Accurate cutoff wavenumbers of a waveguide perturbed by axially aligned inner conductors

Time-harmonic propagating modes in a perfectly electrically conducting waveguide with constant cross-section ∂D and axis aligned with the z-axis have the form u(x,y)e ^-iωt-iγz where the cross-sectional function u satisfies the two-dimensional Helmholtz equation (Δ+λ)u=0; here k denotes the wavenumber and λ = k ² -γ ² . Propagating modes occur at values λ1 ≤ λ2 ≤ λ3 ≤ ... of λ generating non-trivial solutions of the Helmholtz equation; the cutoff wavenumbers correspond to setting γ to zero. Now suppose that axially aligned PEC structures of cross-section Γ are inserted in the waveguide. The propagation constants are perturbed to values that may be denoted λ1+Δλ1,λ2+Δλ2,...; the cutoff wavenumbers of the empty waveguide are correspondingly perturbed. In this paper we present a reliable, effective and efficient method to obtain the perturbed propagation constants. It allows us to examine the inclusion of multiple strips aligned with the z-axis, with the potential for characterizing propagation in structures with a number of small strip inserts, metamaterial-filled waveguides and so on.