The Toroidal Hollow Waveguide with Smoothly Tapered Cross Section

The stationary electromagnetic boundary value problem with harmonic time dependence eiwt is t is treated for loss-free, slightly inhomogeneous hollow waveguides with circular cross section. Starting from the canonical problem of the homogeneous circular cylinder the influence of small changes of the cross sectional radius and of a slightly bent longitudinal axis on the stationary field problem is investigated. Because the shape of the hollow waveguide changes only slowly, approximate analytical solutions of the field equations can be found applying an improved adiabatic mode theory and a perturbational approach of Rayleigh and Schrodinger.