Spatiotemporal dispersion and waveguide properties of 2D-periodic metallic rod photonic crystals

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 < 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 short wavelength part, transform into slow waves of a dielec tric waveguide.

Polaritons and diffraction on the layer of asymmetric hyperbolic metamaterial

“…The fields on both sides have identical dependencies, and can have either an exponential decay in the vacuum side (surface gliding wave), or an exponential growth (antisurface or leakage wave). Therefore, it is enough to enter one constant in (11) with matching the fields on one surface [28]. The gliding means the movement of energy from the vacuum on both sides and absorption it in the plate.…”

“…Strong leakage even with weak dissipation is accompanied by large radiation losses. Signs in (11) are chosen according to the conditions of emission, i.e. outflow of energy.…”

“…Therefore, we will use the method based on the definition the sign of the value it is gliding. The relations (11) are written so that there is a simultaneous gliding or leakage in both half-spaces. The gliding/leakage conditions change with frequency.…”

“…In the case of a layer in a vacuum, this is possible only if an external constant magnetic field is applied, which will be discussed further. For such a solution it is necessary to change the sign either in the first two or in the last two equations of the system (11). This results to four-value solution (…”

Volumetric integro-differential equations in diffraction and eigenvalue problems (r e v i e w)

“…In the work [76] the VIE for the finite cladding of a photonic-crystal waveguide was used to calculate its modes. In the paper [77] the VIE method was used to analyze the modes of a 2D PC from nanowires. VIEs for the analysis of the modes of a rectangular DW were used in the works [9,78].…”