On using coupled mode theory and computer simulations to analyze trapped modes in overmoded waveguides

The trapped mode phenomenon occurs in many waveguide structures which have an increase and then a decrease in transverse dimension. We are particularly interested in the phenomenon which occurs in waveguide mode converters and how it affects the power transmission of the main mode. Also, overmoded waveguides are sometimes used in longer transmission lines to reduce attenuation and/or allow for higher power capability. Trapped mode structures also occur in certain special cases such as some gyrotrons. Trapped modes occur because the structure in which the main mode propagates couples to one or more higher order modes which are trapped within some region of the transmission line. The coupling of the trapped modes to other modes can cause a significant reduction in the main power transmission at their respective resonant frequencies. The resonant frequency of a trapped mode can accurately be determined by tracing its round trip path using its phase constant within the structure between the two cutoff points. We study this phenomenon in simple trapped mode systems with rectangular and circular cross sections where ohmic wall loss is also considered. Cases studied include uniform and nonuniform coupling coefficients.;Coupled mode theory is used in the constant coupling cases because of its mathematical simplicity and also its capability to accurately describe these trapped mode phenomena. A scattering matrix technique is used to derive the transmission coefficient of the main mode where the coupling coefficient between the main mode and the trapped mode is nonuniform. The computer simulation programs Ansoft HFSS (finite element method) and Cascade (mode matching method) are used to study the trapped mode phenomenon in trapped mode structures. A method for simulating TE0n circular waveguide modes using HFSS is also presented.;The theoretical value of the phase of the reflection coefficient at the cutoff point in a taper is verified experimentally in rectangular waveguide tapers to be pi/2 for TE mode to a very good approximation. Results from coupled mode theory, a scattering matrix technique, and computer simulations agree very well with each other and those from measurements.