Diffraction on the eigenwaves on an inclined medium interface in the waveguides with metallic bounds

© 2002 IEEE. The electromagnetic wave diffraction problems on an inclined medium interface with a metallic plate and without it in the plane waveguide and in the rectangular waveguide are considered. It is shown that these problems can be reduced to boundary value problems for the Helmholtz equation or for the Maxwell system in a bounded rectangular domain

The problems of electromagnetic waves diffraction on the dielectric index step in the waveguides with metallic bounds

The problem of eigen wave scattering on the media interface of the arbitrary form in the waveguide with the metallic bounds is investigated. The regularization method for integral or summatorial equations of the diffraction problem derived from the field conjunction condition is proposed. The integral identities connecting the traces on the waveguide section of the solutions of the over-determined Cauchy problems in the semi-infinity parts of waveguide are used

The over-determined boundary value problems for the maxwell equations set in the orthogonal coordinates and some applications for the electromagnetic wave diffraction problems

The necessary and sufficient conditions of solvability of the over-determined problems for the Maxwell equations set are obtained in the cases of Cartesian, cylindrical and spherical coordinates. These conditions are used by reduction of the electromagnetic wave diffraction problems on the thin conducting screen placed on the coordinate surfaces to integral or summatorial equations. Moreover, these conditions can be used for regularization of the integral equations of the first kind obtained by solving the diffraction problems. In the case on three-dimensional problems of electrodynamics the over-determined problems appear when both the tangential components of the electric vector and of the magnetic vector are given on the boundary of the partial domains. It is shown that the conditions of solvability of the over-determined problems can be obtained in the different form. The common form is the dependence of the Fourier transforms or Fourier coefficients of the boundary functions. But the mixed form is possible when both expressions participate. The set of the three-dimensional diffraction problems on the thin conducting screens in the wave-guided structures is considered as examples

The uniqueness theorems in the electromagnetic wave theory and quasi-periodical solutions of the periodical diffraction problems

The simple method to prove the uniqueness of the solution of the electromagnetic wave diffraction problems is proposed in the case of loss-free media. The set of the diffraction problems on the thin conducting screens in the wave-guided structures are considered. The over-determined boundary value problem method is used. It is shown that the limited absorption principle is correct for the considered problems. The uniqueness conditions of the solution of the integral equations with difference kernel are obtained as an auxiliary result. These conditions are used to prove the Floquet theorem: the solution of the quasi-periodical wave diffraction on the periodical set of the heterogeneities can be the quasi-periodical wave (Floquet wave) only. The case of diffraction problem on the bi-periodical set of thin conducting screens in the opened space is considered in detail as an example. The boundary value problem is equivalent to the dual summatorial functional equation for the Floquet coefficients. It is proved that this problem is equivalent to the regular infinite set of the linear algebraic equations for the coefficients of decomposition of the electromagnetic field by Floquet harmonics. By this set of equations the algorithms are constructed for numerical solving the diffraction problem

Parallel algorithm of solving the electromagnetic wave diffraction problem on the spherical screen

The electromagnetic wave diffraction problem on a thin conducting spherical screen is reduced to pair summatorial equation relative to unknown coefficients of expansion into a series of spherical waves. This equation can be transformed to a regular infinite set of linear algebraic equations by integral-summatorial identities method. For all stages of numerical algorithm of solving the problem the parallel calculating processes are possible. At first, if field traces of outside source at the sphere are decomposed onto magnetic and electric parts, then magnetic and electric parts of the unknown field can be found independently. Secondly, if coefficients of field conjugation conditions at the sphere do not depend on longitude coordinate, then calculations also can be fulfilled independently for every number of the series coefficients. Thirdly, if by reduction of infinite set the finite set of linear equations of large dimension is obtained, then it can be solved by one of parallel algorithms. But the most effect can be obtained just at the stage of calculating the auxiliary integrals over screen

On solving diffraction problems for the junctions of open waveguides in the classes of distributions

This study addresses some peculiarities in the application of method of Fourier transformation to solving the problems of electromagnetic wave diffraction on dielectric bodies bounded by coordinate lines or surfaces. Emphasis is on the two dimensional Helmholtz equation with a real piecewise constant coefficient. The solutions to this equation are established in the classes of distributions of slow growth at infinity

Eigen waves of semi-opened waveguide structures

The properties of the eigen waves of two waveguide structures are investigated in two cases: for semi-opened dielectric waveguide and for semi-opened elastic waveguide. It is proved that modes of semiopened waveguides belonging to discrete and to continuous parts of spectrum form the orthogonal system. © 2008 IEEE

Analysis of electromagnetic wave propagation through a layer with graded-index distribution of refraction index

The problem of plane electromagnetic harmonic wave diffraction on a graded-refractive-index layer of some thickness is considered. It is assumed that refractive index of a layer monotonically increases and then monotonically decreases. Cases of the linear, parabolic, sinusoidal, exponential and logarithmic refractive index profiles of the layer are investigated. The diffraction problem is reduced to an ordinary differential equation with appropriate boundary conditions. The problem for the linear profile is solved analytically; for the other profiles it is investigated numerically. The method of approximating an integral identity is applied to increase accuracy of the grid solution of the boundary value problem. Emphasis is given to the cases, in which wave energy, either reflected or transited, reaches maxima

Over-determined boundary value problems for PDE and their application in the wave propagation theory

© 2014 Taylor & Francis. The solvability conditions of the over-determined boundary value problems for PDE with constant coefficients in the form of connection between Fourier transforms of boundary functions are obtained. The jump problem on the hyperplane for PDE is formulated and investigated. Two-dimensional Helmholtz equation is considered as an example. It is proved that the mixed type conjugation problem for Helmholtz equation, to which the diffraction problem of the electromagnetic wave on thin conducting ribbons is reduced, is equivalent to one-sided mixed type boundary value problem. The uniqueness theorem is proved for this problem

On classification of eigen waves of planar, cylindrical and spherical dielectric waveguides

The planar waveguide is usually considered as a basic element of the integrated optics. In the design of mathematical models of devices of integrated optics, a cylindrical dielectric waveguide and a spherical dielectric waveguide are demonstrated