## Analytical study of two-dimensional degenerate metamaterial antennas |

Optics Express, Vol. 19, Issue 15, pp. 13899-13921 (2011)

http://dx.doi.org/10.1364/OE.19.013899

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### Abstract

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 *E*_{1} and *E*_{2} 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

**OCIS Codes**

(280.5600) Remote sensing and sensors : Radar

(350.4010) Other areas of optics : Microwaves

(350.3618) Other areas of optics : Left-handed materials

(160.3918) Materials : Metamaterials

(160.5298) Materials : Photonic crystals

**ToC Category:**

Metamaterials

**History**

Original Manuscript: April 26, 2011

Revised Manuscript: June 16, 2011

Manuscript Accepted: June 17, 2011

Published: July 6, 2011

**Citation**

Kazuaki Sakoda and Haifeng Zhou, "Analytical study of two-dimensional degenerate metamaterial antennas," Opt. Express **19**, 13899-13921 (2011)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-15-13899

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