Electromagnetic Dispersion of a Coaxial Waveguide with an Arbitrary Radial Dielectric Profile

摘要

The electromagnetic dispersion of a coaxial waveguide with an arbitrary radial dielectric profile is obtained by direct integration of Maxwell's equations. The equations are written in cylindrical coordinates and the standard Fourier transformations are performed in the time (t to omega), axial (z to kz), and azimuthal (phi to m) coordinates. The resulting equations are combined to form either one second order differential equation (m = O) or two coupled second order equations (m not equal to O) in the radial coordinate. These equations are integrated for fixed omega and m by a 'shooting' method with kz as the shooting parameter that is, kz is varied until the boundary conditions are satisfied. This yields kz as a function of omega, and hence the dispersion. The field components are directly obtained from the integration. The formulation handles both smoothly varying and discontinuous jumps in the radial dielectric profile. (Author)