OSA's Digital Library

Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 20, Iss. 16 — Jul. 30, 2012
  • pp: 17545–17551
« Show journal navigation

Planar metamaterial based on hybridization for directive emission

Abdelwaheb Ourir, Redha Abdeddaim, and Julien de Rosny  »View Author Affiliations


Optics Express, Vol. 20, Issue 16, pp. 17545-17551 (2012)
http://dx.doi.org/10.1364/OE.20.017545


View Full Text Article

Acrobat PDF (1666 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

We present the first experimental demonstration of a high-directivity using a mu and epsilon near zero (MENZ) metamaterial. We use the hybridization principles to design a planar MENZ structure based on the fishnet unit cell. Resonant mode engineering achieves an effective permittivity and permeability that approaches zeros around 10.5 GHz simultaneously. We use this metamaterial as a superstrate of a microstrip patch antenna. We show that the directivity of the antenna is effectively enhanced compared to that of the patch antenna alone at the desired frequency.

© 2012 OSA

1. Introduction

Metamaterials have gained considerable attention in recent years due to their original physical properties [1

1. D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, “Composite medium with simultaneously negative permeability and permittivity,” Phys. Rev. Lett. 84(18), 4184–4187 (2000). [CrossRef] [PubMed]

4

4. D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, “Metamaterial electromagnetic cloak at microwave frequencies,” Science 314(5801), 977–980 (2006). [CrossRef] [PubMed]

]. This growth of interest has led to novel and interesting possibilities for antenna applications. Novel composite metamaterial concepts have enabled miniaturization of high frequency circuits and antennas and led to numerous practical antennas with unprecedented features [5

5. D. Sievenpiper, L. Zhang, R. F. J. Broas, N. G. Alexópoulos, and E. Yablonovitch, “High-impedance electromagnetic surfaces with a forbidden frequency band,” IEEE Trans. Microw. Theory Tech. 47(11), 2059–2074 (1999). [CrossRef]

10

10. R. W. Ziolkowski, “Propagation in and scattering from a matched metamaterial having a zero index of refraction,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 70(4), 046608 (2004). [CrossRef] [PubMed]

]. In particular, there have been different metamaterial based solutions proposed in literature concerning the design of directive electromagnetic sources [8

8. A. Ourir, A. de Lustrac, and J.-M. Lourtioz, “All-metamaterial-based sub-wavelength cavities (λ/60) for ultrathin directive antennas,” Appl. Phys. Lett. 88(8), 084103 (2006). [CrossRef]

10

10. R. W. Ziolkowski, “Propagation in and scattering from a matched metamaterial having a zero index of refraction,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 70(4), 046608 (2004). [CrossRef] [PubMed]

]. Recently, the method of utilizing coordinate transformation to obtain directive emission has been proposed [11

11. J. Zhang, Y. Luo, S. Xi, H. Chen, L. Ran, B.-I. Wu, and J. A. Kong, “Directive emission obtained by coordinate transformation,” Prog. Electromagn. Res. 81, 437–446 (2008). [CrossRef]

,12

12. J. Zhang, Y. Luo, H. Chen, and B.-I. Wu, “Manipulating the directivity of antennas with metamaterial,” Opt. Express 16(15), 10962–10967 (2008). [CrossRef] [PubMed]

]. However, fabrication of the antenna based on the coordinate transformation approach can hardly be achieved, since the metamaterials with complex space variant dielectric properties are very difficult to realize.

One of the most common methods to reach directive emission is based on adjusting the permittivity and permeability elements of the constitutive matrix. The high-directive antennas were mainly achieved by using point source antennas embedded in low index materials realized with low permittivity periodic metamaterials [10

10. R. W. Ziolkowski, “Propagation in and scattering from a matched metamaterial having a zero index of refraction,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 70(4), 046608 (2004). [CrossRef] [PubMed]

,13

13. K. C. Gupta, “Narrow-beam antennas using an artificial dielectric medium with permittivity less than unity,” Electron. Lett. 7(1), 16–18 (1971). [CrossRef]

17

17. G. Lovat, P. Burghignoli, F. Capolino, D. R. Jackson, and D. R. Wilton, “Analysis of directive radiation from a line source in a metamaterial slab with low permittivity,” IEEE Trans Ant. Propag. 54(3), 1017–1030 (2006). [CrossRef]

]. When the ray is incident from inside low index material into free space, the angle of refraction will be close to zero. In this way, the refracted rays will be normal to the interface. This property provides an interesting method of controlling the direction of emission. Recent works have shown theoretically and numerically that the cylindrical waves emitted from line source can be perfectly converted to plane wave through Mu and Epsilon-Near-Zero (MENZ) Metamaterial slab with planar exit face [10

10. R. W. Ziolkowski, “Propagation in and scattering from a matched metamaterial having a zero index of refraction,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 70(4), 046608 (2004). [CrossRef] [PubMed]

,18

18. G. Lovat, P. Burghignoli, F. Capolino, and D. R. Jackson, “Combinations of low/high permittivity and/or permeability substrates for highly directive planar metamaterial antennas,” IET Microw. Ant. Propag. 1(1), 177–183 (2007). [CrossRef]

,19

19. J. Yang, M. Huang, and J. Peng, “Directive emission obtained by mu and epsilon-near-zero metamaterials,” Radioengineering 18, 124 (2009).

]. These metamaterials provide the property of passive metamaterials that are matched to free space and have an index of refraction equal to zero that enhance the directivity of the source antennas.

In 2003, Prodan et al. [20

20. E. Prodan, C. Radloff, N. J. Halas, and P. Nordlander, “A hybridization model for the plasmon response of complex nanostructures,” Science 302(5644), 419–422 (2003). [CrossRef] [PubMed]

], introduced the concept of electric plasmon hybridization. They draw an analogy between the plasmonic response of metallic nanostructures and the molecular orbital theory. The hybridization effect is caused by the coupling interactions between metamaterial resonators. The hybridization principle provides a simple conceptual approach to design artificial thin materials with desired permittivity and permeability [21

21. N. Liu, H. C. Guo, L. W. Fu, S. Kaiser, H. Schweizer, and H. Giessen, “Plasmon hybridization in stacked cut-wire metamaterials,” Adv. Mater. (Deerfield Beach Fla.) 19(21), 3628–3632 (2007). [CrossRef]

24

24. A. Ourir, R. Abdeddaim, and J. de Rosny, “Double-T metamaterial for parallel and normal transverse electric incident waves,” Opt. Lett. 36, 1527–1529 (2011). [CrossRef] [PubMed]

].

In this paper, we use the hybridization principles to design a MENZ structure based on the fishnet unit cell. We optimize the structure to obtain a permittivity and permeability close to zero around 10 GHz. We use this structure as a superstrate of a microstrip patch antenna. We show that the directivity of the antenna is effectively enhanced compared to that of the patch antenna alone at the desired frequency. Measured results of the implemented experiment are provided and compared with the simulation ones.

2. Design of the metamaterial superstrate

The metamaterial we propose is presented in Fig. 1(a)
Fig. 1 (a) Schematic view of the MENZ metamaterial based on the fishnet structure. (b) the metamaterial unit cell (h = 0.5 mm, w = 10 mm). The lattice constants on the x, y and z directions are 20 mm, 20 mm and 10 mm respectively.
. It is based on the fishnet structure. Figure 1(b) shows the schematic view of the unit cell. The structure consists of two copper gratings etched on two 0.5 mm-thick FR3 epoxy substrates separated by an adjustable air gap. The width of the metallic stripes w is 10 mm. The lattice constants on the x, y and z directions are respectively 20 mm, 20 mm and 10 mm. The structure is optimized to have a plasma frequency around 10 GHz.

In addition to its stop band at low frequencies, the fishnet structure provides magnetic and electric modes. The coupling effect between the two cross resonators leads to a lifting of the degeneracy. It results in the formation of two new hybrid modes. In order to obtain a low permittivity and permeability over a same frequency band, we have to bring the magnetic resonance near from the plasma frequency of the structure. Here, we propose to vary the air gap thickness to tune the magnetic resonant mode frequency.

It has been shown that using a (2λ/3)-thick slab over a source antenna gives high directivity and relatively low sidelobes [25

25. J. J. Zhang, Y. Luo, S. Xi, H. S. Chen, L. X. Ran, B.-I. Wu, and J. A. Kong, “Directive emission obtained by coordinate transformation,” Prog. Electromagn. Res. 81, 437–446 (2008). [CrossRef]

]. We propose here to realize a medium with two metamaterial layers to obtain the 2λ/3 thickness at 10 GHz. All the conception and the characterization stages are made with two metamaterial layers.

We have performed numerical simulations based on a commercial finite difference time domain algorithm (CST software) to investigate the resonant behavior of the proposed structure. Figure 2
Fig. 2 Variation of the plasma frequency, the magnetic and the electric resonant mode frequency as a function of the thickness of the air gap.
presents the variation of the plasma frequency as well as the magnetic and the electric resonant mode frequency as a function of the thickness of the air gap (ga). These frequencies are determined through effective parameters retrieving procedure applied to the numerical results [26

26. D. R. Smith, D. C. Vier, Th. Koschny, and C. M. Soukoulis, “Electromagnetic parameter retrieval from inhomogeneous metamaterials,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 71(33 Pt 2B), 036617 (2005). [CrossRef] [PubMed]

]. The curves show that the magnetic resonance is red-shifted while the electric one is blue-shifted when we decrease the air gap thickness. These phenomena can be explained by increasing coupling effect as reducing the distance between the two cross resonators. Nevertheless, the plasma frequency keeps relatively constant since the metallic surface coverage remains the same for all configurations.

According to the results of Fig. 2, an air gap thickness of 0.5 mm sets the magnetic resonance near from the plasma frequency of the fishnet structure. Experiments are then carried out to demonstrate the possibility of realizing MENZ metamaterial using fishnet structure. Measurements were performed in free space for the 0.5 mm-thick air gap with a vectorial network analyzer and two wide band horn antennas. Figure 3(a)
Fig. 3 (a) Calculated and measured transmission spectra of the two layers metamaterial. Effective permittivity (a) and permeability (d) retrieved from measurements and simulations.
shows the calculated and measured transmission spectra of the proposed metamaterial. A narrow transmission band is observed around 10.5 GHz. Figures 3(b) and 3(c) report respectively the effective permittivity and permeability retrieved from both experiments and calculations [26

26. D. R. Smith, D. C. Vier, Th. Koschny, and C. M. Soukoulis, “Electromagnetic parameter retrieval from inhomogeneous metamaterials,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 71(33 Pt 2B), 036617 (2005). [CrossRef] [PubMed]

]. A permeability resonance, which corresponds to the magnetic resonant mode, is clearly observed near from the plasma frequency (ε = 0) around 10.5 GHz. Subsequently, we obtain a MENZ metamaterial on narrow frequency band around this frequency. In Fig. 3(b), some anomalies are obtained above 12 GHz for the retrieved parameters because of the thickness of the material that becomes comparable with the wavelength.

3. Metamaterial based antenna

We use the designed MENZ metamaterial as a superstrate in order to obtain directive emission. We place the metamaterial superstrate at a distance d above a patch antenna as shown in Fig. 4(a)
Fig. 4 (a) Schematic view of the antenna based on the MENZ metamaterial. The metamaterial is disposed over a coax fed patch antenna at a distance d. (b) Return loss of the path antenna in different configurations: with and without the metamaterial superstrate.
. We use a coaxial fed patch antenna etched on 0.5 mm thick epoxy substrate. The patch antenna is a nearly-square-shaped antenna with dimensions of 5.8 x 7 mm2. The whole structure has lateral dimensions close to 4λ × 4λ.

We characterize the proposed structure using a FDTD electromagnetic simulator (CST software). Figure 4(b) shows the reflection coefficient of the patch antenna in different configurations. It shows that the patch antenna alone has a resonance frequency of 10.5GHz. The matching of the antenna placed under the MENZ metamaterial depends strongly on the distance d. Good matching around the MENZ frequency band is obtained with distances higher than 10 mm. The bad matching obtained when d is 5 mm can be explained by the strong coupling between the patch antenna and the gratings. Finally, we note the appearance of dip resonances on the low frequencies when d is 15 mm. These resonances result from the Fabry-Perot interference phenomenon [8

8. A. Ourir, A. de Lustrac, and J.-M. Lourtioz, “All-metamaterial-based sub-wavelength cavities (λ/60) for ultrathin directive antennas,” Appl. Phys. Lett. 88(8), 084103 (2006). [CrossRef]

].

We maintain the distance d at 10 mm and we carry out experiments to measure the return loss and the radiation patterns of the antennas. Measurements were performed using an Agilent N5230C network analyzer in the range of 7 to 13 GHz.

The reflection coefficients of the antennas are reported in Fig. 5
Fig. 5 (a) Measured and calculated return loss of the patch antenna. (b) Return loss of the antenna based on the MENZ metamaterial for d = 10 mm.
along with numerical simulations. The measurement results are relatively in good agreement with the full wave simulation results. They show the good matching of the metamaterial based antenna around the MENZ frequency band.

Figure 6
Fig. 6 (a) and (b) Calculated and measured radiation patterns of the patch antenna in the E and H planes respectively. (c) and (d) E and H-plane cuts of the radiation pattern of the antenna based on the MENZ metamaterial.
shows the radiation patterns of the designed antennas in the E and H planes at 10.6 GHz. The azimuth E and H-plane cuts reveal a main lobe and a lot of sidelobes for the antenna based on the MENZ metamamterial. Nevertheless, the measured main lobes of the antenna with the metamaterial superstrate were narrower than those of the patch antenna alone. Directivity enhancement is clearly obtained with the MENZ metamaterial superstrate in the two planes. A directivity of about 12.7 dB is obtained in the metamaterial configuration. Actually, the gain of the antenna is also improved. It is increased from 4 dB to about 10.7 dB.

The appearance of sidelobes can be explained by the grating diffraction and by the edge effects. In order to bring out the last phenomenon, we increase the lateral dimensions of the superstrate. Figure 7
Fig. 7 (a) and (b) Radiation pattern of the antenna based on 6x6 and 8x8 cells metamaterial superstrate in the E and H planes respectively.
shows the radiated patterns in the E and H planes obtained with two different lateral sizes of the superstrate. It shows that the increase of the lateral dimensions of the superstrate reduces noticeably some sidelobes. Furthermore, the increase of the lateral dimensions induces an enhancement on the antenna gain and directivity. We obtain 13 dB for the gain and 14.8 the directivity in the last configuration.

7. Conclusion

We have presented the first experimental demonstration of directive emission with a planar MENZ metamaterial. We have designed a MENZ structure based on the fishnet unit cell using use the hybridization process. The electromagnetic parameters of the structure have been investigated. A permittivity and permeability close to zero around 10.5 GHz have been achieved. This structure have been used afterwards as a superstrate of a microstrip patch antenna. We have shown that the directivity of this antenna is effectively enhanced compared to that of the patch antenna alone at the desired frequency. Antennas based on this kind of planar MENZ metamaterial may have important applications in wireless communications and radar technology.

References and links

1.

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, “Composite medium with simultaneously negative permeability and permittivity,” Phys. Rev. Lett. 84(18), 4184–4187 (2000). [CrossRef] [PubMed]

2.

J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85(18), 3966–3969 (2000). [CrossRef] [PubMed]

3.

D. R. Smith, J. B. Pendry, and M. C. K. Wiltshire, “Metamaterials and negative refractive index,” Science 305(5685), 788–792 (2004). [CrossRef] [PubMed]

4.

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, “Metamaterial electromagnetic cloak at microwave frequencies,” Science 314(5801), 977–980 (2006). [CrossRef] [PubMed]

5.

D. Sievenpiper, L. Zhang, R. F. J. Broas, N. G. Alexópoulos, and E. Yablonovitch, “High-impedance electromagnetic surfaces with a forbidden frequency band,” IEEE Trans. Microw. Theory Tech. 47(11), 2059–2074 (1999). [CrossRef]

6.

R. W. Ziolkowski and A. Kipple, “Application of double negative metamaterials to increase the power radiated by electrically small antennas,” IEEE Trans. Ant. Propag. 51(10), 2626–2640 (2003). [CrossRef]

7.

R. W. Ziolkowski and A. Erentok, “Metamaterial-based efficient electrically small antennas,” IEEE Trans. Antenn. Propag. 54(7), 2113–2130 (2006). [CrossRef]

8.

A. Ourir, A. de Lustrac, and J.-M. Lourtioz, “All-metamaterial-based sub-wavelength cavities (λ/60) for ultrathin directive antennas,” Appl. Phys. Lett. 88(8), 084103 (2006). [CrossRef]

9.

S. Enoch, G. Tayeb, P. Sabouroux, N. Guérin, and P. Vincent, “A metamaterial for directive emission,” Phys. Rev. Lett. 89(21), 213902 (2002). [CrossRef] [PubMed]

10.

R. W. Ziolkowski, “Propagation in and scattering from a matched metamaterial having a zero index of refraction,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 70(4), 046608 (2004). [CrossRef] [PubMed]

11.

J. Zhang, Y. Luo, S. Xi, H. Chen, L. Ran, B.-I. Wu, and J. A. Kong, “Directive emission obtained by coordinate transformation,” Prog. Electromagn. Res. 81, 437–446 (2008). [CrossRef]

12.

J. Zhang, Y. Luo, H. Chen, and B.-I. Wu, “Manipulating the directivity of antennas with metamaterial,” Opt. Express 16(15), 10962–10967 (2008). [CrossRef] [PubMed]

13.

K. C. Gupta, “Narrow-beam antennas using an artificial dielectric medium with permittivity less than unity,” Electron. Lett. 7(1), 16–18 (1971). [CrossRef]

14.

I. J. Bahl and K. C. Gupta, “A leaky-wave antenna using an artificial dielectric medium,” IEEE Trans. Antenn. Propag. 22(1), 119–122 (1974). [CrossRef]

15.

G. Poilasne, J. Lenormand, P. Pouliguen, K. Mahdjoubi, C. Terret, and P. Gelin, “Theoretical study of interactions between antennas and metallic photonic bandgap materials,” Microw. Opt. Technol. Lett. 15(6), 384–389 (1997). [CrossRef]

16.

S. Enoch, G. Tayeb, P. Sabouroux, N. Guérin, and P. Vincent, “A metamaterial for directive emission,” Phys. Rev. Lett. 89(21), 213902 (2002). [CrossRef] [PubMed]

17.

G. Lovat, P. Burghignoli, F. Capolino, D. R. Jackson, and D. R. Wilton, “Analysis of directive radiation from a line source in a metamaterial slab with low permittivity,” IEEE Trans Ant. Propag. 54(3), 1017–1030 (2006). [CrossRef]

18.

G. Lovat, P. Burghignoli, F. Capolino, and D. R. Jackson, “Combinations of low/high permittivity and/or permeability substrates for highly directive planar metamaterial antennas,” IET Microw. Ant. Propag. 1(1), 177–183 (2007). [CrossRef]

19.

J. Yang, M. Huang, and J. Peng, “Directive emission obtained by mu and epsilon-near-zero metamaterials,” Radioengineering 18, 124 (2009).

20.

E. Prodan, C. Radloff, N. J. Halas, and P. Nordlander, “A hybridization model for the plasmon response of complex nanostructures,” Science 302(5644), 419–422 (2003). [CrossRef] [PubMed]

21.

N. Liu, H. C. Guo, L. W. Fu, S. Kaiser, H. Schweizer, and H. Giessen, “Plasmon hybridization in stacked cut-wire metamaterials,” Adv. Mater. (Deerfield Beach Fla.) 19(21), 3628–3632 (2007). [CrossRef]

22.

R. Abdeddaim, A. Ourir, and J. de Rosny, “Realizing a negative index metamaterial by controlling hybridization of trapped modes,” Phys. Rev. B 83(3), 033101 (2011). [CrossRef]

23.

A. Ourir and H. Ouslimani, “Negative refractive index in symmetric cut-wire pair metamaterial,” Appl. Phys. Lett. 98(11), 113505 (2011). [CrossRef]

24.

A. Ourir, R. Abdeddaim, and J. de Rosny, “Double-T metamaterial for parallel and normal transverse electric incident waves,” Opt. Lett. 36, 1527–1529 (2011). [CrossRef] [PubMed]

25.

J. J. Zhang, Y. Luo, S. Xi, H. S. Chen, L. X. Ran, B.-I. Wu, and J. A. Kong, “Directive emission obtained by coordinate transformation,” Prog. Electromagn. Res. 81, 437–446 (2008). [CrossRef]

26.

D. R. Smith, D. C. Vier, Th. Koschny, and C. M. Soukoulis, “Electromagnetic parameter retrieval from inhomogeneous metamaterials,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 71(33 Pt 2B), 036617 (2005). [CrossRef] [PubMed]

OCIS Codes
(260.2110) Physical optics : Electromagnetic optics
(350.4010) Other areas of optics : Microwaves
(160.3918) Materials : Metamaterials
(310.6845) Thin films : Thin film devices and applications

ToC Category:
Metamaterials

History
Original Manuscript: May 9, 2012
Revised Manuscript: June 18, 2012
Manuscript Accepted: July 3, 2012
Published: July 18, 2012

Citation
Abdelwaheb Ourir, Redha Abdeddaim, and Julien de Rosny, "Planar metamaterial based on hybridization for directive emission," Opt. Express 20, 17545-17551 (2012)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-16-17545


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  1. D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, “Composite medium with simultaneously negative permeability and permittivity,” Phys. Rev. Lett.84(18), 4184–4187 (2000). [CrossRef] [PubMed]
  2. J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett.85(18), 3966–3969 (2000). [CrossRef] [PubMed]
  3. D. R. Smith, J. B. Pendry, and M. C. K. Wiltshire, “Metamaterials and negative refractive index,” Science305(5685), 788–792 (2004). [CrossRef] [PubMed]
  4. D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, “Metamaterial electromagnetic cloak at microwave frequencies,” Science314(5801), 977–980 (2006). [CrossRef] [PubMed]
  5. D. Sievenpiper, L. Zhang, R. F. J. Broas, N. G. Alexópoulos, and E. Yablonovitch, “High-impedance electromagnetic surfaces with a forbidden frequency band,” IEEE Trans. Microw. Theory Tech.47(11), 2059–2074 (1999). [CrossRef]
  6. R. W. Ziolkowski and A. Kipple, “Application of double negative metamaterials to increase the power radiated by electrically small antennas,” IEEE Trans. Ant. Propag.51(10), 2626–2640 (2003). [CrossRef]
  7. R. W. Ziolkowski and A. Erentok, “Metamaterial-based efficient electrically small antennas,” IEEE Trans. Antenn. Propag.54(7), 2113–2130 (2006). [CrossRef]
  8. A. Ourir, A. de Lustrac, and J.-M. Lourtioz, “All-metamaterial-based sub-wavelength cavities (λ/60) for ultrathin directive antennas,” Appl. Phys. Lett.88(8), 084103 (2006). [CrossRef]
  9. S. Enoch, G. Tayeb, P. Sabouroux, N. Guérin, and P. Vincent, “A metamaterial for directive emission,” Phys. Rev. Lett.89(21), 213902 (2002). [CrossRef] [PubMed]
  10. R. W. Ziolkowski, “Propagation in and scattering from a matched metamaterial having a zero index of refraction,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys.70(4), 046608 (2004). [CrossRef] [PubMed]
  11. J. Zhang, Y. Luo, S. Xi, H. Chen, L. Ran, B.-I. Wu, and J. A. Kong, “Directive emission obtained by coordinate transformation,” Prog. Electromagn. Res.81, 437–446 (2008). [CrossRef]
  12. J. Zhang, Y. Luo, H. Chen, and B.-I. Wu, “Manipulating the directivity of antennas with metamaterial,” Opt. Express16(15), 10962–10967 (2008). [CrossRef] [PubMed]
  13. K. C. Gupta, “Narrow-beam antennas using an artificial dielectric medium with permittivity less than unity,” Electron. Lett.7(1), 16–18 (1971). [CrossRef]
  14. I. J. Bahl and K. C. Gupta, “A leaky-wave antenna using an artificial dielectric medium,” IEEE Trans. Antenn. Propag.22(1), 119–122 (1974). [CrossRef]
  15. G. Poilasne, J. Lenormand, P. Pouliguen, K. Mahdjoubi, C. Terret, and P. Gelin, “Theoretical study of interactions between antennas and metallic photonic bandgap materials,” Microw. Opt. Technol. Lett.15(6), 384–389 (1997). [CrossRef]
  16. S. Enoch, G. Tayeb, P. Sabouroux, N. Guérin, and P. Vincent, “A metamaterial for directive emission,” Phys. Rev. Lett.89(21), 213902 (2002). [CrossRef] [PubMed]
  17. G. Lovat, P. Burghignoli, F. Capolino, D. R. Jackson, and D. R. Wilton, “Analysis of directive radiation from a line source in a metamaterial slab with low permittivity,” IEEE Trans Ant. Propag.54(3), 1017–1030 (2006). [CrossRef]
  18. G. Lovat, P. Burghignoli, F. Capolino, and D. R. Jackson, “Combinations of low/high permittivity and/or permeability substrates for highly directive planar metamaterial antennas,” IET Microw. Ant. Propag.1(1), 177–183 (2007). [CrossRef]
  19. J. Yang, M. Huang, and J. Peng, “Directive emission obtained by mu and epsilon-near-zero metamaterials,” Radioengineering18, 124 (2009).
  20. E. Prodan, C. Radloff, N. J. Halas, and P. Nordlander, “A hybridization model for the plasmon response of complex nanostructures,” Science302(5644), 419–422 (2003). [CrossRef] [PubMed]
  21. N. Liu, H. C. Guo, L. W. Fu, S. Kaiser, H. Schweizer, and H. Giessen, “Plasmon hybridization in stacked cut-wire metamaterials,” Adv. Mater. (Deerfield Beach Fla.)19(21), 3628–3632 (2007). [CrossRef]
  22. R. Abdeddaim, A. Ourir, and J. de Rosny, “Realizing a negative index metamaterial by controlling hybridization of trapped modes,” Phys. Rev. B83(3), 033101 (2011). [CrossRef]
  23. A. Ourir and H. Ouslimani, “Negative refractive index in symmetric cut-wire pair metamaterial,” Appl. Phys. Lett.98(11), 113505 (2011). [CrossRef]
  24. A. Ourir, R. Abdeddaim, and J. de Rosny, “Double-T metamaterial for parallel and normal transverse electric incident waves,” Opt. Lett.36, 1527–1529 (2011). [CrossRef] [PubMed]
  25. J. J. Zhang, Y. Luo, S. Xi, H. S. Chen, L. X. Ran, B.-I. Wu, and J. A. Kong, “Directive emission obtained by coordinate transformation,” Prog. Electromagn. Res.81, 437–446 (2008). [CrossRef]
  26. D. R. Smith, D. C. Vier, Th. Koschny, and C. M. Soukoulis, “Electromagnetic parameter retrieval from inhomogeneous metamaterials,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys.71(33 Pt 2B), 036617 (2005). [CrossRef] [PubMed]

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.


« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited