Solution of Waves Transformation Problem in Axially Symmetric Structures

Abstract

Diffraction problem of the TE 1n -and TM 0n -modes by a system of annular slots in the hollow inner conductor of a coaxial waveguide is considered. Inner conductor is of finite thickness. The waveguide is filled with dielectrics with different permittivities. As a key problem the diffraction problem by a circular-to-coaxial waveguide step discontinuity is solved with the mode-matching technique. The obtained solution is used in the analysis of structures with a finite and semiinfinite number of discontinuities. Dependences of the transmission and reflection coefficients of the dominant mode of a circular and coaxial waveguides as functions of wavenumber and distance between slots are analyzed.

Method of singular integral equations in diffraction by semi-infinite grating: $H$-polarization case

“…The integrand in (17) has singularities at the points that correspond to the cut-off frequencies of Floquet's modes. After accounting for the higher order term of uniform asymptotic presentation obtain the far field representation of the scattered field [34] …”

“…It is used to find the approximation of the solution for the SIG. Specific translation symmetry of the semi-infinite structures meaning that no SIG properties change with its last element removed is used in [15][16][17][18][19]. Scattered field is expressed with the use of the reflection operator obtained by the operator method from the nonlinear operator equation.…”

Wave Diffraction by Semi-Infinite Venetian Blind Type Grating

“…After transformations of (11), (12) and using (16), (17) with an arbitrary function , obtain a nonlinear operator equation to determine the operator R (18) where I is the unit operator.…”

Method of singular integral equations in diffraction by semiinfinite grating: E -polarization case

“…In [8][9][10][11][12][13], the Wiener-Hopf technique was used, while in [14] the canonical problem was solved by the Sommerfeld-Maliuzhinets method. The operator method [15][16][17][18][19] allows us to study different semiinfinite arrays of scatterers. As a result, a nonlinear operator equation may be obtained.…”