Consider a perfectly electrically conducting waveguide of constant cross-section ∂D and axis aligned with the z-axis. Any time-harmonic propagating mode has the form u(x,y)e -iωt-iyz where the function u satisfies the two-dimensional Helmholtz equation (Δ + λ)u = 0, with k denoting the wavenumber and λ = k 2 - γ 2 . Propagating modes occur at values λ 1 ≤ λ 2 ≤ λ 3 … of λ generating non-trivial solutions of the Helmholtz equation; the cutoff wavenumbers correspond to setting γ to zero. If the waveguide is perturbed by the insertion of axially aligned PEC structures, of cross-section Γ, the propagation constants are perturbed to values λ 1 + Δλ 1 , λ 2 +Δλ 2 ,…, with corresponding perturbations to the cutoff wavenumbers of the empty waveguide.