Spatiotemporal dispersion and waveguide properties of 2D-periodic metallic rod photonic crystals
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MOLECULES, OPTICS
Spatiotemporal Dispersion and Waveguide Properties of 2DPeriodic Metallic Rod Photonic Crystals M. V. Davidovicha,* and I. S. Nefedovb,** a
Chernyshevsky Saratov State University, Astrakhanskaya ul. 83, Saratov, 410012 Russia b Department of Radio Science and Engineering, School of Electrical Engineering, Aalto University F100076, P.O. Box 12000, 00076, Aalto, Finland *email: [email protected] **email: [email protected] Received February 2, 2013
Abstract—The method of integral equations based on the Green function of periodically arranged sources with a given phase shift (a periodic Green function) is used to investigate periodic metamaterials in the form of the simplest metallic and dielectric inclusions into a rectangular and cubic lattice in a dielectric medium (matrix) with permittivity ε. Metallic rods with a radius of the order of tens of nanometers are described by a complex macroscopic permittivity Re ε˜ < 0. Waves in the terahertz and infrared ranges propagate along the rods virtually with the speed of light and with small losses weakly dependent on the transverse wave number, while those in the optical range, especially in its shortwavelength part, transform into slow waves of a dielec tric waveguide. DOI: 10.1134/S1063776114040104
1. INTRODUCTION In recent years, the waveguide properties and dis persion in metamaterials in the form of various per fectly conducting and impedance twodimensional periodic (2DP) pin (wire) structures [1–17], metallic photonic crystals (PCs) or wire media (metamateri als), Fig. 1, have been investigated. Ideal metallic PCs [1–5, 12, 13, 16], impedance structures [6, 14–16], and periodic metamaterials based on carbon nano tubes and metallic nanowires [6, 7–9, 15] as well as on ferromagnetic wire PCs [10, 11] were considered and investigated. Homogenization was performed for these metamaterials by various methods [10, 11, 17–20]. At present, the studies of structures with dissipation, when the real properties of metals from the microwave range to the optical one are taken into account, are of greatest interest. Metallic and metallike pin PCs under certain conditions (at low frequencies and in the presence of slow waves with small losses) are hyper bolic metamaterials [8, 21, 22]. Such materials can be used in a number of applications: for the production of artificial impedance and anisotropic surfaces [14, 21] (including those maintaining the propagation of Dya konov surface plasmons), for directional heat transfer [8], as good radiation absorbers [22], for the creation of lenses, imaging [23], and a number of other appli cations. Possible applications of hyperbolic metama terials are given in the review [21].
and, in the case of thin pins, to linear integral equa tions [12, 13]. 2DP structures arise under the assump tion of a large wire length compared to the remaining sizes and to the wavelength λ in a vacuum. The most universal and accurate method of describing such structures is the method of volume integral equations that t
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