SLOW WAVE STRUCTURES FOR MINIATURE ANTENNAS

John L. Volakis and Kubilay Sertel

ElectroScience Lab., Electrical and Comp. Engineering Dept., The Ohio State University,

1320 Kinnear Rd, Columbus, OH 43212, USA

volakis.1@osu.edu, sertel.1@osu.edu

ABSTRACT: Engineered materials, such as new composites, electromagnetic bandgap, and periodic structures have attracted considerable interest in recent years due to their remarkable and unique electromagnetic properties. Among this class of media are the magnetic photonic (MPC) and degenerate band edge (DBE) crystals. These periodic media have the concurrent characteristics of wave slow down and impedance matching at their dielectric interface. The first allows for miniaturization, and the latter is equivalent to radiation efficiency. Overall these properties are a consequence of the anisotropic nature of the periodic media, allowing for internal phase shifting that leads to ray collimation for best aperture utilization. To a degree, they emulate zero index materials, and thus (planar) layers of the material serve the same purpose as a reflector dish. This important property of the MPC and DBE structures will be discussed at the meeting.The main focus of this work is two-fold:

1. The realization (in terms of material availability and fabrication) of the proposed periodic media, and their theoretical and measured performance for antenna applications. Specifically, we will pursue feed arrangements, impedance matching and metallizations/printings for maximum aperture efficiency.

2. Introduction of a concept that allows for emulation of the anisotropic properties of MPC/DBE media using a novel coupled line printed approach. This concept allows for the realization of the wave slow-down and impedance matching within a printed microwave structure, leading to new design methodologies for microwave components, including couplers, filters and printed antenna devices.

Introduction:

The extraordinary electromagnetic behavior of specially engineered composite metamaterial media opened up a wide range of possibilities to dramatically altering the design and operation of ordinary microwave/optical components [1]. Negative index media (NIM) [2, 3, 4, 5] and electromagnetic band gap (EBG) periodic structures are among such promising metamaterials. Although proven extremely hard to implement in full 3-D, left handed transmission line implementations [2, 3] have been more promising for realizing microwave components such as phase shifters, resonators, and couplers. So far, 3-D implementations [6], including the realization of a flat lens have not been as successful [7, 8, 9] due to manufacturing accuracy and inherent material losses in the metallic textures (used to achieve the negative index behavior).

As an alternative to NIMs, a new class of crystals, namely magnetic photonic crystals (MPCs) [10] and degenerate band edge (DBE) [11] crystals have commended strong interest. A major advantage of the latter is their realization using existing off-the-shelf materials. These novel structures realize very special dispersion properties enabling them to support very slow modes (for the case of DBE); and frozen modes (for the case of MPCs). As a result of the wave slow down, the RF wave amplitude entering the MPC or DBE crystal increases significantly with the increase being inversely proportional to wave speed within the crystal (see Fig. 1). We recently demonstrated this property [12] and have shown that wave slow-down and amplitude increase lead to highly directive radiation from embedded antennas within these structures [13].

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Realization of Degenerate Band Edge Crystals using Textured Composites: The leading challenge in manufacturing MPC assemblies is the realization of low-loss ferromagnetic layers present in the design. Thus, our initial effort is to tackle this difficulty by considering the degenerate band edge (DBE) assemblies, obtained by removing the ferromagnetic material from the assembly [11, 12]. DBEs

were shown to exhibit a maximally flat ( ’= ’’= ’’’=0, see Fig. 2) band edge, allowing for a greater coupling efficiency and field penetration into the crystal. We will utilize these degenerate modes to increase the gain and efficiency of antennas and arrays embedded within DBE assemblies. Dependence of the dispersion properties on the direction of propagation (leading to a flat-lens design with maximum aperture efficiency) coupled with the minimal reflection from the air-DBE interface can lead to novel miniature (high sensitivity and high gain antennas and sensors) array configurations.

To achieve the flat band edge and its associated properties [11], it is imperative that the DBE assembly consists of sequential layers of low loss dielectrics with fairly strong anisotropy. Although such materials exist in nature (such as single crystal TiO2: Rutile), their cost may be prohibitive for routine antenna applications. With this in mind, we examined DBE structures using frequency selective surfaces (FSSs) on printed circuit boards (PCB) [12]. However, to address the low material loss to achieve the MPC/DBE modes as well as low manufacturing cost requirements, the assemblies can be constructed from available material structures. Microwave ceramics, such as alumina, titanates, and CVGs as ferromagnetic layers, are good candidates for this purpose. One such concept for realizing the MPC or DBE crystal is shown in Fig. 2(b) and (c). Individual anisotropic layers of the MPC/DBE assembly were designed using textures of alumina (Al2O3) and Barium Titanate (BaTiO3-TD82) as depicted in Fig. 2 (c). To this end, we pursued a full wave analysis of the 3D finite DBE antenna structure using a surface integral equation (SIE) formulation [14]. We

Figure 2: a) Band diagram of the proposed DBE crystal b) Uniaxial stack of Alumina (Al2O3)-Barium Titanate(BaTiO3) layers with the equivalent permittivity tensor c) 1 mm thick slices cut from a commercial Al2O3|TD82 stack with organic adhesion forming the DBE crystal with the shown orientation

0.67mm1mm

K (Bloch Wavenumber)

DBE

RBEF

requ

ency

(GH

z)

a)

b)

eq

45 0 0

0 17.78 0

0 0 45

c)

45 A1 A2 B

x

y

Figure 1: Field compression within the MPC crystal: An incident pulse propagating towards right couples into the MPC and excites the frozen mode within the crystal.

yy

xxA

00

1

xxxy

xyxxA ~~

~~2

uniform,F

A 1 A 2 F

2A1A F

A 1 A 2 F A 1 A 2 F

2A1A F 2A1A F

amplified and compressed pulse

incoming pulse

yy

xxA

00

1

xxxy

xyxxA ~~

~~2

uniform,F

A 1 A 2 FA 1 A 2 F

2A1A F2A1A F

A 1 A 2 FA 1 A 2 F A 1 A 2 FA 1 A 2 F

2A1A F2A1A F 2A1A F2A1A FAmplified and compressed pulse

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designed a 6-unit-cell DBE assembly made from these textured layers to achieve a prototype antenna

displaying around 6.2 dB directivity with 1.9 1.9 1.6 cm3 overall size.

Emulation of MPC/DBE Modes Using Printed Coupled Transmission Lines: A remarkable development in realizing the frozen modes comes from the emulation of the MPC/DBE modes using simple coupled transmission lines. We have recently introduced the concept of using a novel pair of coupled printed microstrip lines (see Fig. 3) to emulate wave propagation within the usual DBE and MPC crystals [15]. Through numerical analysis, we were able to show how small changes in geometrical parameters of the simple structure can be used to generate various dispersion diagrams as shown in Fig. 3. Thus, by adjusting the proximity of the microstrip lines or their width, emulation of the field growth and wave slow down can be done using standard of-the-shelf printed circuit technology.

Currently, we are also investigating the possibility of using the above concept in a printed antenna setting as the concept antennas shown in the lower right corner of Fig. 4. The prototype under investigation is a double-loop antenna, emulating an infinite structure due to the circular repetition of the DBE unit cell (Fig. 4). Dispersion diagram, aperture fields for the DBE resonance and the radiation pattern of the antenna is shown in Fig. 4. We are currently working to match the feed for the subsequent analysis of typical antenna

parameters, such as bandwidth, sensitivity, and pattern. We also have evidence through numerical calculations that MPC dispersion can be emulated using the same coupled line structures printed on a ferromagnetic substrate (see Fig. 5)

References [1] IEEE Trans. on Ant. and Prop., Special Issue on Metamaterials, vol. 51, Oct. 2003. [2] G. V. Eleftheriades and K. G. Balmain, "Negative-Refraction Metamaterials," IEEE Press, John Wiley &

Sons, 2005. [3] C. Caloz and T. Itoh, “Electromagnetic Metamaterials: Transmission Line Theory and Microwave

Applications”, Wiley-IEEE Press, 2005.

Figure 4: Microstrip antenna built from a pair of DBE cells placed in a circle; the band structure is displays the degenerate band edge.

r =10.2

tan =0.0023

2.33 cm

1.31 cm

Antenna Element

Freq

uen

cy

(G

Hz)

K (Bloch Wavenumber)

DBE

~2.8GHz

Band Diagram Surface Fields Radiation Pattern

r =10.2

tan =0.0023

2.33 cm

1.31 cm

Antenna Element

Freq

uen

cy

(G

Hz)

K (Bloch Wavenumber)

DBE

~2.8GHz

Band Diagram Surface Fields Radiation Pattern

DBE modes can be realized via

coupled microstrip lines

Dielectric Substrate 2.50

2.55

2.60

2.65

2.70

2.75

2.80

2.85

2.90

2.95

3.00

7.0 9.08.0kd

Fre

quency [G

Hz]

RBE

DBE

DbBE

2.50

2.55

2.60

2.65

2.70

2.75

2.80

2.85

2.90

2.95

3.00

7.0 9.08.0kd

Fre

quency [G

Hz]

RBE

DBE

DbBE

wDBE modes can be realized via

coupled microstrip lines

Dielectric Substrate 2.50

2.55

2.60

2.65

2.70

2.75

2.80

2.85

2.90

2.95

3.00

7.0 9.08.0kd

Fre

quency [G

Hz]

RBE

DBE

DbBE

2.50

2.55

2.60

2.65

2.70

2.75

2.80

2.85

2.90

2.95

3.00

7.0 9.08.0kd

Fre

quency [G

Hz]

RBE

DBE

DbBE

w

Figure 3: DBE unit cell structure (on the left). Three different band edges can be realized by varying line thickness w.

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[4] E. R. Brown, C. D. Parker, and E. Yablonovitch, “Radiation properties of a planar antenna on a photonic-crystal substrate”, Opt. Soc. Amer. B, vol. 10, no. 2, pp. 404-407, Feb. 1993.

[5] I. Bulu, H. Caglayan, and E. Ozbay, “Highly directive radiation from sources embedded inside photonic crystals,” Applied Physics Letters, volume 83, 3263 2003.

[6] R. A. Shelby, D. R. Smith, and S. Schutz, “Experimental Verification of a Negative Index of Refraction”, Science, vol. 292, pp. 77–79, April 2001.

[7] J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett., vol. 85, no. 18, pp.3966–3969, October 2000.

[8] A. Sanada, C. Caloz, and T. Itoh, “Planar distributed structures with negative refractive index”, IEEE

Trans. Microwave Theory Tech., vol. 52, no. 4, pp. 1252-1263, April 2004. [9] A. Grbic and G.V. Eleftheriades, “Practical limitations of sub-wavelength resolution using negative-

refractive-index transmission-line lenses”, IEEE Trans. Antennas and Propagat., vol. 53, no. 10, pp. 3201-3209, Oct. 2005

[10] A. Figotin and I. Vitebskiy, “Nonreciprocal magnetic photonic crystals”, Physical Review E, vol. 63–066609, pp. 1–17, May 2001.

[11] A. Figotin and I. Vitebskiy, “Gigantic transmission band-edge resonance in periodic stacks of anisotropic layers”, Physical Review E, vol. 72–036619, pp. 1–12, Sep. 2005.

[12] S. Yarga, K. Sertel, and J. L. Volakis, “Degenerate band edge crystals and periodic assemblies for high gain antennas,” IEEE Int. Symposium on Antennas and Propagat., Albuquerque, NM, pp. 7-10, July 2006.

[13] G. Mumcu, K. Sertel, and J. L. Volakis, “Miniature Antennas and Arrays Embedded Within Magnetic Photonic Crystals” IEEE Ant. and Wrl. Prop. Lett. vol. 5, no. 1, pp. 168 – 171, Dec. 2006.

[14] G. Mumcu, K. Sertel, and J. L. Volakis, “Full Wave Modeling of Miniature Antennas Embedded within 3D Finite Degenerate Band Edge Photonic Crystals”, 2006 IEEE AP-S/URSI/AMEREM Symposium, Albuquerque, NM, July 2006.

[15] C. Locker, K. Sertel, and J. L. Volakis, “Emulation of Propagation in Layered Anisotropic Media With Equivalent Coupled Microstrip Lines” IEEE Mw. and Wrl. Comp. Lett., vol. 16, no. 12, pp. 642–644, Dec. 2006.

Degenerate

Band Edge Stationary Inflection Point

DBE modes can be realized via dielectric substrate coupled microstrip lines

Frozen modes can be realized via ferrite substrate coupled microstrip lines

Unit cell of the DBE structure Unit cell of the Frozen Mode structure

Dielectric Substrate Biased Ferrite Substrate

DC magnetic

bias direction

Figure 5: DBE modes of the coupled MS lines (left column) turn into MPC behavior with the proper choice of externally biased ferrite substrate (right column)

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