**3. Polarization dependent metamaterial cover designs**

A considerable part of research at microwave frequencies is focused on isotropic metamaterial covers that are independent on polarization states. Polarization-dependent surfaces have recently found useful applications in changing the polarization state of the incident wave (Yang & Rahmat-samii, 2005; Veysi et al., 2010).

For a traditional metamaterial cover, the transmission phase remains the same regardless of the *x*- or *y*-polarization state of the incident plane wave. In contrast, the transmission phase of a PDMTM cover is a function of both frequency and polarization state. Hence, when a PDMTM cover is employed as a director, the polarization state of the transmitted wave is fully characterized by the transmission phase difference between the *x*- and *y*-polarizations and the polarization state of the incident wave. And thus a proper phase difference between *x*- and *y*-polarized waves leads to a desired change in the polarization state of the transmitted wave.

Directive circularly polarized antennas are widely used in satellite communication systems. To obtain directive circularly polarized antenna, various types of metamaterial antenna have been proposed in the literature (Iriarte et al., 2006; Diblanc et al., 2005; Arnaud et al., 2007). It was demonstrated in (Iriarte et al., 2006) that the directive circularly polarized antenna can be realized by metamaterial antenna with a circular feed. A major limitation of this method is inability to tune mechanically. In other words, the polarization state of the antenna is only determined by the feed mechanism.

Directive circularly polarized antenna can be also realized using either metallic wire polarizer (Diblanc et al., 2005) or meander line polarizer (Arnaud et al., 2007) stacked on the 284 Trends in Electromagnetism – From Fundamentals to Applications


Metamaterial antenna at f=5.6GHz Metamaterial antenna at f=5.7GHz Metamaterial antenna at f=5.8GHz

Conventional antenna

θ [degree]

(b)

A considerable part of research at microwave frequencies is focused on isotropic metamaterial covers that are independent on polarization states. Polarization-dependent surfaces have recently found useful applications in changing the polarization state of the

For a traditional metamaterial cover, the transmission phase remains the same regardless of the *x*- or *y*-polarization state of the incident plane wave. In contrast, the transmission phase of a PDMTM cover is a function of both frequency and polarization state. Hence, when a PDMTM cover is employed as a director, the polarization state of the transmitted wave is fully characterized by the transmission phase difference between the *x*- and *y*-polarizations and the polarization state of the incident wave. And thus a proper phase difference between *x*- and *y*-polarized waves leads to a desired change in the polarization state of the

Directive circularly polarized antennas are widely used in satellite communication systems. To obtain directive circularly polarized antenna, various types of metamaterial antenna have been proposed in the literature (Iriarte et al., 2006; Diblanc et al., 2005; Arnaud et al., 2007). It was demonstrated in (Iriarte et al., 2006) that the directive circularly polarized antenna can be realized by metamaterial antenna with a circular feed. A major limitation of this method is inability to tune mechanically. In other words, the polarization state of the antenna is only

Directive circularly polarized antenna can be also realized using either metallic wire polarizer (Diblanc et al., 2005) or meander line polarizer (Arnaud et al., 2007) stacked on the

Fig. 7. CST simulated radiation patterns at different frequencies over the operating

**3. Polarization dependent metamaterial cover designs** 

incident wave (Yang & Rahmat-samii, 2005; Veysi et al., 2010).


bandwidth, (a) E-plane, and (b) H-plane.

transmitted wave.

determined by the feed mechanism.





Directivity [dB]

0

5

10

15

20

top of the one-layer metamaterial cover. In this section, instead of using meander line or metallic wire polarizer, the geometry of the metamaterial cover is changed to provide circular polarization. Consequently, the second layer (polarizer layer) can be replaced with another metamaterial cover layer, which in turn results in higher directivity.

Moreover, in contrast to the previous directive circularly polarized antennas (Iriarte et al., 2006; Diblanc et al., 2005; Arnaud et al., 2007), polarization state of the directive antennas using our proposed metamaterial cover can be mechanically changed regardless of the feed mechanism.

In this section, a useful guideline has been established as how to use the magnitude and phase of the transmission coefficient to identify the operational frequency band of the directive circularly polarized antennas based on polarization dependent metamaterial covers.

As revealed in the previous sections, when a plane wave normally impinges upon a metamaterial cover, the phase and magnitude of the transmitted wave change with frequency. In order to illustrate the polarization feature of the PDMTM cover, we assume that a left-hand circularly polarized (LHCP) wave, namely,

$$\overrightarrow{E^i} = \overrightarrow{a\_x}e^{-j\,kz} + \overrightarrow{j\,a\_y}e^{-j\,kz}$$

where *k* is the free-space wavenumber, is normally impinged upon a director placed in *X*-*Y* plane. The field transmitted through the director can be easily calculated from the following equation:

$$\overrightarrow{E^{\ddagger}} = e^{-j k x\_x} e^{j \theta\_x} \overleftarrow{(a x\_x} + j \overrightarrow{a}\_y e^{j (\theta\_y - \theta\_x)}) \tag{5}$$

The above field can be decomposed into two circularly polarized components

$$\overrightarrow{E^{i}} = e^{-j kz} e^{j \theta \mathbf{x}} \left[ \overrightarrow{e} \left( \frac{\mathbf{1} - e^{j(\theta y - \theta \mathbf{x})}}{\sqrt{2}} \right) + \overrightarrow{e} \left( \frac{\mathbf{1} + e^{j(\theta y - \theta \mathbf{x})}}{\sqrt{2}} \right) \right] \tag{6}$$

Where

$$\overrightarrow{\mathcal{e}\_I} = \frac{(\overrightarrow{a\_{\overline{x}}} + j\overrightarrow{a\_{\overline{y}}})}{\sqrt{2}}, \text{ } \overrightarrow{\mathcal{e}\_{\overline{r}}} = \frac{(\overrightarrow{a\_{\overline{x}}} - j\overrightarrow{a\_{\overline{y}}})}{\sqrt{2}}$$

and *θx* and *θy* denote the transmission phases for the *x*- and *y*-polarized waves, respectively. For a traditional metamaterial cover (*θy*- *θx*=0), the transmitted wave is purely LHCP and thus the polarization does not change. In order to change the polarization state of the antenna, the PDMTM cover can be used as a director. At a certain frequency where phase difference is 180° and transmission is considerable, the transmitted wave is purely righthand circularly polarized (RHCP).

The left-hand circularly polarized incident wave can be also converted to the linearly polarized (LP) wave where the phase difference is 90° and the transmission is also considerable. One can follow the same procedure for the linearly polarized incident wave,

$$
\overrightarrow{E^i} = \overrightarrow{a\_x} \overrightarrow{e^{-jkz}} + \overrightarrow{a\_y} \overrightarrow{e^{-jkz}} \dots
$$

Theory and Applications of Metamaterial Covers 287

The axial ratio of the transmitted wave is plotted in Fig. 8. Also, Fig. 9 shows the transmission curve for both *x*- and *y*-polarized incident plane waves. The frequency band inside which the axial ratio of the RHCP transmitted wave is below 6dB and the magnitudes of the transmission coefficients for both the *x*- and *y*-polarized incident waves are more than

Another approach to realize PDMTM covers is to add space between the *x*- and *y*-directed strips of each layer (Veysi et al., 2011), as shown in Fig. 10. For a traditional metamaterial

For the nonplanar case discussed here the dimensions are chosen as follows: *L*=*W*=13.5mm, *P*=18.5mm, *h*=27.5mm, *hr1*=3.5mm, and *hr2*=7mm, where *hr1* denotes the relative height between the *x*- and *y*-directed strips of the first layer and *hr2* denotes the same height for the

Fig. 11 shows the magnitudes of the transmission coefficients for both *x*- and *y*-polarized waves. The axial ratio of the wave radiated from linearly polarized antenna is also plotted in Fig. 12. It can be seen from Figs. 11-12, that the operating frequency of the proposed structure is around 9.1GHz where the metamaterial cover has both the desired transmission

4 4.2 4.4 4.6 4.8 5 5.2 5.4 5.6 5.8 6

X: 4.764 Y: 1.279

 **Frequency(GHz)**

The FDTD simulated results presented in this section confirm the concepts of the proposed approach to control both the direction and the polarization of the transmitted wave. The

Fig. 8. Axial ratio of the transmitted plane wave from the rectangular hole metamaterial

cover, the *x*-directed strip is located on the same plane as the y-directed strip.

3dB RHCP 6dB RHCP

For a linearly polarized antenna, namely

90% ranges from 4.75GHz to 5GHz (5.12%).

second layer.

**3.2 Metamaterial cover with nonplanar strips** 

phase difference and the remarkable transmission.


cover (Veysi et al., 2011).

 **Axial Ratio**

, *<sup>i</sup> jkz jkz E ae ae x y* − − = +

so that the transmitted field then becomes:

$$\begin{split} \overrightarrow{E^{i}} &= \overrightarrow{a\boldsymbol{\omega}} \, e^{-j(kz-\theta\boldsymbol{x})} + \overrightarrow{a\boldsymbol{y}} \, e^{-j(kz-\theta\boldsymbol{y})} = \\ &e^{-jkz} \, e^{j\theta\boldsymbol{x}} [\overrightarrow{e^{r}} (\frac{1+e^{j(\theta\boldsymbol{y}-\theta\boldsymbol{x}+\pi f/2)}}{\sqrt{2}}) + \overrightarrow{e} \, (\frac{1-e^{j(\theta\boldsymbol{y}-\theta\boldsymbol{x}+\pi f/2)}}{\sqrt{2}})] \end{split} \tag{7}$$

Consequently the radiation mechanism of the linearly polarized antenna with metamaterial cover is conceptually described by Eq. 7. For an isotropic metamaterial cover, the phase difference between two orthogonal polarizations is zero and thus the polarization state does not change.

An interesting feature of the PDMTM covers can be revealed by a closer investigation. When a PDMTM cover with 90° transmission phase difference is used as a director, the polarization state of the transmitted wave becomes LHCP. Moreover, when the phase difference is -90° the polarization state of the transmitted wave is RHCP. Consequently we can easily switch between LHCP and RHCP using a rotatory cover, which can be rotated smoothly with a 90° steps.

Based on above discussion, one can conclude that the metamaterial cover can be used as a changing polarization plane. The operational frequency band of an antenna with PDMTM cover is defined as the frequency region within which the magnitudes of the transmission coefficients for both *x*- and *y*-polarized waves are close to their maximum values and transmission phase difference takes the desired value.

This interesting feature has been realized by changing the unit cell geometry, such as cutting rectangular holes instead of square holes and changing the relative height difference between the *x*- and *y*-directed strips of each layer (Veysi et al., 2011).

## **3.1 Rectangular hole metamaterial cover**

The traditional metamaterial cover uses symmetric square holes so that its transmission phase for normal incidence remains the same regardless of the *x*- or *y*-polarization state of the incident plane wave. Therefore, the logical step is to replace the square holes by rectangular ones (Veysi et al., 2011).

First, the design parameters of the metamaterial cover are selected to have a reasonable transmission at a specified frequency. The effect of different design parameters of the metamaterial cover on the magnitude of the transmission coefficient can be found in (Huang et al., 2009).

After the successful design of the isotropic metamaterial cover, the width or/and length of the square holes are changed to obtain both the desired transmission phase difference and the maximum transmission within the specified frequency band. When the hole width is increased, the plasma frequencies shift down to the lower frequencies.

Thus, by adjusting the width and length of the rectangular hole, the polarization sense of the transmitted wave can be changed. An example design for these parameters is as follows:

 *h*= 24.5mm, *P*=20.5mm, *L*=17.5mm, *W*=16.5mm

For a linearly polarized antenna, namely

286 Trends in Electromagnetism – From Fundamentals to Applications

( 2) ( 2) 1 1 [ ( ) ( )] 2 2 *<sup>l</sup>*

θθπ

(7)

() ()

*jy x jy x jkz j x <sup>r</sup>*

− + − + <sup>−</sup>

θθπ

*e e*

Consequently the radiation mechanism of the linearly polarized antenna with metamaterial cover is conceptually described by Eq. 7. For an isotropic metamaterial cover, the phase difference between two orthogonal polarizations is zero and thus the polarization state does

An interesting feature of the PDMTM covers can be revealed by a closer investigation. When a PDMTM cover with 90° transmission phase difference is used as a director, the polarization state of the transmitted wave becomes LHCP. Moreover, when the phase difference is -90° the polarization state of the transmitted wave is RHCP. Consequently we can easily switch between LHCP and RHCP using a rotatory cover, which can be rotated

Based on above discussion, one can conclude that the metamaterial cover can be used as a changing polarization plane. The operational frequency band of an antenna with PDMTM cover is defined as the frequency region within which the magnitudes of the transmission coefficients for both *x*- and *y*-polarized waves are close to their maximum values and

This interesting feature has been realized by changing the unit cell geometry, such as cutting rectangular holes instead of square holes and changing the relative height difference

The traditional metamaterial cover uses symmetric square holes so that its transmission phase for normal incidence remains the same regardless of the *x*- or *y*-polarization state of the incident plane wave. Therefore, the logical step is to replace the square holes by

First, the design parameters of the metamaterial cover are selected to have a reasonable transmission at a specified frequency. The effect of different design parameters of the metamaterial cover on the magnitude of the transmission coefficient can be found in (Huang

After the successful design of the isotropic metamaterial cover, the width or/and length of the square holes are changed to obtain both the desired transmission phase difference and the maximum transmission within the specified frequency band. When the hole width is

Thus, by adjusting the width and length of the rectangular hole, the polarization sense of the transmitted wave can be changed. An example design for these parameters is as follows:

+ − +

 θ

*<sup>t</sup> j kz x j kz y x y*

−− −−

=+=

θ

*eee e*

*E ae ae*

θ

transmission phase difference takes the desired value.

**3.1 Rectangular hole metamaterial cover** 

rectangular ones (Veysi et al., 2011).

et al., 2009).

between the *x*- and *y*-directed strips of each layer (Veysi et al., 2011).

increased, the plasma frequencies shift down to the lower frequencies.

 *h*= 24.5mm, *P*=20.5mm, *L*=17.5mm, *W*=16.5mm

so that the transmitted field then becomes:

not change.

smoothly with a 90° steps.

$$\overrightarrow{E^l} = \overrightarrow{a \times e}^{-j/k \cdot x} \overrightarrow{+a \cdot y} e^{-j/k \cdot x}$$

The axial ratio of the transmitted wave is plotted in Fig. 8. Also, Fig. 9 shows the transmission curve for both *x*- and *y*-polarized incident plane waves. The frequency band inside which the axial ratio of the RHCP transmitted wave is below 6dB and the magnitudes of the transmission coefficients for both the *x*- and *y*-polarized incident waves are more than 90% ranges from 4.75GHz to 5GHz (5.12%).

#### **3.2 Metamaterial cover with nonplanar strips**

Another approach to realize PDMTM covers is to add space between the *x*- and *y*-directed strips of each layer (Veysi et al., 2011), as shown in Fig. 10. For a traditional metamaterial cover, the *x*-directed strip is located on the same plane as the y-directed strip.

For the nonplanar case discussed here the dimensions are chosen as follows: *L*=*W*=13.5mm, *P*=18.5mm, *h*=27.5mm, *hr1*=3.5mm, and *hr2*=7mm, where *hr1* denotes the relative height between the *x*- and *y*-directed strips of the first layer and *hr2* denotes the same height for the second layer.

Fig. 11 shows the magnitudes of the transmission coefficients for both *x*- and *y*-polarized waves. The axial ratio of the wave radiated from linearly polarized antenna is also plotted in Fig. 12. It can be seen from Figs. 11-12, that the operating frequency of the proposed structure is around 9.1GHz where the metamaterial cover has both the desired transmission phase difference and the remarkable transmission.

Fig. 8. Axial ratio of the transmitted plane wave from the rectangular hole metamaterial cover (Veysi et al., 2011).

The FDTD simulated results presented in this section confirm the concepts of the proposed approach to control both the direction and the polarization of the transmitted wave. The

Theory and Applications of Metamaterial Covers 289

X: 9.112 Y: 0.9951

X-pol Y-pol

3dB RHCP 6dB RHCP

4 5 6 7 8 9 10 11 12

 **Frequency(GHz)**

8 8.2 8.4 8.6 8.8 9 9.2 9.4 9.6 9.8

Metamaterial covers can be applied to conventional antenna to improve their performance. These include conventional metamaterial covers to increase both the impedance and directivity bandwidths of the proximity coupled microstrip patch antenna and polarization dependent metamaterial covers to change the polarization state of the antenna. Thin lattices of ungrounded metal plates can behave as a metamaterial cover and can be analyzed using a simple FDTD code. These surfaces have two important properties: (1) increasing of the transmission rate and (2) control of the direction and polarization of the transmission. Polarization dependent metamaterial covers can be realized by cutting rectangular holes instead of square holes and

Fig. 12. Axial ratio of the transmitted plane wave from the metamaterial cover with

changing the relative height difference between the *x*- and *y*-directed strips of each layer.

 **Frequency(GHz)**

X: 9.112 Y: 1.269

Fig. 11. FDTD simulated transmission of the metamaterial cover with offset strips (Veysi et

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1


 **Axial Ratio**

nonplanar strips (Veysi et al., 2011).

**4. Conclusions** 

al., 2011).

 **Transmission**

authors believe that the proposed cover can find many applications in the broad electromagnetic areas such as antenna engineering and optical sources.

However, a rigorous characterization should take into account the complex interactions between the antenna and the metamaterial cover, such as finite size of the ground plane and the antenna height. Consequently, it is indispensable to use full wave analysis method, such as the finite difference time domain (FDTD), in the antenna designs in order to obtain accurate results.

Fig. 9. FDTD simulated transmission of the rectangular hole metamaterial cover (Veysi et al., 2011).

Fig. 10. A unit cell of metamaterial cover with offset strips (Veysi et al., 2011).

288 Trends in Electromagnetism – From Fundamentals to Applications

authors believe that the proposed cover can find many applications in the broad

However, a rigorous characterization should take into account the complex interactions between the antenna and the metamaterial cover, such as finite size of the ground plane and the antenna height. Consequently, it is indispensable to use full wave analysis method, such as the finite difference time domain (FDTD), in the antenna designs in order to obtain

4 4.2 4.4 4.6 4.8 5 5.2 5.4 5.6 5.8 6

X-pol Y-pol

*P*

 **Frequency(GHz)**

Fig. 9. FDTD simulated transmission of the rectangular hole metamaterial cover (Veysi et al.,

Fig. 10. A unit cell of metamaterial cover with offset strips (Veysi et al., 2011).

*P*

electromagnetic areas such as antenna engineering and optical sources.

accurate results.

2011).

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

*hr*

 **Transmission**

Fig. 11. FDTD simulated transmission of the metamaterial cover with offset strips (Veysi et al., 2011).

Fig. 12. Axial ratio of the transmitted plane wave from the metamaterial cover with nonplanar strips (Veysi et al., 2011).

## **4. Conclusions**

Metamaterial covers can be applied to conventional antenna to improve their performance. These include conventional metamaterial covers to increase both the impedance and directivity bandwidths of the proximity coupled microstrip patch antenna and polarization dependent metamaterial covers to change the polarization state of the antenna. Thin lattices of ungrounded metal plates can behave as a metamaterial cover and can be analyzed using a simple FDTD code. These surfaces have two important properties: (1) increasing of the transmission rate and (2) control of the direction and polarization of the transmission. Polarization dependent metamaterial covers can be realized by cutting rectangular holes instead of square holes and changing the relative height difference between the *x*- and *y*-directed strips of each layer.

## **5. References**


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