Theory of reflections in a tapered waveguide

The tapered waveguide is regarded as a two-mode system, the modes being the forward and reverse waves. A reflection parameter can be defined, relating the amplitude of the reverse wave generated at a point in the taper to the amplitude of the forward wave at that point. The reflection parameter can be regarded as a coupling parameter between the two modes, and coupled-mode theory can be used to obtain theoverall reflection coefficient of the taper. It is shown how to estimate the error in this result. The error may become large if the frequency approaches the cut-off frequency of a guide whose cross-section is the same as that of the narrow end of the taper. The estimation of the error can be used to show how close to cut-off the theory is valid. A detailed analysis is given for the case of a homogeneously-filled tapered waveguide, with perfectly conducting walls, working in the dominant mode. The design of reflectionless tapers is discussed in the light of the results obtained.