A set of second-order differential equations associated with reflections in rectangular wave guides — Application to guide connected to horn

In dealing with corners and similar irregularities in rectangular wave guides it is sometimes helpful to transform the system, conformally, into a straight guide. Propagation in the straight guide may then be studied by an integral equation method, as is done in a companion paper, or by a more general method based upon a certain set of ordinary differential equations. Here the second method is developed and applied to determine the reflection produced at the junction of a straight guide and a sectoral horn — a problem the first method is unable to handle. The WKB approximation for a single second-order differential equation is extended to a set of equations and approximate expressions for the reflection coefficient are derived.