Low Temperature Physics: 34, 846 (2008); https://doi.org/10.1063/1.3006391 (7 pages)
Физика Низких Температур: Том 34, Выпуск 10 (Октябрь 2008), c. 1072-1080    ( к оглавлению , назад )

Index of refraction of a photonic crystal of carbon nanotubes and homogenization of optically anisotropic periodic composites

L.N. Gumen1 and A.A. Krokhin2

1Universidad Popular Autonoma del Estado de Puebla, 21 Sur, #1103, 72160, Mexico

2Department of Physics, University of North Texas, P.O. Box 311427, Denton, TX, 76203, USA
E-mail: arkady@unt.edu

Received January 31, 2008


We consider the long-wavelength limit for a periodic arrangement of carbon nanotubes. Using the Fourier expansion method we develop an effective-medium theory for photonic crystal of aligned optically anisotropic cylinders. Exact analytical formulas for the effective dielectric constants for the E and H eigenmodes are obtained for arbitrary 2D Bravais lattice and arbitrary cross-section of anisotropic cylinders. It is shown that depending on the symmetry of the unit cell photonic crystal of anisotropic cylinders behaves in the low-frequency limit like uniaxial or biaxial optical crystal. The developed theory of homogenization is in a good agreement with existing experimental results for the dielectric tensor of photonic crystals of carbon nanotubes.

PACS: 42.70.Qs Photonic bandgap materials;
PACS: 41.20.Jb Electromagnetic wave propagation; radiowave propagation;
PACS: 42.25.Lc Birefringence;
PACS: 78.67.Ch Nanotubes.

Key words: photonic crystal, carbon nanotubes, dielectric constants.