Analysis of global eigenmodes in an oversized rectangular waveguide with a hard surface on one broad wall for planar slot array antenna applications

The problem of determining the eigenmodes of a rectangular waveguide with one broad hard wall formed by longitudinal corrugations with grooves filled with dielectric is considered. The dispersion equation is derived on the basis of using the asymptotic boundary conditions for corrugated surfaces. It is shown analytically that if the groove depth is equal to the value 0.25lambda/(epsiv-1)^1/2 corresponding to the hard wall condition, the TE eigenmode spectrum of the waveguide comprises an infinite set of degenerated quasi-TEM modes with different transverse propagation constants and identical longitudinal propagation constants equal to the wavenumber k. Such solutions are important for understanding the local waves appearing along ridges in such waveguides, that has inspired to the invention of new so-called gap waveguides.