Dispersion curves of metamaterial steerable antennas composed of two-dimensional arrays of metallic unit structures with the C_4v and C_6v symmetries are calculated both qualitatively by the tight-binding approximation and quantitatively by the finite-difference time-domain method. Special attention is given to the case of eigenmodes of the E symmetry of the C_4v point group and those of the E₁ and E₂ symmetries of the C_6v point group, since they are doubly degenerate on the Γ point of the Brillouin zone so that they naturally satisfy the steerability condition. We show that their dispersion curves have quadratic dependence on the wave vector in the vicinity of the Γ point. To get a linear dispersion, which is advantageous for steerable antennas, we propose a method of controlled symmetry reduction. The present theory is an extension of our previous one [Opt. Express 18, 27371 (2010)] to two-dimensional systems, for which we can achieve the deterministic degeneracy due to symmetry and the controlled symmetry reduction becomes available. This design of metamaterial steerable antennas is advantageous in the optical frequency.

© 2011 OSA

1. V. G. Veselago, “Electrodynamics of substances with simultaneously negative values of sigma and mu,” Sov. Phys. Usp. 10, 509–514 (1968). [CrossRef]
2. J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312, 1780–1782 (2006). [CrossRef] [PubMed]
3. 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, 4184–4187 (2000). [CrossRef] [PubMed]
4. R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental verification of a negative index of refraction,” Science 292, 77–79 (2001). [CrossRef] [PubMed]
5. 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, 977–980 (2006). [CrossRef] [PubMed]
6. D. R. Smith, S. Schultz, P. Markos, and C. M. Soukoulis, “Determination of effective permittivity and permeability of metamaterials from reflection and transmission coefficients,” Phys. Rev. B 65, 195104 (2002).
7. S. A. Ramakrishna and T. M. Grzegorczyk, Physics and Applications of Negative Refractive Index Materials (SPIE Press, 2008). [CrossRef]
8. S. Matsuzawa, K. Sato, Y. Inoue, and T. Nomura, “W-band steerable composite right/left-handed leaky wave antenna for automotive applications,” IEICE Trans. Electron. E89-C, 1337–1344 (2006). [CrossRef]
9. A. Grbic and G. V. Eleftheriades, “Experimental verification of backward-wave radiation from a negative refractive index metamaterial,” J. Appl. Phys. 92, 5930–5935 (2002). [CrossRef]
10. C. Caloz and T. Ito, “Application of the transmission line theory of left-handed (LH) materials to the realization of a microstrip LH line,” IEEE-AP-S Int. Symp. Dig. 2, 412–415 (2002).
11. S. Tokoro, K. Kuroda, A. Kawakubo, K. Fujita, and H. Fujinami, “Electronically scanned millimeter-wave radar for pre-crush safety and adaptive cruise control system,” Proc. IEEE Intelligent Vehicles Symp. , 304–309 (2003).
12. K. Sakoda and H.-F. Zhou, “Role of structural electromagnetic resonances in a steerable left-handed antenna,” Opt. Express 18, 27371–27386 (2010). [CrossRef]
13. K. Sakoda, Optical Properties of Photonic Crystals , 2nd Ed. (Springer-Verlag, 2004).
14. T. Inui, Y. Tanabe, and Y. Onodera, Group Theory and its Applications in Physics (Springer, 1990). [CrossRef]
15. A. Taflove, Computational Electrodynamics (Artech House, 1995).
16. D. M. Sullivan, Electromagnetic Simulation Using the FDTD Method (IEEE Press, 2000). [CrossRef]

IEEE-AP-S Int. Symp. Dig.

• C. Caloz and T. Ito, “Application of the transmission line theory of left-handed (LH) materials to the realization of a microstrip LH line,” IEEE-AP-S Int. Symp. Dig. 2, 412–415 (2002).

IEICE Trans. Electron.

• S. Matsuzawa, K. Sato, Y. Inoue, and T. Nomura, “W-band steerable composite right/left-handed leaky wave antenna for automotive applications,” IEICE Trans. Electron. E89-C, 1337–1344 (2006). [CrossRef]

J. Appl. Phys.

• A. Grbic and G. V. Eleftheriades, “Experimental verification of backward-wave radiation from a negative refractive index metamaterial,” J. Appl. Phys. 92, 5930–5935 (2002). [CrossRef]

Opt. Express

• K. Sakoda and H.-F. Zhou, “Role of structural electromagnetic resonances in a steerable left-handed antenna,” Opt. Express 18, 27371–27386 (2010). [CrossRef]

Phys. Rev. B

• D. R. Smith, S. Schultz, P. Markos, and C. M. Soukoulis, “Determination of effective permittivity and permeability of metamaterials from reflection and transmission coefficients,” Phys. Rev. B 65, 195104 (2002).

Phys. Rev. Lett.

• 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, 4184–4187 (2000). [CrossRef] [PubMed]

Proc. IEEE Intelligent Vehicles Symp.

• S. Tokoro, K. Kuroda, A. Kawakubo, K. Fujita, and H. Fujinami, “Electronically scanned millimeter-wave radar for pre-crush safety and adaptive cruise control system,” Proc. IEEE Intelligent Vehicles Symp. , 304–309 (2003).

Science

• R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental verification of a negative index of refraction,” Science 292, 77–79 (2001). [CrossRef] [PubMed]
• 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, 977–980 (2006). [CrossRef] [PubMed]
• J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312, 1780–1782 (2006). [CrossRef] [PubMed]

Sov. Phys. Usp.

• V. G. Veselago, “Electrodynamics of substances with simultaneously negative values of sigma and mu,” Sov. Phys. Usp. 10, 509–514 (1968). [CrossRef]

Other

• S. A. Ramakrishna and T. M. Grzegorczyk, Physics and Applications of Negative Refractive Index Materials (SPIE Press, 2008). [CrossRef]
• K. Sakoda, Optical Properties of Photonic Crystals , 2nd Ed. (Springer-Verlag, 2004).
• T. Inui, Y. Tanabe, and Y. Onodera, Group Theory and its Applications in Physics (Springer, 1990). [CrossRef]
• A. Taflove, Computational Electrodynamics (Artech House, 1995).
• D. M. Sullivan, Electromagnetic Simulation Using the FDTD Method (IEEE Press, 2000). [CrossRef]

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• A highly symmetric two-handed metamaterial spontaneously matching the wave impedance (OE)
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• Low-loss and high-symmetry negative refractive index media by hybrid dielectric resonators (OE)

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