Two layer graphene heterostructures for waves slowing down: operator approach to waveguide problem

Slowing down the phase velocity of light in media has various applications. The generation of electromagnetic radiation using coherent Cherenkov mechanism is among them. Meanwhile, there is a need for compact terahertz radiation sources. Due to outstanding graphene properties, heterostructures consisting of alternating graphene/dielectric layers can operate as a medium for the generation of terahertz radiation. In the present paper, the slowing down and propagation coefficients for the modes supported in a two-layer graphene structure are studied. The study is conducted by means of the operator approach to wave propagation in stratified structures. The operator approach allows one to use coordinates-free notations and to consider consequently arbitrarily complex heterostructures (including anisotropic layers, for instance). The influence of interlayer distance and the value of graphene chemical potential on waves slowdown is determined. The obtained results open up prospects for creating a new type of terahertz radiation sources.

Leaky waves in planar dielectric waveguide

A new analytical and numerical solution of the electrodynamic waveguide problem for leaky modes of a planar dielectric symmetric waveguide is proposed. The conditions of leaky modes, corresponding to the Gamow-Siegert model, were used as asymptotic boundary conditions. The resulting initial-boundary problem allows the separation of variables. The emerging problem of the eigen-modes of open three-layer waveguides is formulated as the Sturm-Liouville problem with the corresponding boundary and asymptotic conditions. In the case of guided and radiation modes, the Sturm-Liouville problem is self-adjoint and the corresponding eigenvalues are real quantities for dielectric media. The search for eigenvalues and eigenfunctions corresponding to the leaky modes involves a number of difficulties: the problem for leaky modes is not self-adjoint, so the eigenvalues are complex quantities. The problem of finding eigenvalues and eigenfunctions is associated with finding the complex roots of the nonlinear dispersion equation. To solve this problem, we used the method of minimizing the zero order. An analysis of the calculated distributions of the electric field strength of the first three leaky modes is given, showing the possibilities and advantages of our approach to the study of leaky modes.

Theory for anomalous refraction of visible light by the plane array of metallic waveguides

The effect of anomalous or negative angle refraction in the periodic systems of silver waveguides is investigated. This effect arises solely due to the waveguide interaction and requires the system of specific geometrical configuration. It is also shown that the propagation constant provides a flexible mechanism to manipulate the anomalous refraction. We employ the multiple scattering formalism based on the exact solution of the Maxwell equations for a single waveguide problem. Also the method based on the lattice sum transformation into a fast convergent series is involved. This technique dramatically decreases the time necessary for performing the numerical simulations and increases the accuracy of the computational process. It is shown that all the directions, which the periodic system is possible to radiate, can be obtained beforehand, i.e. analytically, without numerical simulations. The latter ones are needed to determine energy the flux going into each of those directions.