The electromagnetic properties of various classes of metamaterials (MTMs), such as double-negative (DNG) and single-negative (SNG) materials, have stimulated recent interest in antenna and device applications. It has been shown that MTM-based source and scattering structures have performance characteristics which significantly surpass the corresponding configurations made with conventional double-positive (DPS) materials; see [1] and the works referenced therein. In particular, the possibility of achieving the so-called highly sub-wavelength resonant structures has been demonstrated [1], [2]. These structures include waveguides, cavities, scatterers, and radiators. It has been shown that electrically small resonant source and scattering structures can be designed by cleverly pairing DPS, DNG, and/or SNG materials. Despite their electrically small sizes, the configurations exhibit significant enhancements of their total radiated and scattered powers, as well as their total scattering cross sections.

In this work, the problem of an arbitrarily located line source radiating in the presence of a MTM-coated cylinder is treated analytically and numerically. It will be demonstrated that electrically small resonant MTM-coated cylinders can be designed with the procedures outlined in [2]. Their near-field distributions, directivity properties, and differential scattering cross sections will be presented; they show resonant enhancements not present with the DPS counterparts. In particular, it will be demonstrated that the additional degree of freedom of properly positioning the line source with respect to the DPS-DNG or DPS-SNG interfaces can be exploited to achieve directive electrically small antennas and scatterers by re-shaping their near-field and directivity patterns. Dipolar and quadrupolar mode behaviors will be emphasized. Changes in these behaviors as the geometry and MTM parameters are varied will be discussed.

References

[1] N. Engheta and R. W. Ziolkowski, "A Positive Future for Double Negative Metamaterials," IEEE Microwave Theory Tech., vol. 53, no.4, pp. 1535-1556, Apr. 2005.
[2] S. Arslanagic, R. W. Ziolkowski, and O. Breinbjerg, "Line Source Excitation of Multilayered Metamaterial Cylinders: Source and Scattering Results," IEEE Antennas and Propagation Society Symposium, Albuquerque, NM, USA, July 9-14, 2006 - Accepted.

Split-ring resonators (SRR) first introduced by Pendry et al. (IEEE MTT, Vol. 47, 1999) are commonly used to synthesise negative permeability in NRI metamaterials. The physical mechanism by which a magnetic response is obtained from a metal dielectric composite is generally explained by quasi-static analysis whereby only electric and magnetic fields are considered. However, it has been shown that SRR can react to both electric and magnetic fields (Phys. Rev. B, Vol. 665, 144440, 2002) ; they are said to be bianisotropic.

To account for both fields, one must consider the interaction of an electromagnetic wave on the SRR. To this end, an analysis based on King`s theory of electrically small loop antennas (Collin and Zucker, Antenna theory, McGraw Hill, 1969) is developed. Besides, it is worthwhile noting that a correct description of the artificial media in terms of a macroscopic permeability (given the constitutive relationships : B= µ H and D=ε E) can be provided only if one can make sure that the SRR has a predominant magnetic response at resonance.

The aim of our paper is to propose a physical insight into the synthesis of artificial permeability from metallic loop resonators through an analogy between King’s theory of loop antennas and the interaction of a plane electromagnetic wave on the open metallic loop.

This analysis consists in (i) a Fourier-Bessel decomposition of the current induced in the open loop by the wave and (ii) deducing the effective electric length (analogous to a dipole antenna) to give the first terms of the series at resonance. Basically, the first two terms can be shown to contribute to the magnetic and electric dipolar moments respectively. The magnetic or electric nature are deduced from the dependence of these terms on the incident wave parameters and the geometric parameters of the loop. The first term ("magnetic mode") is dependent on the area of the loop and independent of the position on the loop ; it is the contribution of the constant part of the current. The second term ("electric mode") depends on the perimeter of the loop and the position on the loop ; it represents the contribution of sinusoidal part of the current.

We show that to make sure that the magnetic dipolar moment term is predominant at resonance, either the gap of the open loop should be kept perpendicular to the incident electric field or an appropriate capacitor must be inserted in the gap. Thus, no potential difference is induced by the sinusoidal part of the current and the resonance phenomena is only due to the non-sinusoidal part of the current. In this way, one makes sure that at resonance only a magnetic dipole moment is obtained.

The main outcomes of this analysis are twofold. First, physical insight has been provided in the resonance phenomena of SRR or any open loop based resonator. Secondly, the charge distribution on the loop resonator as well as the distributed capacitive coupling in strip-line loop resonators such as SRR is known. A quasi-static model of SRR is finally given providing for design rules for SRR at a given operating frequency. Results from our quasi-static model are shown to be in agreement with full wave analysis of the SRR media.

The composite right/left handed transmission line (CRLH-TL) is a particular class of metamaterial which consists in usual 'right-handed' transmission lines sections loaded by dual 'left-handed' elements (shunt L and series C). This structure exhibits unusual dispersion properties whose interest has been demonstrated in various applications (e.g. phase shifters for series-fed antenna arrays, dual-band couplers and leaky-wave antennas [1-3]).

This paper concerns the modeling, design and realization of CRLH-TL in the case where it cannot be considered as an effective medium. The effective medium assumption is widely used to model the propagation of an electromagnetic wave in a metamaterial and is valid only if the unit cell dimension is much smaller than the wavelength in the unloaded host medium of the metamaterial. In this work, we first show that a significant class of balanced CRLH-TLs cannot meet this effective medium condition, making existing design expression inaccurate. In particular, we show that although the matching of effective media CRLH-TL structures is straightforward, it is not the case for non-effective ones. Indeed, it is observed that the equivalent impedance of non-effective CRLH-TLs is highly frequency-dependant, depends on the basic architecture of the CRLH-TLs, and is related to the impedance of the unloaded transmission line in a non-trivial manner.

As a result, we use a periodic structure¯or Bloch wave¯ formulation to model the CRLH-TL and derive a method which allows designing non-effective medium CRLH-TLs with optimal phase shift and matching within a large bandwidth. The proposed procedure is exact based on the CRLH-TL unit cell circuit and can be used to match 1-D to 3-D CRLH-TLs. Finally, we demonstrate that the periodic structure equivalents represent a general approach from which the effective parameters can be derived on the condition that the wavelength in the unloaded medium is much larger than the unit cell dimension.

In order to illustrate the presented theoretical developments, we present the design and measurements of an optimally matched integrated CRLH-TL 1-D phase shifter, which will be compared with a design that do not consider the Bloch wave impedance of the structure. Other applications, such as integrated leaky-wave antennas and MEMS-based variable CRLH-TL will also be discussed.

[1] G. V. Eleftheriades, A. K. Iyer, and P. C. Kremer, "Planar negative refractive index media using periodically L-C loaded transmission lines," IEEE Trans. Microwave Theory Tech., vol. 50, no. 12, pp. 2702 - 2712, Dec. 2002.

[2] I.-H. Lin, M. DeVincentis, C. Caloz, and T. Itoh, "Arbitrary dual-band components using composite right/left-handed transmission lines," IEEE Trans. Microwave Theory Tech., vol. 52, no. 4, pp. 1142 - 1149, April 2004.

[3] J. Perruisseau-Carrier and A. K. Skrivervik, "Composite Right/Left Handed Transmission Line Metamaterial Phase Shifters (MPS) in MMIC Technology," IEEE Trans. Microwave Theory Tech. (Accepted for publication), April 2006.

Artificial Magnetic Conductors (AMC) are designed primarily from a layer of a Frequency Selective Surface composed by a periodic arrangement of conducting elements, loops, patches or GA optimized structures on a dielectric substrate and backed by a ground plane [1]. Other geometries without a ground plane can also behave as good PMC surfaces [2].

Two different AMC designs will be presented here. The first one uses metal split cylinders as an AMC surface, as introduced by Pendry [3]. The initial design is an AMC surface composed by an arrangement of split aluminium tubes with square cross section. From the measurements, this surface shows a 13% fractional bandwidth related to ±45° of the phase of the S11 parameter (Fig. 1 right), and losses smaller than 0.2 dB for the entire operational frequency band (Fig. 1 left). The electrical thickness is about lambda/7 for the whole structure.

Moreover, this surface has been improved using the previous metal cylinders, but now attached to a corrugated ground plane. This new structure shows two modes of AMC operation, each for one frequency band. The lower frequency range is due to a conventional open loop arrangement (the aluminium cylinders themselves). And the higher frequency range is performed by a short circuit transformed into an open circuit by a lambda/4 transformer line present between the cylinders. First simulations results show a very good bifrequency behaviour. Further designs using two aluminium cylinders, one inside the other as a SRR tube, and measurements will be shown at the conference.

The second design is a surface made of dielectric strips with spirals on them showing a bidirectional AMC behaviour when the incident field reflects on both sides of the surface, as shown in Fig. 2, where the S11 and S22 phase results agree very well. From the simulated results, this surface achieves a 5.1% fractional bandwidth, losses below 0.5 dB and an electrical thickness about lambda/9. Measurements of the designed structure and its applications for decoupling two close antennas in MIMO systems will be presented at the conference.

Acknowledgements:
This work has been supported by the Spanish Comisión Interministerial de Ciencia y Tecnología (CICYT) del Ministerio de Ciencia y Tecnología and FEDER funds through grant TIC 2003-09317-03-03 and through the Ramon y Cajal Programme, and by the European Commission through the METAMORPHOSE Network of Excellence (FP6/NMP3-CT-2004-500252).

References:
[1] F. Yang, K. Ma, Y. Qian, and T. Itoh, "A uniplanar compact photonic-bandgap (UC-PBG) structure and its applications for microwavecircuits," IEEE Trans. Microwave Theory Tech., vol. 47, no. 8, pp.1509–1514, Aug. 1999.
[2] A. Erentok, P. Luljak, R. Ziolkowski, "Characterization of a Volumetric Metamaterial. Realization of an Artificial Magnetic Conductor for Antenna Applications", IEEE Trans. on Antenna and Propagation, vol. 53, no. 1, pp 160-172, Jan. 2005.
[3] J. B. Pendry, A. J. Holden, D.J. Robbins, W. J. Stewart, "Magnetism from Conductors and Enhanced Nonlinear Phenomena", IEEE Trans. on Microwave Theory and Techniques, vol. 47, no. 11, pp. 2075-2084, Nov. 1999.

Figures:

Fig. 1: Metal cylinders surface design: measurements of S11 magnitude (left) and phase (right)

Fig. 2: Bidirectional pmc surface: simulations of S11 phase (blue solid) and S22 (red dashed)

Spiral structures have been extensively used in several microwave applications, such as the design of broadband antennas, the synthesis of microwave filters and the fabrication of on-chip inductors or transformers. In this paper, spiral resonators are incorporated for the design of uniplanar, microstrip-based left-handed metamaterials.

Subsequently to the recent advances in the analysis and synthesis of left-handed media, the purpose of this work is to come up with novel, low profile, fully printed metamaterial structures that will be compatible with standard microwave technology and will further enable the use of such materials in microwave applications. Toward this direction, the theoretical study of [1] showed that spiral resonators, backed on a grounded substrate, support backward waves, for a certain range of frequencies, due to the series capacitance between the adjacent windings and the shunt inductance created by the currents on the loops of the spirals.

In the following, the fabrication and measurement of a prototype that is composed of the double spirals of [1] are presented. Six of these double spirals are routed on a 50 Ohm transmission line (Fig. 1), resulting in a uniplanar, easily-fabricated structure. The formulated passband, in which left-handed modes are supported, extends from 2.9 GHz to 3.3 GHz, while fairly satisfying transmission is succeeded within this range of frequencies (Fig. 2). Additional details on the design, analysis and measurement of this structure and further discussion on the impact of ohmic losses to its operation will be included in the final paper.

Figure 1: The fabricated left-handed metamaterial structure that is based on the spiral loops of [1].  

Figure 2: Measured S-parameters (in dB) of the prototype of Fig. 1.

References

[1] Y. Guo, G. Goussetis, A.P. Feresidis and J.C. Vardaxoglou, "Efficient modeling of novel uniplanar left-handed metamaterials", IEEE Trans. Microwave Theory Tech., vol. 53, no. 4, pp. 1462-1468, Apr. 2005.

In this work, we present the results of the application of composite right/left handed transmission lines (CRLH-TL) to antenna matching. The antenna matching is achieved by means of quarter-wavelength single and multisectional transformers. Several interesting applications have been proposed for CRLH-TL in [1, 2]; we will show here that, in the case of antenna matching, the unique characteristics of CRLH-TL allow size reduction of the matching network and bandwidth enhancement.

The design of a quarter-wavelength transformer requires the control of the phase shift and the impedance of the CRLH TL at a desired frequency. For this purpose, a new circuit-based design method has been developed and used to design CRLH-TLs, with the required phase shift and impedance characteristics at the frequency of interest. Two different approaches of building the CRLH-TL will be presented, an approach using SMT devices and a purely integrated implementation of both antenna and matching network using interdigital capacitors and stub inductors layout elements.

Fig. 1 shows an example of a CPW-fed slot loop antenna matched by a two-stage Chebyshev transformer made of two sections of CRLH-TL based on SMT devices. Measured results are plotted in Fig. 2, and compared with measurements for a classical quarter-wavelength transformer. A bandwidth enhancement of 11% is measured (see Fig. 2) with a size reduction of 66% in the matching network length for the Chebyshev transformer. For both designs, we have performed computer simulations using Ansoft Designer which agree quite well with measurements.

References

[1] I.-H. Lin, M. DeVincentis, C. Caloz and T. Itoh, "Arbitrary dual-band components using composite right/left-handed transmission lines," in IEEE Trans. Microwave Theory Tech., vol. 52, no. 4, pp. 1142-1149, April 2004
[2] M. Antoniades and G. Eleftheriades, "Compact linear lead/lag metamaterial phase shifters for broadband applications," IEEE Antennas Wireless Propagat. Lett., vol. 2, no.7, pp. 103-106, 2003

Microstrip fed slot antenna (MSA) is widely used as an element antenna in conventional phased array antenna due to its low profile, light weight and low cost. It is usually made of a single piece of dielectric substrate with a slot etched on one side and microstrip line etched on the other side. On its own, MSA is not an efficient antenna. This is due to its bidirectional radiation pattern behaviour where almost half of the radiated power is wasted in the unwanted direction. As a result, the overall performance of the conventional phased array antenna using MSA as an element is normally not satisfactory. To achieve an efficient phased array antenna, it is therefore crucial to design an element antenna that can deliver reasonably high gain and symmetrical radiation patterns in both E and H planes. Several attempts have been made to improve the efficiency of the element antenna. A metal ground plane has been used in an attempt to redirect radiated energy from an unwanted direction to the desired direction.

Some gain improvement has been achieved, but return loss and radiation pattern performances have been degraded due to the surface wave created on the metal back plane and the ground plane of the MSA itself. This element antenna still causes unwanted effects such as radiation distortion and angle blindness to the phased array antenna. These problems are also concurrent in conventional phased array antenna. To minimise these problems, a suspended microstrip fed slot antenna on the High Impedance Surface (HIS) ground plane as seen in Figure 1 has been proposed. Ansoft HFSS software is used to create and simulate this structure. The high impedance ground plane has the ability to suppress surface wave and give in phase reflection within the desired band gap frequency.

Bandwidth and resonant frequency of the ground plane can be tuned by changing the value of sheet capacitance and sheet inductance of the structure. With the use of this ground plane, radiation performance of the conventional microstrip fed slot antenna can be dramatically improved within the desired band gap frequency of the HIS ground plane. Figure 2 shows the comparison between radiation patterns obtained from the conventional MSA and radiation patterns obtained from MSA on HIS ground plane in both E and H planes. Desired return loss performance can be achieved by changing both the separation between MSA and HIS structures and some parameters of the MSA. Furthermore with this new type of element antenna, the overall size of the phased array antenna can be greatly reduced due to the lower level of mutual coupling between the elements. Figure 1. Suspended MSA on HIS. Figure 2. Comparison between radiation patterns obtained from convention MSA and MSA on HIS.

In recent years, many directivity enhancement methods based on resonant cavities have been investigated. The same physical phenomenon is exploited to obtain high directivity with electromagnetic bandgap antennas, Perrot-Fabry resonators, leaky wave antennas and superstrate gain enhancement technique. Classically, in all these approaches, a source is placed between a reflective layer and a ground plane. At the cavity resonant frequency, a radiating aperture with a uniform phase distribution is achieved, which leads to an enhancement of the surface efficiency and thus of the directivity. The directivity level increases with the cavity quality factor (i.e. with the top layer reflectivity) but the directivity bandwidth decreases in the same time.
In this paper, we investigate a reflective layer designed to increase the directivity bandwidth. Theoretically, it can be shown that this is achieved if the reflective layer exhibits a reflection coefficient phase that increases with the frequency.
To reach this goal, a dual layer Frequency Selective Surface (FSS) is proposed. Each FSS layer is made up of an array of strip rectangular dipoles and works as a bandpass filter (see figure 1). The center frequency of each layer as well as the distance separating them has been optimized in order to obtain the increasing phase.
Figure 1 shows the reflection response of a two infinite FSS layers structure simulated with Ansoft HFSS. As expected, magnitude presented in figure 1(a) exhibits two resonant frequencies corresponding to each FSS layer. The reflection coefficient phase in figure 1(b) increases with the frequency over a 200 MHz bandwidth centered on 4.8 GHz. These results show that the expected phase is obtained only when the reflectivity falls. This property will limit the directivity performance of the antenna designed with the proposed reflective layer.

Fig. 1 Reflection response of the two infinite FSS layers structure (a) Magnitude (b) Phase and diagram of an elementary cell

Antenna results have been validated for a two layers 3x3 finite arrays antenna structure. The dipoles arrays are placed above a ground plane at an optimum distance. Figure 2 presents the directivity as a function of the frequency. The directivity reaches 14.8 dB at 4.85 GHz and the 1dB directivity bandwidth is 6.9%. As regards of radiation patterns, results will be presented in the final paper.

Fig. 2 Directivity of the two layers 3x3 finite arrays antenna structure

In this paper, a novel circularly-polarized annular-ring microstrip patch antenna which is fabricated on an EBG groundplane is presented. This recently proposed annular-ring antenna structure has been shown to be significantly smaller than conventional annular-ring patch antennas, even on standard groundplanes [1]. The addition of the EBG structure to the annular-ring embedded patch yields an increase in the impedance bandwidth, axial-ratio bandwidth and antenna gain by 46 %, 50% and 2.2 dBi respectively, when compared to the same antenna on the same size groundplane without EBG.

Geometry of the annular-ring embedded circular patch antenna loaded with EBG

The geometry of the structure is shown below, which consists of an annular-ring embedded circular patch antenna loaded with an unequal lateral cross-slot in the EBG groundplane. The EBG groundplane structure consists of an array of annular-ring slot cells.

Performance

The results for the proposed antenna were simulated using the Finite Element Method and subsequently measured. The measured and simulated return loss for the antennas with EBG and without EBG are compared below (same groundplane size). For the antenna without EBG, the impedance bandwidth for which the return loss is greater than 10dB is only 57MHz (1.827GHz to 1.884GHz), but for the EBG loaded antenna, the impedance bandwidth is 83 MHz (1.782GHz to 1.865GHz), a significant improvement of 46 %. This effect is due to the reduction of spurious waves travelling on the substrate. The measured and simulated axial-ratio (AR) for the antennas with and without EBG are also shown. For the antenna without EBG, the axial-ratio bandwidth (AR 3dB) is 14MHz (1.838GHz to 1.852GHz), and for the EBG antenna, the axial-ratio bandwidth is 24MHz (1.800GHz to 1.824GHz), an improvement of 50%. A slight reduction in resonant frequency is also achieved, yielding an electrically smaller antenna.

Conclusions

The proposed structure shows significant improvements in antenna performance including impedance bandwidth, axial-ratio bandwidth and gain. The antenna radiation efficiency is increased.

Reference

X. L. Bao and M. J. Ammann, Compact Annular-ring Embedded Circular Patch Antenna with a Cross-slot Ground Plane for Circular Polarization, Electronics Letters, 2006, 42, (4), 192-193.

The present work focuses on the characterization of metamaterial (MTM) slabs in terms of reflection and transmission coefficients (scattering parameters) under oblique plane wave incidence (Fig. 1). In most of previously reported works, the scattering parameters were obtained by considering a single unit cell (of the periodic structure forming the MTM) in a PEC-PMC waveguide, where the PEC and PMC walls simulate the periodicity. The fundamental mode of this waveguide is a TEM wave, allowing then to simulate plane wave incidence. However, this approach suffers from the following disadvantages:

Abstract: A low-profile microstrip delay line is proposed for feeding networks of waveguide-fed array antennas. It consists of a simple microstrip line with periodically-loaded inductors, and can realize the same frequency-dispersion characteristics as those of waveguides with smaller size. The delay line has quite a similar structure to a composite right/left-handed transmission line, which is one of the latest and hottest topics in RF communities. In our case, though, it is used just as a frequency-dispersive right-handed line.

Fig. 1 shows a simplified block diagram of a feeding network of a waveguide-fed array antenna. When each sub-array has a different length of feeding waveguide, delay lines must be employed in order to combine each signal in phase. As the delay lines, planar or coaxial delay lines are preferred to metal waveguides from the viewpoints of volume and weight. However, they are (quasi-) TEM-lines and their frequency- dispersion characteristics are different from those of feeding waveguides, resulting in a narrow bandwidth for phase-error compensation.

To overcome this problem, a microstrip delay line with periodically-loaded shunt inductors is employed as in Figs. 1 and 2. Phase constant of the inductor-loaded microstrip line is given by (eq1). On the contrary, that of a rectangular waveguide is given by (eq2), where c0 and a are speed of light and the width of the rectangular waveguide, respectively.

Since (eq1) and (eq2) have the same dependence on the frequency, the microstrip line in Fig. 2 can have the same delay characteristics as the waveguide. Fig. 3 plots the phase error [(theta)a-(theta)b] in Fig. 1, which are obtained from measured data of the fabricated delay line in Fig. 2(b), and measured reflection characteristics of the delay line. The phase error has been successively suppressed within 12 [deg] by the inductor-loaded microstrip delay line, although it exceeds 25 [deg] in the case without the microstrip delay line.

High-gain and compact antennas composed of a single feed present an attractive solution for several wireless communication systems. Their single-feed system allows to increase the gain with low complexity compared to feeding networks used in conventional antenna arrays. In addition, the compactness represents an important advantage compared to parabolic antennas.
To design low profile high-gain antennas with a single feed, various methods have been recently proposed, such as the employment of Fabry-Perot type cavities (T. Akalin et al., IEEE Microwave Wireless Compon Lett 12 (2002), 48-50; H. Boutayeb et al., Microw. Opt. Technol. Lett. 48 (2006), pp. 12-17; N. Guerin et al., IEEE Trans. On Anten. And Propag. 54 (2006), pp. 220-224, A.P. Feresidis et al., IEEE Trans. Antennas Propag. 53 (2005), pp. 209-215), or ectromagnetic crystals or zero index metamaterials (C. Cheype et al., IEEE Trans.Antennas Propag. 50 (2002),pp. 1285-1290; S. Enoch et al., Phys. Rev. Lett. 89 (2002), pp. 213902-1-213902-4, H. Boutayeb et al., Journ. of Electrom. Waves and Appl. 20 (2006), pp. 519-614).
The inconvenient of high-gain antennas based on Fabry-Perot cavities, Electromagnetic Band Gap (EBG) materials or metamaterials is their narrow directivity bandwidth. This can represents an important drawback of these antennas compared to parabolic antennas, which have large directivity bandwidths. In this work, we propose different techniques to widen the bandwidth of these types of antennas.
For this, three different configurations employing Partially Reflecting Surfaces (PRSs) have been considered. In these configurations, a monopole has been used for the excitation (at the center), and the structures are composed of metallic wires. The first configuration considers a Fabry-Perot cavity with aperiodic PRSs. The second configuration considers two different PRSs. The third structure uses an elliptical PRS.
These different configurations were analyzed. More details on the design techniques and numerical results (FDTD) will be presented and discussed in the long paper version and during the conference.

Abstract

Compact SRR loaded waveguide diplexers are presented. Incorporating an SRR loaded dielectric slab, electromagnetic properties of the structure are changed to allow propagation of backward waves in the rectangular waveguide. Using the printing-circuit-board (PCB) technique, split ring resonators (SRRs) are etched on a dielectric substrate and the slab is then inserted in the central plane of the metallic waveguide. Diplexer is formed by incorporation of metal discontinuities realized as copper rectangular-shaped septa, etched on the top surface of the substrate. Diplexer was designed and measured at X-band. The structure is compact and suitable for mass production.

Summary

From electromagnetic theory, it is well known that rectangular waveguide is characterized by its broad wall inner dimension, to be at least half the wavelength in order to satisfy the boundary conditions for propagation of electromagnetic waves. Thus, the available bandwidth for a particular system is been determined by the corresponding waveguide frequency range. In this paper we make use of a composite dielectric insert in order to allow for reduction of physical dimensions of the waveguide structure.

Such dielectric slab is patterned with small resonant elements, constructed in the form of two square shaped rings interrupted by a small gap (split ring resonators), etched on the top surface of the substrate. Permittivity of a dielectric material år = 2.2, thickness h = 1.52 mm, and the substrate used is Rogers RT/Duroid 5880. The stopband characteristic of the SRRs is then switched to a bandpass behavior by introducing loading the slab with metallic discontinuities, which act like impedance inverters integrated with adjacent lengths of the dielectric waveguide. The dielectric slab is then inserted into the central (E-plane) of the waveguide, therefore changing electromagnetic properties of the propagation medium. Diplexer is designed as a two-section SRR loaded waveguide. Conventional rectangular waveguide housing WR-90 (WG-16), with broad wall inner dimension a = 22.86 mm, provides metallic housing for the diplexer. The finite-element method (FEM) based commercial package was used in order to analyze the proposed structure. As shown in Fig. 1, both channels of the diplexer are 800 MHz wide, with the corresponding midband frequencies at 9.85 GHz for the first channel and 12.6 GHz for the second channel. The proposed dielectric slab is easily fabricated using the PCB technology, and inserted in the rectangular waveguide to form a compact SRR loaded waveguide diplexer. Total length of the diplexer, including waveguide feeding, is 29.3 mm.

The purpose of this work is to compare different strip-type soft surfaces and mushroom-type EBG in different aspects. Firstly, strip-type soft surfaces are characterized in the same way as electromagnetic bandgap (EBG) surfaces, i.e. in terms of dispersion diagrams and bandgaps [1]. As these soft surfaces stop surface wave propagation only in one direction, the bandgap is calculated in that direction. Secondly, they are also studied in terms of the bandwidth of a system related performance parameter; when they are used as narrow ground planes to reduce back radiation [2]. To this aim a vertical electrical source is used. The results are in both cases compared with those of mushroom-type EBG surface.

The strip loaded soft surface can be realized both with vertical metal walls in the dielectric (resembling corrugations) and with periodic via holes (like in mushroom-type EBGs). In the second case the via period is used as an extra parameter to optimize the bandgap, resulting in larger bandgaps than for musroom-type EBGs. It was found that the bandgap region moves to lower frequencies when the distance between vias is increased, in the same way as the relative bandwidth of the bandgap decreases. Also, we investigate placement of the vias either in the centre or at the edge of the strip, both for strips and for mushroom-type EBGs. The lateral position moves the bandgap to lower frequencies, thus gives smaller period of the surface for a given frequency.

Dispersion diagrams of mushroom surfaces and those of strip-loaded surface with metalized via holes and corresponding dimensions are very similar (Figure 1 shows the dispersion diagram for lateral vias position). Furthermore, for strip-loaded surfaces with vias we can use the period of the vias to move the bandgap towards lower frequencies, therefore reducing physical size which is advantageous. When the surfaces are used as small (1.5lambda) ground planes both have similar performances (Figure 2) for TM case (vertical polarization) whereas the strip surface has larger bandwidth for TE case (horizontal polarization) (Figure 3).

In conclusion, lateral vias position are useful to reduce size of strips and mushrooms and in the strip case, the optimization of the vias period allows a further reduction. For narrow ground plane applications the strips offers an advantage for TE case (horizontal polarization).

[1] P.-S. Kildal and A. Kishk, "EM modeling of surfaces with STOP or GO characteristics- artificial magnetic conductors and soft and hard surfaces," Applied Computational Electromagnetics Society Journal, vol. 18, no. 1, pp. 32–40, March 2003.

[2] Z. Ying, P.-S. Kildal, and A. Kishk, "Study of different realizations and calculation models for soft surfaces by using a vertical monopole on a soft disk as a test bed," IEEE Trans. on Antennas and Propagation, vol. 44, no. 11, pp. 1474–1481, 1996.

For many years, general interest has grown around Electromagnetic Band Gap (EBG) material applications. These materials are well known for their spatial and frequency filtering properties [1]. This paper presents a general design method for beam steering EBG antennas. This method is based on the analytical study of the EBG material properties, and the feeding probe radiation. Prototype measurements will support computation results.

In the published previous works [2], the EBG antenna was studied with full wave codes like FDTD. We propose in the first part to study 1D dielectric EBG antennas using an analytical method. It allows to highly decrease computation time (5s for analytical method versus more than one hour for full wave analysis). This method relies on the EBG stack transfer matrix calculation, a concept developed for Partially Reflecting Walls [3] (which we call "EBG selectivity") and the feed radiation pattern calculation. The transfer matrix will consider reflectivity of each dielectric interface and also the propagation in each medium. This matrix is frequency, angular incidence and polarization dependant. When it is calculated, reflectivity of EBG stack is deduced and used to determinate the EBG structure selectivity. This function will render of the angular and frequency nature of the structure. This selectivity is then coupled with the feed radiation pattern. So, we estimate the EBG antenna radiation pattern. It allows to know precisely the antenna directivity, side lobes level, and finally to choose the better EBG material/feeding probe couple according to the specifications. This method has been evaluated comparing with FDTD computations. We will see that the results of both methods converge.

In a second part a (è=30°, ö=0°) EBG beam steering antenna example will illustrate this method. The feeding source has been chosen to realize an azimuthal radiation filtering function. Indeed, EBG material will allow the è=30° direction for all ö angles. A 4*4 array will select a particular (è ,ö) direction. It would be established that the conception of the feeding source can not be separated from the general conception of the antenna. Indeed, EBG material largely affects the impedance matching of the elementary radiating element, so the distribution network has to be tuned according to this EBG material which will cover it.

The last part is devoted to the prototype measurements, where experimental results will be compared with simulated results.

References
[1] E.Yablonovitch, « Inhibited spontaneous emission in solid state physics and electronics », Phys. Rev. Lett., Vol. 58, 1987, pp 2059-2062.
[2] M.Thevenot, C.Cheype, A.Reineix, and B.Jecko, « Directive photonic bandgap antennas », IEEE Transactions on microwave theory and techniques, Vol. 47, n°11, November 1999, pp 2115-2122
[3] G.V.Trentini, «Partially reflecting sheet arrays», IRE Trans on antennas and prop., vol 4, pp. 666-671,

Electromagnetic Bandgap (EBG) materials have found possible applications in antenna technology as substrates to improve performances. In this work we present a new use of EBG substrates as a support of slowly attenuating, very fast, leaky waves, so as to produce a narrow beam at broadside. The proposed new structure is planar and it is excited by a transverse elementary dipole, though other excitations like slots in the ground plane would lead to the same conclusions. The EBG substrate of finite height analyzed have a square lattice, and the basic cell is made of a dielectric rod of Alumina embedded in Teflon material over a perfect electric conductor.

The radiated electric field by a transverse elementary dipole placed in the middle the EBG substrate is calculated by reciprocity. In the computer simulations the EBG substrate is infinite in both transverse directions, and only the basic cell with periodic boundary conditions is numerically modelled. The radiation patterns at two frequencies, are computed with the commercial simulator CST Microwave Studio. The upper Figures show the radiation pattern at 18.8 GHZ, that exhibits very high directivity along the E-plane due to the excitation of a TM-like leaky mode; on the upper-right, along the H-plane, two peaks are present. The situation is inverted at a slightly higher frequency of 20.2GHz.

Radiation trends, that will be shown at the conference presentation, reveal that the directive radiation patterns are produced by leaky waves. We aim here at tailoring the EBG material such that the performance on the E and H planes are similar. A typical situation that we have encountered is that leaky waves that propagate along the two principal planes (E and H) exhibit forward and backward transverse propagation, respectively. We will show that the difficulty is in finding geometries that permit both TE-like and TM-like leaky wave excitations with approximative the same propagation constant.

The presentation will be devoted to show how to obtain very directive beams by using all-dielectric substrates. At very high frequencies, where metallic structures have high losses, these new radiating structures offer some advantages.

Bottom side: Normalized radiation pattern of the infinite structure excited by a short dipole at f=20.2 GHz (high directivity on H-plane produced by a TE-like leaky mode).

Practical applications, such as mobile communications systems, usually require smaller antenna size in order to meet the miniaturization requirements of mobile units.

Many techniques have been reported to reduce the size of printed antennas at a fixed operating frequency. A common way is to load the volume under the patch with an high-permittivity substrate. The main drawback is the reduction of the bandwidth. A solution is to use an high-permeability substrate. Unfortunately, there doesn't exist any natural low-loss magnetic materials operating at microwave frequencies. Recently, artificial magnetic materials were proposed : metasolenoids consisting of periodically stacked and closely spaced split-ring resonators (SRR) [IEEE APS'05, Ikonen et al.] or new impedance surface [IWAT'05, Ermutlu et al.].

The aim of this paper is to study structures based on SRR to provide an artificial magnetic media with high values of Re(μ) so as to reduce the size of patch antennas. Our work consists in three main steps.

The first one is an analytical study of the resonant frequency of a circular SRR particle composed of a metallic strip of width c, and radius r printed on a dielectric substrate (ε, d). The resonant frequency is defined by that of a resonant LC circuit. The inductance of the SRR is deduced through the calculation of the magnetostatic energy of the metallic loop and the capacitance is that of two broadside-coupled microstrip lines. A parametrical study of the resonant frequency is then achieved in varying either geometrical parameters (r,c) of the SRR or the substrate parameters (,d). Design rules for an SRR at a given operating frequency are thus obtained.

The next step is the study of different configurations of periodic arrangements of the previously designed SRR's. From numerically S-parameters, the effective parameters are extracted : artificial magnetic media are obtained in our case.

Based on this study, the optimal media is selected for the design of the reduced-size patch antenna. A size reduction of 20% can be obtained, without spoiling the radioelectric performances of the antenna.

In phased arrays scan blindness occurs when the propagation constant of a Floquet mode coincides with that of a mode supported by homogeneous dielectric substrate, resulting in large input mismatch and in a propagating mode with complex propagation constant. Note that due to this synchronous condition and due to the periodicity, the surface mode that is usually supported by the substrate becomes leaky. In our study we analyze the possibility to replace a standard homogeneous dielectric substrate with a grounded dielectric EBG substrate made of dielectric resonator antennas (DRA) to eliminate the scan blindness for a phased array. The electromagnetic band gap (EBG) substrate consists of a periodic arrangement of DRA, as shown in Fig. 1. In other words, the DRA are used to radiate and at the same time to form a transverse EBG to avoid propagation of surface waves and inhibit leaky waves. First, investigation on dispersion diagrams to show that there are no surfaces modes are provided. The rods are also used as DRA. So the main idea is to use the rods of a periodic EBG substrate as a phased array of DRA. The DRA are here fed by a simple electric probe but other possible excitations are considered. The geometry and the position of the probe are determinant to excite the dominant mode at the lowest frequency. Furthermore, at a chosen frequency the active reflection coefficient is calculated for various scan angles to show that no blind spots are present. The same analysis has been carried out when a small conducting patch of different shapes and sizes is placed over each DRA. Comparisons in terms of dispersion diagrams and radiation patterns will be shown between the two phased arrays: with and without metallic patches.

Electromagnetic bandgap structures (EBG), also known as photonic bandgap structures (PBG) in optics, are now finding numerous applications in microwave and millimeter wave devices. In general, EBGs are periodic structures consisting of dielectric or metallic elements, and exhibit forbidden frequency bands (bandgap). There are two important attributes of EBGs: the first is to block the propagation of the electromagnetic waves within a bandgap, whilst the second is that the EBGs display localized frequency windows within the forbidden frequency band when the periodicity is broken due to the presence of defects. The former is useful for applications such as waveguides, spatial filters, and antenna substrates, and the latter could be used to improve the directivity of an antenna when the EBG is used as a superstrate for the antenna. At the defect frequency, the superstrate alters the distribution of the electromagnetic fields along the specific direction, which makes the effective aperture much larger than the original antenna resulting in increased directivity. Several researchers have investigated such resonator antenna structures; however, the experiments were mainly performed at microwave frequencies. In this work, we extend our frequency of interest to millimeter wave frequencies (W-band) and employ a new technique to fabricate EBG structures in millimeter wave regime. For the simulation of 3-D EBG unit cells, an in-house FDTD simulator with periodic boundary conditions (PBC) is used. The fabrication of EBG structures is carried out using the computer controlled extrusion free-forming technique. The lattice parameters of the fabricated EBG structure are: lattice constant, a = 1297µm, and width and height of the rod, w = h = 324.3µm. We use alumina rods with a relative permittivity of ε_r = 9.6. Fig. 1-(a) shows the fabricated woodpile structure and the simulated results are shown in Fig. 1-(b) and (d)-(e). A complete bandgap is observed in the dispersion diagram. The fabrication facility is currently capable of making ceramic filament as thin as 80µm with 20µm spacing and we have successfully fabricated woodpile structures with 120µm thick filament, which can be used for higher frequency ranges (200-300GHz). The measurement results for the material in this frequency range will be reported in the future. In order to characterize the fabricated EBG structures, we measure transmission coefficients for different directions and polarizations as a function of frequency. The complete antenna system is composed of a W-band horn (93-97GHz) antenna and the fabricated EBG structures on top of the millimeter wave horn (see Fig. 1-(c)). The separation distance between the horn and the EBG material is chosen such that the defect frequency lies within the bandgap. The complete antenna system is measured in anechoic chamber and the results are presented.

The concept of metamaterial provides the possibility to obtain electromagnetic properties, at certain frequencies, that are difficult or impossible to achieve with conventional materials [1]. Applying this concept it is possible to build an artificial magnetic conductor (AMC) that can be used in a reflector [2]. The AMC, compared to an electric conductor, allows the dipole to be closer to the reflector while keeping the maximum of radiation normal to the plane.

An AMC based on spiral resonators has been considered with the purpose of studying the effects in the behaviour of the reflector of spacing between resonators and the size of the plane. The operating frequency of the screen is 2.45 GHz. The performance of the AMC is evaluated when placing a folded dipole close to the screen. Figure 1 shows (from left to right) the mesh of the AMC and the folded dipole (including balun and bifilar transmission line), a side view of the structure and a detail of the spiral resonators. The influence of the distance between the folded dipole and the screen is assessed in terms of input impedance and radiation pattern. A simulation tool based on method of moments (MoM) and an accelerating technique (MLMDA: multilevel matrix decomposition algorithm [3]) are used in the analysis. This tool allows taking into account the small details of the basic cell and the fact that the structure is periodic but finite, with low computational requirements.

In order to validate the numerical results, the structure will be implemented and characterized. The AMC and the folded dipole will be fabricated with standard photo etching techniques. Measurements will be carried out at the facilities of AntennaLab at UPC.

Acknowledgments: This work is supported by the Spanish Comisiòn Interministerial de Ciencia y Tecnologìa (CICYT) del Ministerio de Ciencia y Tecnologìa and FEDER funds through grants TIC 2003-09317-C03-02 and TIC 2003-09317-C03-03.

REFERENCES
[1] D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, S. Schultz, "Composite medium with simultaneously negative permeability and permittivity", Physical Review Letters, 84, 18, pp. 4184-4187, May 2000.

[2] A. Erentok, P. Luljak, R. Ziolkowski, "Characterization of a Volumetric Metamaterial. Realization of an Artificial Magnetic Conductor for Antenna Applications", IEEE Trans. on Antenna and Propagation, vol. 53, n° 1, Jan. 2005, pp 160-172.

[3] J. Parrón, J. M. Rius, and J. R. Mosig, "Application of the Multilevel Decomposition Algorithm to the Frequency Analysis of Large Microstrip Antenna Arrays", IEEE Trans. on Magnetics, Vol.38, No.2, pp. 721-724, March 2002.

Figure 1. (Left) View of the AMC and folded dipole (including balun and bifilar transmission line); (middle) a side view of the structure; (right) a detail of the spiral resonators

It has been shown theoretically that single negative (SNG) and double negative (DNG) metamaterials (MTMs) can be used to achieve a variety of resonant, electrically small radiating and scattering systems [1]-[5]. As a result, there is now a great deal of interest in the realization of the MTMs required by these applications as well as in the associated experimental verifications of their properties. Unfortunately it has been found that it is very difficult to achieve the desired epsilon negative (ENG) properties in extremely small unit cell sizes in the UHF frequency regime. We will present a set of specifically designed ENG building blocks that are highly sub-wavelength in size at 300 MHz. These ENG elements are resonant and anisotropic. We will then introduce a set of ENG elements with a higher degree of isotropy. Both RF circuit-based and lumped element implementations are considered. Comparisons of the anisotropic and isotropic elements will be made. The objective is to characterize thoroughly the metamaterial behavior of these ENG metamaterials over the frequency bands of interest.

Connections between the proposed realistic ENG structures and theoretical, well-established dispersive material models are made. The reflection and transmission properties of the ENG unit cells are established using ANSOFT’s High Frequency Structure Simulator (HFSS). The effective permittivity and the permeability values and their frequency dependencies are extracted from these S-parameter results. Variations of these effective values with respect to the angle of incidence of the source field are considered. The extraction results for several of the highly sub-wavelength three dimensional unit cells that potentially could be used to achieve the desired ENG parameters for MTM-based antenna applications will be reported. The design and fabrication challenges will be discussed. Examples of fabricated elements and confirmation of their predicted behaviors will be presented.

REFERENCES

[1] R. W. Ziolkowski and A. Kipple, "Application of double negative metamaterials to increase the power radiated by electrically small antennas," IEEE Trans. Antennas Propagat., vol. 51, pp. 2626-2640, October 2003.

[2] R. W. Ziolkowski and A. D. Kipple, "Reciprocity Between the Effects of Resonant Scattering and Enhanced Radiated Power by Electrically Small Antennas in the Presence of Nested Metamaterial Shells," Phys. Rev. E., vol. 72, 036602, September 2005.

[3] R. W. Ziolkowski and A. Erentok, "Metamaterial-based efficient electrically small antennas," to appear in IEEE Trans. Antennas Propagat., 2006.

[4] R. W. Ziolkowski and A. Erentok, "At and beyond the Chu limit: passive and active broad bandwidth metamaterial-based efficient electrically small antennas," submitted to IEE Proceedings, December 2005.

[5] Phillipe Gay-Balmaz and Olivier J. F. Martin, "Efficient isotropic magnetic resonators," Appl. Phys. Lett., vol. 81, no. 5, pp. 939-941, Jul. 2002.

See the attachment

The mutual coupling due to surface waves deteriorates the performance of microstrip antenna arrays. In this work, we compare the performance of several compact EBG structures designed on a thin substrate (h = 1.524 mm, εr = 3.38) and propose a novel compact EBG structure suitable for thin substrates to decrease the mutual coupling. The structures are applied to improve the isolation between E-plane coupled antenna elements in linear microstrip antenna arrays at 2.4 GHz. The isolation results are verified by measurements and also radiation patterns and the gain of the fabricated array are measured and compared to the reference case. In addition to this, the impedance behavior of the antennas is studied with and without the EBG structure while scanning the main beam of a linear antenna array.

The proposed 2D-fork-like mushroom structure is found to be the most isolative structure as a result of the comparison simulations. Two other mushroom structures are less efficient, and a UC-EBG structure without via is the least efficient. Figure 1 shows both the simulated and measured mutual coupling for the reference and the EBG case with the fork-like structure. Then, the EBG is applied to a four-antenna linear group, which is beam-scanned by adding phase shift between antenna elements. Simulations with EBG structure show more stabile impedance behavior than with the reference simulations. Also according to measurements with the fabricated two antenna array, the EBG structure between antenna elements does not disturb the main beam, and very slightly decreases side lobes as shown in Figure 2.

Abstract:

A novel S-shaped SRR loaded rectangular E-plane waveguide resonators are proposed. Comparison with standard E-plane rectangular waveguide resonators has shown an increase in the loaded Q value for resonators of same physical dimensions. The proposed structure maintains the low-cost and mass-producible characteristics of E-plane circuits and is an ideal element for high performance waveguide E-plane filters. Figure 1 shows the proposed S-shaped SRR waveguide resonator. The simulated S-parameters of the proposed resonator are presented in Figure 2.

We report the electromagnetic modeling of large metamaterial (MM) structures employing multilevel fast multipole algorithm (MLFMA). MMs are usually constructed by periodically embedding unit cells, such as split-ring resonators (SRRs), into a host medium. Without utilizing any homogenization techniques, we accurately model large numbers of unit cells that translate into very large computational problems. By considering all of the electromagnetic interactions, the resulting dense matrix equations are solved iteratively with the accelerated matrix-vector products by MLFMA. The number of unknowns ranges from 1000 to well over 1,000,000. We employ parallel computing to solve these very large problems.

In this work, we specifically investigate the MM structures consisting of a single layer or multiple layers, each of which is an array of SRRs as depicted in Fig. 1(a). Unit cell dimensions are in the order of microns to obtain an effective permeability around 100 GHz. We consider different orientations, various numbers of layers, and several directions of illuminations. As an example, Fig. 1(b) presents the power transmission in the x direction through a single-layer SRR structure in Fig 1(a), where we observe a shadowing around 100 GHz as expected.

By employing MLFMA, we are also able to model irregularities, such as misalignments and deficiencies in the SRR models. In addition to these, we can simulate antennas placed inside the SRR structures. We also investigate the negative refraction and sub-wavelength focusing properties of the MMs. Since the periodicity and unit-cell dimensions are small compared to the wavelength, some low-frequency adjustments are considered for the MLFMA to increase the efficiency of the simulations. In the presentation, we will provide various examples on the accurate simulations of MMs.

The idea to design the composite materials (metamaterials) that are able to acquire negative values of their effective (measured or calculated constitutive parameters) in the microwave and millimeter wave ranges has received intensive development [1-3]. It is caused by the facts that rather unusual phenomena may appear in metamaterials.

The periodic structures designed on the base of metamaterials represent rather special type of objects, showing various properties, this turns them into key elements of antennas and waves guiding structures in millimeter wave range. Slow surface and leaky waves, that are typical for periodic structures, can also be supported by the periodic boundary of metamaterials. Their special characteristics are widely exploiting in antenna design [1-3].

The metamaterials that have been successfully manufactured [1] are characterized by essential frequency dispersion. In some frequency range the real parts of permittivity and permeably acquire negative values.

It is easy to show that under certain conditions for parameters of the material in certain frequency range even plane surface of metamaterial can support backward waves (see for example [3]) , that are the waves in which the phase velocity is opposite to the energy velocity. Under different condition within other frequency range the direct surface wave can exist. The investigation of the influence of periodicity on the existence and behavior of backward waves on the boundary of metamaterials is an important problem.

The profound study of the nature and properties of eigen surface waves that are supported by such dispersive periodic structure are in the focus of our presentation.

The mathematical model of interaction of plane electromagnetic waves with periodic boundary of metamaterial with dispersion has been developed on the base of C-method [4]. The homogeneous boundary value problems are reduced to the problems for characteristic values of operator-functions. The numerical algorithms and corresponding codes have been constructed and implemented for computation of complex propagation constants of surface waves. The numerical experiments oriented to the study of regularities and peculiarities in the eigen wave characteristics for the metamaterials with dispersion (propagation constants of surface waves, corresponding electromagnetic field patterns, etc) have been carried out.

1. J.B. Pendry, "Negative refraction" Contemporary Physics, vol. 45, No. 3, pp. 191-203, January-February 2004.
2. P. Baccarelli, P. Burghignoli, G. Lovat, S. Paulotto, Surface-Wave Suppression in a Double-Negative Metamaterial Grounded Slab. IEEE Antennas And Wireless Propagation Letters, vol. 2, 2003.
3. A. Grbic and G. V. Eleftheriadesa. Experimental verification of backward-wave radiation from a negative refractive index metamaterial. Journal of Applied Physics Volume 92, Number 10 15 November 2002.
4. A. Ye. Poyedinchuk, Yu. A. Tuchkin, N. P. Yashina, J. Chandezon, and G. Granet. C-method: Several Aspects of Spectral Theory of Gratings. PIER 59, 2006, pp.113-149.

Propagation of the electromagnetic waves in modulated media presents interesting features, as the presence of pass/stop band. A complete characterization is usually carried out by the dispersion diagram, i.e. the representation of the actual wave number versus the frequency.

In this work, we will concentrate on the suppression of the surface waves, i.e. waves that propagate at the air-dielectric interface of a single layer microstrip structure. Since the surface wave is concentrated in the dielectric, we will use a 1D modulation of the effective dielectric constant of the substrate.

For a microstrip-like structure the modulation of the effective dielectric constant can be obtained by varying the width of a line oriented in the direction of the propagation. This can be done in continuous way, or by loading the dielectric sheet with smaller than wavelength metal strips of different dimensions. With an adequate choice of the transverse dimensions of the line/patches, one can guaranty a variation of the type:

Inserting this expression into the Maxwell equations, one can obtain two different expressions for the transverse electric and magnetic fields with respect to the modulation direction. Because of the different nature of the resulting equations, TE and TM cases are treated separately.

Analytical computations of the TM response of the structure is carried out in terms of Hill's functions, while the TE case reduces to Mathieu's functions, that are a special case of the Hill's functions. Stop/pass band limits can be obtained from the intersections between a line corresponding to the modulation parameters and the borders of the stability zones of these functions. The in-band behavior is described by the relative functions of non-integer order.

In this work we consider the variation of the effective dielectric constant of a single layer microstrip structure. The 1D modulation is realized by patches shorter than wavelength: their length (along the modulation direction) is considered constant and their width is varied in order to obtain a sinusoidal varying value of the effective dielectric constant. Distances between the centers of the patches are maintained constant.

Numerical results for the TE case were computed by commercial available eigensolver code. The unit cell corresponds to one period of the modulation. The phase difference between the two boundaries of the unit cell (along the modulation direction) is varied in order to construct the dispersion diagram. Preliminary numerically results for low values of the modulation constant fit the analytical solution.

References:
[1] L.Brillouin, Wave Propagation in Periodic Structures. New York: Dover, 1953.
[2] Ch. Elachi, Waves in Active and Passive Periodic Structures: A Review, Proc. of the IEEE, Vol. 64, No. 12, pp. 1666-1698, Dec. 1976.
[3] T. Tamir, H. C. Wang, A. A. Oliner, Wave propagation in Sinusoidally Stratified Dielectric Media, IEEE Trans. on Microwave Theory and Tech., Vol. MTT-12, pp. 323-335, May 1964.

The trend in consumer electronics is towards small hand-held devices incorporating several different radio systems operating simultaneously within the device. Many systems will share the same multiband antenna, however, not all systems can be served by a single antenna (e.g., due to the close proximity of the frequency bands). This results in multiple antennas with antenna separation of the order of a few centimeters posing a problem for antenna design. In this work, we propose new highly miniaturized EBG structures to improve antenna isolation in hand-held devices at the GPS and 2.4 GHz ISM bands. The EBG structures are fabricated on a ceramic substrate with relative permittivity of 82, and have a highly miniaturized period of 2.5 - 3.5 mm. The metallizations are realized by using conducting silver paste sintered at high temperature.

The test board size is 37 x 90 x 1 mm. Two cases a considered: (i) GPS and 2.4 GHz ISM band antennas, and (ii) two 2.4 GHz ISM band antennas. Due to the strict size limitations, both are equally difficult to realize despite the narrower bandwidth of the GPS system. The size of both antennas is 3.2 x 10 x 2 mm, fabricated on a ceramic substrate with relative permittivity of 35. A test board is shown in Fig. 1. The EBG structures are placed between the antennas. However, due to the close proximity of antennas particular attention needs to be paid in order not to disturb the antenna operation. Placement of EBGs is therefore critical to ensure that antenna matching is not affected. The initial EBG locations were chosen based on the surface current distribution on the board. The total area of the EBG structure is limited to 10-15 x 10-15 mm². The height of the EBG structures in practical hand-held devices is limited to 2 mm, reducing the bandwidth of the EBG structures. To extend the bandwidth, several designs such as the spiral mushroom [Baracco et al., IEEE T. AP, vol. 53, pp. 173-180, Jan. 2005] were adapted to the problem and new low-profile EBGs including slotted-patch mushroom and dual-fork mushroom were designed (Fig. 2).

The measured and simulated scattering parameters for the case (i) without EBG structures are shown in Fig. 3. Simulated results for a 2-by-4 element slotted-patch EBG are also shown. At center frequency maximum attenuation of over 10 dB was achieved. The matching and gain of the antennas were not significantly changed within the band. Measured data for various EBG structures at both GPS and 2.4 GHz ISM bands will be presented in the final manuscript.

Acknowledgments: This work is funded by the Finnish Funding Agency for Technology and Innovation under contract no. 40014/06. The test boards (designed by P. Nissinen) and ceramic antennas were provided by LK Products Oyj, Kempele, Finland.