High-Frequency Behavior of Waveguides with Finite Surface Impedances

It is known1-8 that in certain waveguides the field becomes, under certain conditions, very small at the boundary. Consider, for instance, a corrugated waveguide of radius a and let X be the free-space wavelength. This waveguide is characterized at the boundary by finite surface impedance Z2 in the longitudinal direction. The frequency dependence of which is determined by the depth of the corruga89 tions, causes the transverse field distribution f/(x, y) of a mode to vary with the frequency k = 2-n/X. However, this frequency dependence virtually disappears (for all modes except surface waves) if the waveguide dimensions are large enough. In fact, one finds that p(x, y) approaches for ka --> oo a frequency independent distribution that vanishes at the boundary.5 This behavior is responsible for the low attenuation constant, for the excellent radiation characteristics, and the wide bandwidth of corrugated waveguides.5 We show here that the same behavior also occurs, under quite general conditions, in a variety of uncorrugated waveguides.1"21 Figures la and lb show two examples, a dielectric waveguide7,8,13-16 of general cross section and a hollow waveguide with metal walls coated by a dielectric layer.4,17 Other examples can be obtained by modifying the boundary conditions in a variety of different ways. For instance, several dielectric layers may be used in Fig. lb, or a metal grid of transverse wires may be placed at the boundary, as pointed out in Section II. Other examples are the waveguides of dielectric or lossy metal considered in Ref.