This paper presents a rigorous approach for the propagation of electromagnetic (EM) fields along a helical waveguide with slab and rectangular dielectric profiles in the rectangular cross section. The main objective is to develop a numerical method for the calculation of the output fields, for an arbitrary step's angle and the radius of the cylinder of the helical waveguide. The other objectives are to present the technique to calculate the dielectric profiles and their transverse derivatives in the cross-section and to demonstrate the ability of the model to solve practical problems with slab and rectangular dielectric profiles in the rectangular cross section of the helical waveguide. The method is based on Fourier coefficients of the transverse dielectric profile and those of the input wave profile. Laplace transform is necessary to obtain the comfortable and simple input-output connections of the fields. This model is useful for the analysis of helical waveguides with slab and rectangular dielectric profiles in the metallic helical waveguides in the microwave and the millimeter-wave regimes. The output power transmission and the output power density are improved by increasing the step's angle or the radius of the cylinder of the helical waveguide, especially in the cases of space curved waveguides.
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