Electromagnetic radiation from the finite size metamaterial

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Homogenization for Layered Medium

In this section, the capability of classical homogenization to predict the transmission property of layered structure at the sub-wavelength scale is demonstrated. The periodic interfaces in the real problem are replaced by a slab of a homogeneous medium, with an effective mass density tensor and an effective bulk modulus. Thus, explicit dispersion relation can be derived, corresponding to guided waves in the homogenized problem [47].
Homogenization approaches provide effective parameters by considering the permittivity e, permeability m of the materials and the geometry of the microstructure, which is different from the retrieval methods. As we mentioned before, a periodic structure can be
regarded as effective medium, as long as the periodicity of the structure is much smaller than the wavelength of the electromagnetic wave. Classical homogenization related to periodic structures in this thesis should satisfy kh1, where k is the wavenumber of EM wave and h is the periodicity of the structure. Next, the simplest one dimension periodic multilayer structures are first taken into consideration. Secondly, analytical expression and numerical validation are given to describe the transmission property of EM wave in such medium.
In the following, we calculate the field in a layered structure that consists of two kinds of penetrable dielectric for electromagnetic waves, shown in Figure.3.1(a). Transmission property of such structure described by an analytical expression derived from Helmholtz Equation is given. Furthermore, the result reveals that the transmission property can be strongly affected by not only the permittivity of the materials but also the filling fraction of the two dielectrics.
Consider a plane wave propagating in the free space, the magnetic field H can be obtained from the Helmholtz Equation Ñ [aÑH(x;y)]+k2bH(x;y) = 0.

Corrugated Metallic Surface

In the following part, the simplest 1-D textured metallic surface is studied, furthermore, transmission property of such structure will be derived from the method that we used for the dielectric configurations. Figure.3.4 shows the side view of the 1-D corrugated metallic surface whose periodicity is h = 3mm with metal fraction j = 2=3. However, the method that we deal with metallic layers is different from of dielectric materials, because of its impenetrable property for eletromagnetic waves.

Experimental Validation of Metallic Thin structure Vertical thin cylinder array

Surface plasmons cannot be supported by the smooth electric conductor at frequency band lower than the optical spectrum. From the investigation in the last section, the corrugated metal surface is able to sustain ”spoof surface plasmons” at microwave frequency band, which has similar properties with the real surface plasmons that mainly due to its geometry, but also was restrained to be applied to some portable or miniaturized situation.
Actually, there are several kinds of structures are able to support spoof plasmons. Recently, a split-ring resonator designed to sustain spoof plasmons was proposed in [50]. A planar waveguide based on the element of the split-ring resonator is numerically analyzed to show high out- and in-plane confinement. Moreover, in [59], the concept of conformal surface plasmons (CSPs), surface plasmon waves that can propagate on ultrathin and flexible films too long distances in a wide broadband range from microwave to mid-infrared frequencies.
The aim of this experiment is to demonstrate the capability of the printed array to support spoof plasmons on the surface of a metallic ground plane. The rods of the proposed structure are made here by bolting cylindrical screws in a metallic plane. The schematic view and a photography of the designed structure are shown in Fig.3.7. The length of the screws is L = 27 mm and their diameter is 3 mm. They are disposed of in a onedimensional array using a lattice constant of a=21 mm. The array is mounted on a metallic ground plane that is placed next to a waveguide which is used to produce surface wave on the metallic ground, see Fig.3.8 (a). The detector is fixed on a motor that can move along the horizontal bar, which is mounted to another motor. The second motor is able to move along a fixed vertical, shown in Figure.3.8 (b). The field distribution near the array can be measured when the two motors moving correspondent to each other.

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Reshaping the radiation pattern of antenna

We now inspect the ability of our metamaterial substrate to avoid such unpleasant effects by preventing surface wave, or spoof plasmon, to propagate. We realize a patch antenna resonating around 10 GHz. The radiating patch fed by a coax cable via a hole near the center of the ground plane is 65:8mm2, shown in Figure.3.17 (a). The antenna element is then placed in the center of a 6 by 6 cylinder array with L = 6 mm, as shown in the Fig. 3.17(a), and from Fig. 3.16(b), we know that this structure provides a band gap that surrounds the resonant frequency of the antenna even after adding the thin layer of the epoxy substrate.

Table of contents :

1 Introduction 
1.1 Background
1.2 Aim of this thesis
1.3 Outline of thesis
2 State of art 
2.1 Metamaterials
2.1.1 Introduction
2.1.2 Application of Metamaterials
2.2 Homogenization
2.2.1 Field averaging method
2.2.2 Retrieval method
2.2.3 Near Resonance method
3 Classical homogenization for metamaterials structures at the subwavelength scale 
3.1 Homogenization for Layered Medium
3.1.1 Multilayer Slab
3.1.2 Corrugated Surface
3.1.3 Slanted Slab
3.2 Spoof plasmons
3.2.1 Corrugated Metallic Surface
3.2.2 Experimental Validation of Metallic Thin structure
3.3 Application to patch antennas
3.3.1 Background
3.3.2 Dispersion Relation
3.3.3 Reshaping the radiation pattern of antenna
3.3.4 Electromagnetic radiation from the finite size metamaterial
4 Classical homogenization of Second Order 
4.1 Theory
4.2 Experimental Validation for Structured Metallic Layers
4.2.1 Experiment Set up
4.2.2 Results
4.3 Application to the tuning of the reflection phase of AMC
4.3.1 Theory
4.3.2 Validation
5 Conclusion

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