A numerical approach to the solution of cylindrical waveguide with discontinuities

Abstract

The wave scattering due to discontinuities in a cylindrical structure with axial symmetry has many applications. Borehole geophysical exploration, wave propagation in optical fibers, and metallic waveguide junctions are a few examples. A systematic approach to solve the general problem using a modal-finite element technique is .presented here. A variational equation is derived from the functional corresponding to the wave equation and its associated boundary conditions. By expanding the fields as a linear combination of waveguide modes, the variational equation is translated into an eigenvalue problem involving symmetric tri-diagonal matrices. Triangular basis functions are used to approximate the waveguide modes. Using the Fortran codes from Eigensystem Package(EISPAC), its eigenvalues and eigenvectors are computed to determine the propagation constants and the amplitude distributions of the waveguide modes. The effect of scattering due to the discontinuities are investigated by calculating the reflection and transmission coefficients. Several computational results are presented and compared with existing data in the literature as well as some experimental data.