"Mode-coupling" regions in the dispersion curves of modulated slow wave antennas

It is known that the fields present on an open periodic structure can be expressed as an infinite sum of space harmonics, and that each of these space harmonics which is a fast wave along the surface corresponds to a radiating beam. The radiation characteristics can be conveniently represented in the form of a k vs. B diagram, or dispersion curve, on which radiation generally occurs when the operating point is located outside of a set of specified triangles.