270 90 -35 -25 -30 -25 -20 -20 -15 - 240 120 240 120 15 -10 -10 -5 -5 210 150 210 150 0 0 180 180

Figure 10: The antenna patterns of a waveguide ra- Figure 11: The antenna patterns of a waveguide radiator loaded by the metamaterial tube (d = 30 mm) diator loaded by the metamaterial tube (d = 20 mm) at the frequency 3.1 GHz. at the frequency 4 GHz.

4. CONCLUSIONS Therefore, at the frequencies, at which a metamaterial possess negative refractive index n < 0, and the metamaterial tube thickness exceed 5 mm, and abnormal antenna pattern diagram of waveguide structure with the maximal radiation in the backside direction (<>) are observed. At the frequencies, at which n > 0, the antenna patterns present ordinary diagrams with the maximal radiation in the front direction for any metamaterial tube thickness.

REFERENCES 1. Veselago, V. G., “The electrodynamics of substances with simultaneously negative values of ε and µ,” Sov. Phys. Usp., Vol. 10, 509–514, 1968. 2. Caloz, C. and T. Itoh, Electromagnetic Metamaterials: Transmission Line Theory and Mi- crowave Applications, John Wiley & Sons, Inc., 2006. 3. Lagarkov, A. N., V. N. Semenenko, D. E. Ryabov, S. A. Tretyakov, and C. R. Simovski, “Resonance properties of bi-helix media at microwaves,” Electromagnetics, Vol. 17, No. 3, 213–237, 1997. 4. Lagarkov, A. N., V. N. Semenenko, V. N. Kisel, and V. A. Chistyaev, “Development and simulation of microwave artiﬁcial magnetic composites utilizing nonmagnetic inclusion,” Journal of Magnetism and Magnetic Materials, Vol. 258–259, 161–166, 2003. 5. Lagarkov, A. N. and V. N. Kissel, “Near-perfect imaging in a focusing system based on a left-handed-material plate,” Phys. Rev. Lett., Vol. 92, 077401, 2004.