Solution Of Vector Wave Equation Research Articles

Efficient 2-D Finite-Element Solution of Vector Wave Equation in a Class of Curved Polygons

We propose an efficient finite-element analysis of the vector wave equation in a class of relatively general curved polygons. The proposed method is suitable for an accurate and efficient calculation of the propagation constants of waveguides filled with pieces of homogeneous materials. To apply the method, we first decompose the 2-D problem domain into a set of curved polygons of a specific characteristic. Then, we divide every polygon into a set of triangular elements with two straight edges. Finally, we introduce a set of hierarchical mixed-order curl-conforming vector basis functions inside every triangular element to discretize the vector wave equation. The advantages of the method are as follows. The curved boundaries of the elements are modeled exactly, and hence, there is no approximation in the geometrical modeling. The 2-D integrals of the matrix elements are reduced to 1-D integrals. Therefore, the matrix filling can be performed very fast. The total number of elements due to the discretization of a given domain is very small, and hence, the discretization of the problem domain takes up a very small percentage of the total computational time. We validate the method by comparing the results with those of the Ansoft High Frequency Structure Simulator simulator and investigate the accuracy and efficiency of the method through a numerical example.

Scattering of electromagnetic plane wave from a chiral cylinder placed in chiral metamaterials

Analytical solution of vector wave equation describing the scattering of electromagnetic plane waves from an infinitely long circular chiral cylinder placed in another chiral metamaterial is presented. Cylindrical vector wave functions are used to express the fields both inside and outside the circular cylinder. The unknown are determined by applying the appropriate boundary conditions at the cylindrical interface. The numeric results are presented taking different combinations of metamaterials for inner and outer mediums of the cylinder. For this purpose chiral and/or chiral nihility cylinder placed in chiral and/or chiral nihility mediums are considered. Extreme cases of permittivity and permeability corresponding to PEC and PMC cylinder are also considered.

THE WAVE EQUATION AND GENERAL PLANE WAVE SOLUTIONS IN FRACTIONAL SPACE

This work presents the analytical solution of vector wave equation in fractional space. General plane wave solution to the wave equation for flelds in source-free and lossless media is obtained in fractional space. The obtained solution is a generalization of wave equation from integer dimensional space to a non-integer dimensional space. The classical results are recovered when integer-dimensional space is considered.

Solution of the vector wave equation by the separable effective adiabatic basis set method

A novel separable effective adiabatic basis (SEAB) for the solution of the transverse vector wave equation by the variational method is presented. The basis is constructed by a suitably modified adiabatic approximation. The method of SEAB construction is applicable to the waveguides of a general cross section. By calculating scalar modes in rectangular and rib waveguides, we show that the use of SEAB entails computational effort several orders of magnitude less than the use of the more conventional Fourier basis. As an illustrative example, the polarized modes of a rib waveguide are calculated.

An unconditionally stable finite element time-domain solution of the vector wave equation

This paper presents an implicit finite element time-domain (FETD) solution of the time-dependent vector wave equation. The time-dependent formulation employs a time-integration method based on the Newmark-Beta method. A stability analysis is presented demonstrating that this leads to an unconditionally stable solution of the time-dependent vector wave equation. The advantage of this formulation is that the time step is no longer governed by the spatial discretization of the mesh, but rather by the spectral content of the time-dependent signal. A numerical example of a three-dimensional cavity resonator is presented studying the effects of the Newmark-beta parameters on the solution error. Optimal choices of parameters are derived based on this example. >

Simple approximations for chromatic dispersion in single- mode fibers with various index profiles

Simple approximate formulas of chromatic dispersion and zero-chromatic dispersion wavelength are empirically derived for single-mode fibers with various index profiles having the deformations such as a central dip, hump, and/or tailing at a core cladding interface. These profiles are typical which are commonly obtained in current single-mode fibers. The approximation is based on the exact solution of vector-wave equation. These accuracies are better than 0.3 and 0.03 percent for the chromatic dispersion and zero-chromatic dispersion wavelength, respectively. With the aid of the simple approximations, the properties of chromaric dispersion and zero-chromatic dispersion wavelength for practical single-mode fibers are discussed. The relation between the chromatic dispersion and basic fiber parameters of single-mode fibers, effective cutoff wavelength of the LP 11 mode, and the spot-size of the LP 01 mode, are clarified.