In the past few years, materials that exhibit both negative permittivity and permeability have been thoroughly studied. The dispersion diagrams of these materials (known as LH (Left-Handed) materials, DNG (Double Negative) materials or simply Metamaterials) reveal some exciting characteristics [1]. This paper is focused on one of the potential applications of these new class of materials: the synthesis of materials with Near-Zero Refractive Index to simplify the feeding of antenna arrays.

Electromagnetic fields in a Near-Zero Refractive Index material (NZRI) propagate with a near-zero phase constant [2]. As a result of this, the fields along the structure spread with a near-constant amplitude and phase. This exotic property can be exploited to uniformly feed a whole antenna array from a single feeding point on the structure. figure 1: Center-fed array, aperture phase distribution. (conventional RH material). figure 2: Center-fed array, aperture phase distribution. (NZRI material). figure 3: Radiation pattern generated by the aperture phase distribution of figure 1 (conventional RH material). figure 4: Radiation pattern generated by the aperture phase distribution of figure 2 (NRZI material)

The paper is arranged in the following parts: first, an equivalent circuit model for the structure is introduced, from which several design equations are extracted. Next, the model is extended to cover the distributed-parameters structures, and after that a complete antenna array is designed using this technique. The design theory is validated using the radiation patterns and S-parameters computed by a full-wave electromagnetic software.

REFERENCES

[1] Atsushi Sanada, Christophe Caloz, Tatsuo Itoh, "Planar Distributed Structures With Negative Refractive Index", IEEE Transactions on Microwave Theory and Techniques, vol. 52, n°4, April 2004. [2] Nader Engheta, Richard W. Ziolkowski, "A Positive Future for Double-Negative Materials", IEEE Transactions on Microwave Theory and Techniques, vol. 53, n°4, April 2005.

During the last decade the theory of bi-isotropic media (BI-media) was developed as a result of the ever-growing interest in metamaterials. In contrast to the usual isotropic media, described by only 2 parameters, BI-media is described using a set of 4 complex parameters, defined by the following relations:

D=εE+iαB, H=iβE+B/µ. Technically the bi-isotropic admittances can be obtained by doping small structural elements into usual dielectric. Depending on their structure, those elements exhibit resonant properties on certain frequencies. Also, there may be chiral elements etc. The resulting compound materials represent powerful building blocks of functional elements for integral devices in microwave and terahertz ranges. However, the creation of such devices using conventional fabrication techniques is rather expensive and time consuming as it requires accurate manipulation with tiny particles. That’s why the computer-aided design and simulation is perspective, and there is a need in high-performance application that will provide the framework for both creation and simulation of various types of such devices.

In the paper several aspects of computer simulation of 3D complex-material based PBG devices are discussed. Currently several software packages exist that can simulate PBG devices. Most of them include high performance numerical simulation engines and user-friendly 2D/3D layout editors, making it possible to easily simulate a crystal with a large number of nodes. However, they are not designed to work with metamaterials.

We state the problem as following: a 3D periodic structure of cells, having certain defects, is placed inside a dielectric body (DB). Given the fixed distribution of EM field sources we need to find the total and scattered near- and far- electric and magnetic fields. This problem is solved using the Method of Auxiliary Sources (MAS) with the collocation point and averaged boundary conditions methods. The unknown amplitudes of node elements and auxiliary sources are determined by putting down the boundary conditions in certain collocation points. The accuracy of calculations is evaluated through comparing the rate of boundary condition satisfaction in the area between the collocation points.

Our software provides the interface for creation of 3D periodic structures, EM solver that evaluates the distribution of EM fields and the user-friendly interface for observation of the results. The grid, sensors and sources positions and properties can be saved for future use. We support the following node elements: PEC sphere, E-, M- and combined EM- dipoles, right - and left - handed helixes.

The supported types of field sources are: electric, magnetic, combined and dual phase-shifted EM dipoles. Incident plane waves with optional polarization rotation can also be activated. We provide the possibility to dynamically zoom the whole system in certain directions at run time, preserving the exciters' frequencies. This provides the convenient way to detect the resonant responses at given frequency.

A metamaterial made of a loop-wire medium (fig.1) has very interesting applications such as compact antennas with high directivity and Magnetic Resonance Imaging (MRI) devices operating at radio frequencies. In this particular application the metamaterial is used as a lens with very short focal length in order to improve the resolution of the medical scans. The RF field, detected by the antennas in last-generation MRI systems, has a frequency close to 128 MHz. The proposed material in combination with low frequency spiral resonator (SR) behaves like homogeneous and ultra-refractive medium in a narrow frequency band.

Two structures have been proposed in the literature to obtain negative permittivity: arrays of closely spaced thin wires [1] and loop wires [2]. The first one is widely used but its scaling at radio frequencies, leads to huge structures difficult to fabricate and to introduce in MRI systems. The second structure allows to reduce the plasma frequency and to achieve the desired negative permittivity at low frequencies.

In this paper, we show how the plasma frequency decreases, when the loop wires inductance is increased. To demonstrate this idea, a parametric study has been carried out, showing the influence of the loop wires dimensions on the plasma frequency (fig. 2). An equivalent circuit is also derived and the dependence of the plasma frequency with the inductance of the wires is made explicit.

A similar approach not detailed in this paper is used to design inductors, in order to obtain a negative permeability at 128Mhz.

As a result, the total metamaterial exhibits a low negative index of refraction (fig.3). We obtain a "perfect" lens made of periodic structures whose unit cell is about two orders of magnitude smaller than the wavelength. Simulations were made using an in-house (Method of Moments code) and a commercial software based on FDTD. Both approaches are in good agreement, and allow to calculate from the S-parameters, the permittivity and permeability [3] of the proposed loop-wire medium. A significant reduction of the plasma frequency is obtained, as compared to straight wires.

The behavior of this wire medium will be validated in near future by free-space measurements on fabricated prototypes.

References

[1] J. B. Pendry, A. J. Holden, W. J. Stewart, and I. Youngs, "Extremely low frequency plasmons in metallic mesostructures," Phys. Rev. Lett., vol. 76, pp. 4773-4776, (1996).
[2] D. R. Smith, D. C. Vier, Willie Padilla, Syrus C. Nemat-Nasser and S. Schultz," Loop-wire medium for investigating plasmons at microwave frequencies,"Appl. Phys. Lett., Vol. 75, No. 10, 6 September 1999
[3] D. R. Smith, S. Schultz, P. Markos and C. M. Soukoulis, "Determination of effective permittivity and permeability of metamaterials from reflection and transmission coefficients," Physical Review B, Vol. 65, 195104, 2002.

The use of materials with negative permeability or permittivity is very promising in the design and fabrication of microwave planar stop-band filters with characteristics and performance not achievable with other techniques. A structure composed of electrically-small resonant particles periodically arranged along a microstrip or coplanar waveguide (CPW) line, shows a negative effective permeability or permittivity around the resonant frequency that inhibits the signal propagation. This effect is only due to the constituent particles, so the period of the structure can be much smaller than the wavelength and small-size filters can be obtained. Some research has been done in this field and various topologies of filters with reduced size have been proposed. In this paper, we propose three new configurations of stop-band filters with still reduced size or larger bandwidth, compared to prior works.

The first structure consists of a three-layer CPW line with triple-turn spiral broadside-coupled resonators printed on both sides of the line. Arlon is the material employed as dielectric, with a relative permittivity of 2.43 and a loss tangent of 0.003. The filter dimensions are 15x12x1.3mm. The filter characteristics are the following: central frequency at 2.52GHz with an attenuation of 29dB and insertion losses of 0.65dB. The -10dB bandwidth equals 160MHz. This filter shows to a size reduction of approximately 28% compared to the CPW stop-band structures previously proposed.

The second structure is a microstrip line with complementary spiral square resonators etched in the ground plane of an Alumina substrate. The filter dimensions are 28x4x1.3mm. The central frequency of the filter is at 1.3GHz, with 49dB of attenuation. The allowed band exhibits negligible insertion losses (~0.3dB). The -10dB bandwidth is 130MHz. As in the previous case, this filter configuration is very compact compared to previous stop-band structures (size reduction is approximately 50%).

The third structure has a similar configuration as the first one (three-layer CPW line). The resonant particles consist of BC-SRRs (Broadside Coupled Split Ring Resonators) that are printed on the upper and lower face of the top and bottom Arlon substrates. The filter dimensions are 23x12x0.5mm. When aligning resonator slits in the same direction than the line, an important bandwidth increase is obtained. For the proposed design, the central frequency is 7.12GHz with a -10dB bandwidth of 3.13GHz (44%). Attenuation in a large band of frequency around central frequency is over 40dB and insertion losses are around 0.5dB. This filter is destined for applications that need a broad bandwidth while keeping the dimensions small. Compared to previous designs, the bandwidth is roughly enlarged by a factor 4.8.

The three structures have been studied in detail. The influence of a number of parameters on the filter characteristics has been studied numerically, namely the number of stages, the size of the resonant particles, the thickness of each layer and the arrangement of the metamaterial. These data enable one to define design guide lines. Finally experimental results will be compared to numerical simulations.

Impedance boundary conditions originally introduced by Shchukin and Leontovich in the 1940's have been widely applied in antenna synthesis over many decades. The concept of impedance boundary has usually been applied to approximate certain physical structures. In the present study an exact representation for any impedance boundary expressable by a surface admittance dyadic is introduced through a realization involving a slab of metamaterial, labeled as wave-guiding medium. The theory is applied to a certain class of impedance boundaries called that of perfectly anisotropic boundaries (PABs). The definition of PAB is based on a decomposition of boundary impedance dyadics. It is shown that a suitably designed PAB can be applied as a polarization transformer which can transform linearly polarized wave to an elliptically polarized wave with any axial ratio and handedness and change of polarization is effected by simple rotation of the boundary. As another application, it is shown that, unlike an isotropic surface, the PAB can simultaneously support two surface or leaky waves with orthogonal polarizations. This property may be of use for the design of surface-wave or leaky-wave antennas when the possibility of a change in polarization is required without changing the structure.

In this proof of concept study we employ numerical and measured results at X- band to demonstrate that the electrical properties of nematic state liquid crystal can be exploited to produce phase shifters for beam scanning printed reflectarray antennas. Phase agility is realized by inserting a thin layer of liquid crystal in the region between the resonant patch array and the conductive ground plane and applying a low frequency bias voltage to create a controllable electrostatic field. A small change in the permittivity of the substrate is shown to create a large variation in the phase of the reflected signal. A Finite Element Method computer model is employed to study the scattering behaviour of the array elements in the range 9-11 GHz using the dielectric properties of the commercially available MERCK K15 liquid crystal material. The simulated phase range and reflection loss are shown to be in close agreement with measurements that were obtained from a waveguide simulator. The most significant impact of this new active control strategy is shown to be in the mm wave and sub mm wave band, where the properties of liquid crystals are still unknown. In this paper we present the results of an experimental study to establish the complex permittivity of commercially available mixtures using transmission/reflection measurements of liquid crystal filled rectangular waveguide in the frequency band 100-170GHz. The experimental data has been used in the computer model to predict the phase agility and efficiency factor of a tunable reflectarray cell that operates within this frequency range. These results summarise the progress that has been made in the first stage of a collaborative academic/industrial project to investigate the feasibility of creating mm and sub mm wave beam scanning reflectarray antennas for future space science applications.

A reflectarray antenna combines some of the best features of reflectors and microstrip arrays. A feed antenna illuminates the reflecting surface which consists of isolated radiating elements. These elements are pre-designed with a particular phase delay such that the illuminating electric field from the feed will be re-radiated and scattered from these elements to form a planar phase surface in front of the aperture. The microstrip reflectarray has several advantages over conventional reflectors and phased arrays such as it can be conformed to a planar surface shape and there is no complex feed network required.

One of the main aspects of microstrip reflectarray is how the individual isolated elements are made to scatter. Several methods have been developed and reported in the past for the reflectarray elements to achieve a planar phase front. Some of them are - identical microstrip patches with stubs of variable lengths, variable size dipoles or microstrip patches, identical circularly polarized patches with variable angular rotations (for circular polarization only), identical patch elements on the top layer and variable length slots on the ground plane, identical patches loaded with variable length slots to control the reflection phase.

The concept of reconfigurable reflectarray element is beneficial for reflectarray design as it allows for dynamic phase control of a single radiating element where the element can be manipulated electronically. Such a dynamic beam forming approach can reduce the complexity and costs in the scanning system architecture. In this work, we discuss several novel concepts used to design reconfigurable reflectarray elements. They are a) Design of a microstrip patch with concentric rings (using the concept of variable size patches). The concentric rings are connected to the main patch using switches (PIN diodes, MEMS). Thus, by turning the switches on and off, the size of the patch can be varied and the reflection phase can be controlled. b) Design of identical patches on the top layer and a slot of fixed length on the ground plane. The length of the slot is changed by using switches, which changes the coupling to the patch and thus controls the reflection phase. c) Design of identical patches loaded with fixed slot. The length of the slot can be changed using switches (turning them on and off) and the elements can be made to scatter the desired phase. Initial designs have shown that a phase swing of around 300° can be achieved using these concepts.

The perfect electromagnetic conductor (PEMC) is an idealized media, which is a generalization of both the perfect electric conductor (PEC) and the perfect magnetic conductor (PMC). Since electromagnetic energy cannot enter the PEMC, it is mainly interesting as an ideal boundary.

The tangential component of H + M E vanishes at the PEMC boundary, where M is the PEMC admittance. PMC corresponds to M = 0, while PEC corresponds to infinite M. For finite nonzero M, the PEMC boundary is nonreciprocal: The polarization of a reflected plane wave is rotated by an angle depending on the PEMC admittance M.

As shown by Lindell and Sihvola (IEEE T-AP, 53, 3012-3018, 2005), the PEMC boundary can be realized using a gyrotropic layer backed by a PEC plane.

The above structure can satisfy the ideal PEMC boundary condition for a fixed frequency, if the axial parameters ε_z and µ_z are infinite and we choose the other real (lossless) parameters appropriately.

In a practical realization, we cannot get infinite axial parameters and there are always some losses. The question is: can we get a good PEMC approximation using realistic material parameters?

To answer the question, we study the reflection of plane waves from the structure. First, we consider the effect of the finite axial parameters in the lossless case, and separately, the lossy case with infinite axial parameters. Finally, we study the reflection using realistic material parameters.

The finite axial parameters make the polarization and phase of the reflected wave dependent of the incident angle, while the losses attenuate the reflected wave and make a linear polarization elliptic. Fortunately, the deviations from the ideal case are small, if the axial parameters are large and the losses are small.

This paper characterizes the novel metallic wire substrate (MWS) microstrip structure introduced in [1] and depicted in Fig. 1, and presents a patch antenna application for it. It shows numerically and experimentally that the MWS exhibits artificial magneto-dielectrics properties with simultaneously enhanced effective permittivity and permeability over a large frequency band, and demonstrates an MWS miniaturized patch antenna.

The MWS provides a novel possibility for continuously designable permittivity and permeability over a large range of values and allows miniaturization of planar circuits thanks to its enhanced refractive index compared to that of the host substrate material.

The MWS microstrip structure is characterized in terms of its effective permittivity and permeability parameters, ε_eff and µ_eff as a function of its parameters shown in Fig. 1b. These parameters are extracted from the full-wave simulated or measured scattering parameters [1]. A parametric study, mainly regarding the variation of the constitutive parameters as a function of the via holes diameter and substrate thickness h₂, is subsequently performed to provide appropriate design guidelines. From a conventional Duroid host substrate with permittivity ε_r=2.94, an MWS’s with values of ε_eff ranging from 4 to 12 and of µ_eff ranging from 1 to 2 have been achieved using parameters in the laser-drilling and holes-plating technology currently available at the Poly-Grames Research Center.

As an application, a 1.9 GHz inset-fed MWS patch antenna was designed. This antenna exhibits a 56% size reduction compared to a patch antenna on a conventional substrate, with similar return loss (~ 20 dB) and co-cross polarization isolation (~ 30 dB).

References:

[1] H. V. Nguyen, J. Gauthier, J. M. Fernández, M. Sierra-Castañer and C. Caloz, "Metallic Wire Substrate (MWS) for Miniturization in Planar Microwave Applications", 9th European Microwave week, Manchester, UK, September 2006.

Artificial magnetic conductors (AMCs) potentially allow horizontal antennas to be placed very close to the ground-plane surface without being short-circuited by their image. But given the narrow bandwidth of AMC surfaces, their application remains a challenge for broadband antennas. Moreover, we have observed that the patterns of an antenna placed above an AMC split at broadside at frequencies near and beyond the PMC resonance. So, the direction of the maximum is no longer at broadside, reducing the real useful band. An analytical study on the currents on the patches of the AMC structure has been carried out. A phase shift between successive cells close to 180 degrees is observed in the y-component of the surface currents along successive patches perpendicularly to the antenna. It results in the cancelation of their E-field contributions, producing a deep in the broadside directivity.

In this paper, a rectangular non-periodic PMC is proposed as a solution to achieve a high-gain wideband low-profile design, when placing a double-dipole planar antenna parallel to it. Reducing the AMC size in the H-plane of the antenna and making it non-periodic in the E-plane does not especially affect the impedance bandwidth performances, but it strongly improves the directivity achieved at broadside (right plot in Figure 1). More uniform current phases on the patches along the antenna are observed when making the PMC non-periodic. These phenomena support the directivity improvements referred to above. The dependence of this phase shift versus frequency and incidence angle will be further analyzed with the help of an eigenmode analysis based on Method-of-Moment technique [1]. A design providing more than 9.2 dB over a 32.6% bandwidth with a lambda_min/6.5 profile is presented (see performances in Figure 1). The horizontal dimensions of the structure are 1.9 lambda_min x 0.7 lambda_min. The achieved directivity is very close to the theoretical one achievable for such an effective area.

Figure 1: S₁₁ coef. (left) and broadside directivity (right) for a dual-dipole antenna placed parallel above a rectangular non-periodic PMC and a square periodic one (discontinuous line in right plot).