Characteristics of bound modes in coupled dielectric waveguides containing negative index media

We investigate the characteristics of guided wave modes in planar coupled waveguides. In particular, we calculate the dispersion relations for TM modes in which one or both of the guiding layers consists of negative index media (NIM)-where the permittivity and permeability are both negative. We find that the Poynting vector within the NIM waveguide axis can change sign and magnitude, a feature that is reflected in the dispersion curves

Mode Bifurcation and Fold Points of Complex Dispersion Curves for the Metamaterial Goubau Line

In this paper the complex dispersion curves of the four lowest-order transverse magnetic modes of a dielectric Goubau line ($\epsilon>0, \mu>0$) are compared with those of a dispersive metamaterial Goubau line. The vastly different dispersion curve structure for the metamaterial Goubau line is characterized by unusual features such as mode bifurcation, complex fold points, both proper and improper complex modes, and merging of complex and real modes

Guided Modes of Elliptical Metamaterial Waveguides

The propagation of guided electromagnetic waves in open elliptical metamaterial waveguide structures is investigated. The waveguide contains a negative-index media core, where the permittivity, $\epsilon$ and permeability $\mu$ are negative over a given bandwidth. The allowed mode spectrum for these structures is numerically calculated by solving a dispersion relation that is expressed in terms of Mathieu functions. By probing certain regions of parameter space, we find the possibility exists to have extremely localized waves that transmit along the surface of the waveguide

The spectral element method (SEM) on variable-resolution grids: evaluating grid sensitivity and resolution-aware numerical viscosity

We evaluate the performance of the Community Atmosphere Model's (CAM) spectral element method on variable-resolution grids using the shallow-water equations in spherical geometry. We configure the method as it is used in CAM, with dissipation of grid scale variance, implemented using hyperviscosity. Hyperviscosity is highly scale selective and grid independent, but does require a resolution-dependent coefficient. For the spectral element method with variable-resolution grids and highly distorted elements, we obtain the best results if we introduce a tensor-based hyperviscosity with tensor coefficients tied to the eigenvalues of the local element metric tensor. The tensor hyperviscosity is constructed so that, for regions of uniform resolution, it matches the traditional constant-coefficient hyperviscosity. With the tensor hyperviscosity, the large-scale solution is almost completely unaffected by the presence of grid refinement. This later point is important for climate applications in which long term climatological averages can be imprinted by stationary inhomogeneities in the truncation error. We also evaluate the robustness of the approach with respect to grid quality by considering unstructured conforming quadrilateral grids generated with a well-known grid-generating toolkit and grids generated by SQuadGen, a new open source alternative which produces lower valence nodes

DEGENERACY CURVES IN THE SPECTRA OF DIRICHLET PARALLELOGRAMS-Version 2

In this paper we consider the problem of solving the Helmholtz equation over the space of all parallelograms subject to Dirichlet boundary conditions and determining the degeneracies occurring in their spectra upon changing simultaneously the two parameters, angle and side ratio. This problem is solved numerically using the finite element method (FEM) for eigenvalue levels one through ten. We can specify uniquely the family of parallelograms (which contains the rectangle, the rhombus, and the square as special cases) in two different but equivalent ways. Because the parallelogram is composed of two congruent triangles, we can specify this family in the same way Berry and Wilkinson specified the family of triangles using the area and two of the angles [9]. This set of parameters determines a unique parallelogram as well as a unique triangle. Equivalently a unique parallelogram can be characterized by knowing the two side lengths and the included angle between them. Using the first method of characterization the parameters of the family of triangles and those of the parallelogram can be made the same. However the addition of the fourth boundary, and the fact that the parallelogram has an extra 180 degree rotation symmetry introduces a difference in the degeneracies found for the two different families of shapes. Specifically the degeneracies occurring in the spectra of the space of all parallelograms subject to Dirichlet boundary conditions appear to form degeneracy curves (with some exceptions) as opposed to isolated points. For most adjacent normalized eigenvalue levels of the family of parallelograms, the number of degeneracies between levels appears to be uncountably infinite. There are two notable exceptions-the 2, 3 eigenvalue levels and the 4, 5 eigenvalue levels. These levels have only isolated degeneracies associated with the rectangle, the rhombus, or the square. No other general parallelogram degeneracies have been determined for these levels. But all other levels (within the lowest ten eigenvalue levels) contain at least one degeneracy curve. The first ten levels also contain at least four isolated diabolical points, one found for the 6,7 levels and three for the 8,9 levels. These isolated points or diabolical parallelograms are more difficult to determine numerically and cannot be found as precisely as the component points of the degeneracy curves