JOURNAL OF TELECOMMUNICATIONS, VOLUME 3, ISSUE 2, JULY 2010 45

Periodically Loaded Rectangular Waveguide with FSS Strip Layer Supporting Wideband Backward Wave A.Akbarzadeh-Jahromi, M.Tayarani, and M.Khalaj-Amirhosseini Abstract— In this paper, a negative refractive index guided-wave structure is realized using a rectangular waveguide loaded with H-shaped frequency selective surface (FSS) strip layer. This new structure shows wideband double negative (DNG) and backward wave properties. Indeed these properties can be controlled well over wide frequency range with control of physical dimension of the structure. Using the FSS, two wideband band-pass filter proposed which are inexpensive to fabricate due to using printed layer which are ideal for mass production. Index Terms— Double negative metamaterial, FSS, Metamaterial, Waveguide bandpass filter.

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1 INTRODUCTION

W

ith the recent resurgence of interest in Metamaterials (MTMs) and the reported construction of a metamaterial with both negative permittivity and permeability (DNG) characteristics, applications of these materials become feasible, and examination of the behavior of systems and devices becomes a potentially fruitful topic. These materials, were studied by Veselago theoretically, he referred them to as "Left-Handed (LH)" medium due to their peculiar characteristics they exhibit [1]. Since such materials were not available until recently, the interesting concept of negative refraction, and its various electromagnetic consequences, suggested by Veselago had received little attention. Synthesis of physically realizable medium or transmission line has raised a great deal of interest in recent years. Most of these proposed Metamaterials (MTMs) are composite materials which are formed by embedding inclusions and material components in host media. These artificial materials firstly reported by Pendry et al. [2] and Smith et al. [3] by arranging periodic arrays of small metallic wires and using split-ring resonators, respectively. Among all guided-wave structures, waveguides are characterized by their low losses, high power handling capability, and absence of leakage and other extraneous phenomena due to their closed geometries. Waveguides exhibiting left handed negative refraction properties have been realized using insertions having printed split-ring resonators [4] or cascaded crossed strips [5] or arranging periodic arrays of small metallic wires

(a)

(b) Fig.1. (a) Geometry of an infinite periodic waveguide structure loaded with double H-shaped FSS strip layer. (b) The dimension of the H-shaped FSS which is etched on a double-sided substrate.

[2]. Also, waveguides with dielectric-filled transverse corrugations were proposed in [6]. In [7] the periodic waveguide structures loaded with cross shape FSS strip layers lead to interesting backward wave propagation. In this paper, we proposed a double H-shaped FSS strip layer which exhibits double negative phenomena over wide frequency region indeed this property can be ———————————————— controlled well over wide frequency range with control of • A.Akbarzadeh-Jahromi is with the Electrical Engineering Department, Iran physical dimension of the structure. The guided wave University of Science and Technology UniversityTehran, Iran. • M.Tayarani is with the Electrical Engineering Department, Iran Universi- properties of the structure extracted through the study of per unit parameters of the structure. Finally, two bandty of Science and Technology UniversityTehran, Iran. • M.Khalaj-Amirhosseini is with the Electrical Engineering Department, pass filters in both single mode band and beyond that of the hollow waveguide are proposed. Iran University of Science and Technology UniversityTehran, Iran © 2010 JOT http://sites.google.com/site/journaloftelecommunications/

JOURNAL OF TELECOMMUNICATIONS, VOLUME 3, ISSUE 2, JULY 2010 46 5

4 3.5 3 2.5 2 1.5 1

2 THEORY

width of waveguide is a and the height is b . Here, WR90 waveguide is used with a = 22.86 mm and b = 10.16 mm . Fig.1 (b) depicts the cross section of the proposed structure and its parameters are specified by L1 , L2 , W1 , and W2 . In this case, to deal with the ideal infinite-periodic structure, the structure can be modeled by one dimensional guided-wave structure. Therefore, it is just needed to extract per-unit length parameters which can be simply achieved through analyzing a single cell of the structure [7], [8]. It is worth to note that this analysis is valid till adjacent cells have no mutual coupling. Under this assumption, the guided wave medium is modeled in terms of equivalent wave impedance Ze = Zer + jZei and the equivalent phase propagation constant γ e = α e + j β e . The structures have been simulated with the commercial software Ansoft HFSS (based on finite element method). After extracting scattering parameters of the single cell, one can convert them to two-port ABCD parameters. After that, using ABCD matrix elements, i.e. A, B, C and D, the derivation of effective medium parameter can be done explicitly as follows:

A+D ) 2

(1)

B (2) C We set the parameters of geometry as: L2 = 7 mm , Ze = Zer + jZei =

W1 = 3 mm and W2 = 2 mm and these parameters are kept fixed in all simulation, whereas L1 is varied from

L1 = 8,14

and 17 mm . Each FSS is supported by a

dielectric of the relative permittivity ε r = 10 and the thickness of h = 0.5 mm .

3 EXTRACTION OF GUIDED-WAVE PARAMETERS In this section, we extract some of the guided-wave proerties based on the theory which has been presented

0.5 0 0.6

0.8

1

1.2 1.4 Frequency

Fig.2. Normalized phase constant ( β

1.6

1.8

2 x 10

10

/ k 0 ), for various FSS arm

( L1 ) dimension. Increasing the length of arm push the pass band to lower frequency. 6

Real part of normalized wave impedance

Fig.1 (a) illustrates three dimensional (3-D) geometry of rectangular waveguide loaded with double H-shaped (dumbbell-shaped) strips etched on both side of dielectric layer. The proposed double H-shaped FSS placed transversely in the waveguide and cascaded periodically with the period of p inside a rectangular waveguide. The

γ e = α e + j β e = cosh −1(

L1=8 mm L1=14 mm L1=17 mm

4.5

Normalized phase constant

Potential applications of this type of technology can be of interest according to the very compact longitudinal size of the structures achieved. Compactness of the devices is, in turn, based on a sub-wavelength operation regime, as compared with classic cavities. Also, the motivation of this paper for proposing filters using this FSS is that resulting filters are inexpensive to fabricate because the building block (printed layer) is ideal for mass production.

L1=8 mm L1=14 mm L1=17 mm

5

4

3

2

1

0 0.6

0.8

1

1.2 1.4 Frequency

1.6

1.8

Fig.3. Real part of normalized wave impedance Z er

2 10

x 10

/ Z 0 for

various FSS arm ( L1 ) dimension

in the previous section.

3.1 Brillouin Diagram Following many early works for analyzing periodically loaded structure [7], [9] brillouin diagram is extracted. Fig.2 shows k0 − β diagrams for this structure. Besides, it can be observed that the guided-wave propagates in the form of backward wave [10] in the passband, in which the phase velocity ω β > 0 is opposite or anti-phase to its corresponding

group

velocity ∂ ω ∂β < 0 .

As

a

consequence, the periodic structure loaded with double H-shaped FSS exhibits negative refractive index metamaterials (NRIM) in a wide frequency band. Also, as it may be concluded from the diagram there exist both slow-wave ( β k0 < 1 ) and fast wave ( β k0 > 1 ) behaviors. As it can be inferred from Fig.2, increasing the arm length decreases the passband frequency.

3.2 Wave Impedance Fig.3 depicts real part of the real part of normalized wave impedance ( Zer Z0 < 1 ). It can be noticed that in the

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the waveguide structure loaded with closely spaced H-shaped FSS layers calculated using (3) and (4) are plotted in Fig. 4 and Fig.5 for different arm length ( L1 ).

600 L1= 8 mm L1= 14 mm L1= 17 mm

500 400

The effective permittivity and permeability for L1 = 17 mm are both negative in the frequency region

Effective permittivity

300 200

from 10.75 to 12.5 GHz and for L1 = 14 mm from 11.5 to 13.75 GHz and for L1 = 8 mm from 14.75 to 17.5 GHz. In

100 0

all three cases the region is bounded by effective permeability. The wide band DNG properties achieved in the waveguide structure and one can easily controlled the DNG region with one physical parameter.

-100 -200 -300 -400 0.6

0.8

1

1.2 1.4 Frequency

1.6

1.8

2 10

x 10

Fig.4. Effective relative permittivity 40 L1= 8 mm L1= 14 mm L1= 17 mm

30

4.2 Waveguide Filter Waveguide filters are extensively studied in literature [12],[13]. In this part, a low cost and easily fabricated bandpass filter is proposed using the H-shaped FSS layers. These structures are very suitable for mass production. As we explain in previous section, we can use the FSS printed layer in their pass band region as 0

10

-10

-20

-30 0.6

0.8

1

1.2 1.4 Frequency

1.6

1.8

2 x 10

10

Fig.5. Effective relative permeability

major part of the passband for each case, Zer Z0 decreases slowly to zero except for the sharply decrease in the start of the passband.We can also infer that in the major passband the wave impedance of this periodic structure have slight slope with the frequency so that we can employ this periodic structure with finite periodic and with the two waveguide feeders as a waveguide bandpass filter.

4 APPLICATION 4.1 Novel Waveguide Based Metamaterial As we describe in pervious section, such waveguide structures loaded with FSS strip layers can be perceived as an equivalent uniform waveguide of characteristic wave impedance Ze and phase constant β e .In this way, we can employ the formulas developed in [8],[11] to extract the above-described material parameters of this artificial medium from the elements of the ABCD matrix. C ε= (3) j ωε0 pA

µ=

B j ωµ0 pA

(4)

The extracted relative permittivity and permeability of

Magnitude of scattering parameter(dB)

-5 0

-10 -15 -20 -25 -30 -35 -40 6

|S11|(dB) |S21|(dB) 8

10

12 14 Frequency(GHz)

16

18

20

Fig.6. Scattering parameters of the three-layer bandpass filter. L1 = 14mm , p = 9.5mm 0 -10 Magnitude of scattering parameter

Effective permeability

20

-20 -30 -40 -50 -60 -70 -80 -90 6

|S11|(dB) |S21|(dB) 8

10

12 14 Frequency(GHz)

16

18

20

Fig.7. Scattering parameters of the three-layer bandpass filter. L1 = 8mm , p = 8mm

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waveguide filter. Here we design two wideband bandpass filter, one in the single mode operation of the WR90 from 8 GHz to 10.3 GHz and the other one from 10.8 GHz to 13.8 GHz. In design we use three cells of printed H-shaped FSS layer. It is worth to say that to get better filter property we increase the unit cell length, therefore, (3) and (4) are not valid. Althogh the spacing between cells are not small compared with a wavelength but as can be seen in some paper such as [14], a structure might works even though the above constraints are not quite satisfied [14],[15]. The parameter of design are L2 = 7 mm , W1 = 3 mm and W2 = 2 mm for both filter .for the latter we choose L1 = 8 mm , and p = 8 mm and select L1 = 14 mm , and p = 9.5 mm for the former. Fig.6 and Fig.7 show the results of simulations for these filters.

5

CONCLUSION

In this paper, an H-shaped strip layer has been used to load a rectangular waveguide periodically for realizing a wideband DNG transmission line. It has been shown that the DNG frequency region has been controlled using just one parameter. In addition, two bandpass filters have been also proposed using this structure which is suitable for low cost mass fabrication.

REFERENCES [1] V. G. Veselago, “The electrodynamics of substances with simultaneously negative values of ε and µ ,” Sov. Phys.—Usp., vol. 47, pp. 509–514, Jan.–Feb. 1968. J. B. Pendry, J. A. Holden, J. D. Robbins, and J. W. Stewart, “Low frequency plasmons in thin-wire structures,” J. Phys. Condensed Matter , vol. 10, pp. 4785–4809, 1998. [3] A. Shelby, D. R. Smith, and S. Schultz, “Experimental verification of a negative index of refraction,” Science, vol. 292, pp. 77– 79, Apr. 2001. [4] S. Hrabar, J. Bartolic and Z. Sipus, “Waveguide miniaturization using uniaxial negative permeability metamaterial”, IEEE Trans. Antennas Propag., vol. 53, no. 1, pp. 110–119, Jun. 2005. [5] J. Esteban, C. Camacho-Penalosa, J.E. Page, T.M. MartinGuerrero, and E. Marquez-Segura, “Simulation of negative permittivity and negative permeability by means of evanescent waveguide modes - theory and experiment,” IEEE Trans. Microw. Theory Tech., vol. 53, no. 4, pp. 1506–1514, Apr. 2005. [6] I.A. Eshrah, A.A. Kishk, A.B. Yakovlev and A.W. Glisson, “Rectangular waveguide with dielectric-filled corrugations supporting backward waves,” IEEE Trans. Microw. Theory Tech., vol 53, no.11, pp. 3298–3304, Nov. 2005 [7] R. E. Collin, “Chapter 9: periodic structures,” in Field Theory of Guided Waves, 2nd ed. New York: IEEE Press, 1991. [8] R. S. Kshetrimayum and L. Zhu, “Guided-wave characteristics of waveguide based periodic structures loaded with various FSS strip layers,” IEEE Trans Antennas Propag, vol. 53, no. 1, pp. 120–124, Jan. 2005. [9] A. A. Oliner, “Periodic structures and photonic-band-gap terminology: historical perspective,” in Proc. 29th Eur. Microwave Conf., Munich, Germany, pp. 295–298, Oct. 1999 [10] S. Ramo, J. R. Whinnery, and T. V. Duzer, Fields and Waves in Communication Electronics, 3rd ed. New York: Wiley, 1993. [11] C.-Y. Cheng and R. W. Ziolkowski, “Tailoring double-negative metamaterial responses to achieve anomalous propagation ef[2]

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[13]

[14]

[15]

fects along microstrip transmission lines,” IEEE Trans. Microw. Theory Tech., vol. 51, no. 12, pp. 2306–2314, Dec. 2003. G. Matthaei, L. Young, and E. M. T. Jones, Microwave Filters, Impedance Matching Networks and Coupling Structures. Norwood, MA: Artech House, 1980, ch. 3, 4, 6–9. G. Matthaei, “An overview of some important contributions to microwave engineering,” in IEEE MTT-S Int. Microwave Symp. Dig., 1989, p. 745. C. R. Simovski, M. S. Kondratjev, P. A. Belov and S. A. Tretyakov, “Interaction effects in Twodimensional bianisotropic arrays,” IEEE Trans. Antennas Propag, Vol. 47, No. 9, Sep. 1999. N.G. Alexopoulos, C.A. Kyriazidou, H. F. Contopanagos, “Effective Parameters for Metamorphic Materials and Metamaterials Through a Resonant Inverse Scattering Approach,” IEEE Trans. Microw. Theory Tech., vol. 55, no. 2, pp. 254–267, Feb. 2007.

Abbas Akbarzadeh was born in Jahrom, Iran, on April 13, 1984. He received the B.S. and M.S. degrees (with honors) in electrical engineering from the University of Iran University of Science and Technology “IUST”, Tehran, Iran, in 2006 and 2009, respectively. His research interests include of RF/microwave passive structures and antennas, RF circuit design and circuit components in presence of complex materials. Majid Tayarani was born in Tehran, Iran, in 1962. He received the B.Sc. degree from the University of Science and Technology, Tehran, Iran, in 1988, the M.Sc. degree from Sharif University of Technology, Tehran, Iran in 1992, and the Ph.D. degree in communication and systems from the University of Electro- Communications, Tokyo, Japan, in 2001. From 1990 to 1992, he was a Researcher with the Iran Telecommunication Center, where he was involved with nonlinear microwave circuits. Since 1992, he has been a member of the faculty with the Department of Electrical Engineering, Iran University of Science and Technology, Tehran, Iran, where he is currently an Assistant Professor. His research interests are qualitative methods in engineering electromagnetic, electromagnetic compatibility (EMC) theory, computation and measurement techniques, microwave and millimeter-wave linear and nonlinear circuit design, microwave measurement techniques, and noise analysis in microwave signal sources. Mohammad Khalaj Amirhosseini was born in Tehran, Iran in 1969. He received his B.Sc, M.Sc and Ph.D. degrees from Iran University of Science and Technology (IUST) in 1992, 1994 and 1998 respectively, all in Electrical Engineering. He is currently an Associate Professor at College of Electrical Engineering of IUST. His scientific fields of interest are electromagnetic direct and inverse problems including microwaves, antennas and electromagnetic compatibility.