We model guided modes for an infinitely long metallic structure in the lateral direction that is invariant in the transverse direction, and mechanically supported by a dielectric layer This modeling is done without making any assumptions about the width of the slots relative to the spatial period. We do this by representing the electric field by their Floquet series in combination with a plane wave representation for the field between the plates. Applying the appropriate boundary conditions leads us to a determinantal (or dispersion) equation. Complex solutions to this dispersion equation have been found numerically using a sophisticatedly adjusted downhill method in two dimensions. Finally this new method has been used to show the effect of the variation of four important parameters in the modeling of a periodically loaded open waveguide. These parameters are: the number of space harmonics, the permittivity of the dielectric layer, the slot size and the height of the dielectric layer.