Suppose there was a parallel component of electric field. However, E fields perpendicular to the surface can end on local surface charge. These currents prevent the changing magnetic field from meeting the conductor surface at right angles. Thus, considering the inside surface of a pipe of circular cross section, there can be no component of electric field close to the surface either circumferentially, or along the axis of the pipe. Similarly, there can be no component of changing magnetic field meeting the pipe in the radial direction.
Corrugations Now consider circumferential slots cut in the inner wall of the pipe.
This has implications for the effective boundary conditions for electric and changing magnetic fields on a hypothetical surface formed by the envelope of the tops of the ridges either side of the slots. As before, there can be no circumferential component of electric field but there can be a radial component. If the ridges between the slots are very thin, there can be no circulating currents and so there can be a component of changing magnetic field perpendicular to the hypothetical surface. We see therefore that the boundary conditions are the same for both E and H fields, and therefore the propagation constant must be the same for hybrid modes formed originally from a mixture of waveguide TE modes and waveguide TM modes. This fact greatly improves the performance of feeds which generate the hybrid modes needed by reflector antenna structures.