The determination of the propagation constant for the traveling wave in an infinite ground plane

The propagation constant for the travelling wave in a trough in an infinite ground plane is examined. The null-field integral is used to determine the electromagnetic field in the trough structure, and pulse basis functions give the distribution of the aperture fields. From this, the propagation constant is solved for, using the Newton-Raphson iterative scheme. Various sizes of geometries are examined. The far-field patterns are calculated and compared with other solutions, thereby validating the integral formulation which subsequently provided the propagation constant. Measurements of two trough geometries are performed to validate the theoretical results