Abstract-This paper presents an improved approach for the propagation of electromagnetic (EM) fields along a helical dielectric waveguide with a circular cross section. The main objective is to develop a mode model for infrared (IR) wave propagation along a helical waveguide, in order to provide a numerical tool for the calculation of the output fields, output power density and output power transmission for an arbitrary step's angle of the helix. Another objective is to apply the inhomogeneous cross section for a hollow waveguide. The derivation is based on Maxwell's equations. The longitudinal components of the fields are developed into the FourierBessel series. The transverse components of the fields are expressed as functions of the longitudinal components in the Laplace plane and are obtained by using the inverse Laplace transform by the residue method. The separation of variables is obtained by using the orthogonalrelations. This model enables us to understand more precisely the influence of the step's angle and the radius of the cylinder of the helix on the output results. The output power transmission and output power density are improved by increasing the step's angle or the radius of the cylinder of the helix, especially in the cases of space curved waveguides. This mode model can be a useful tool to improve the output results in all the cases of the hollow helical waveguides (e.g., in medical and industrial regimes). 160 Menachem and Mond

A transfer matrix function (TMF) is derived for the analysis of electromagnetic (EM) wave propagation in dielectric waveguides with arbitrary profiles, situated inside rectangular metal tubes. The TMF relates the wave profile at the waveguide output to the (arbitrary profile) input wave in the Laplace space. The TMF consists of the Fourier coefficients of the transverse dielectric profile and those of the input-wave profile. The method is applicable for inhomogeneous dielectric profiles with single or multiple maxima in the transverse plane. The TMF is useful for the analysis of dielectric waveguides in the microwave and the millimeter-wave regimes and for diffused optical waveguides in integrated optics.

Abstract-A rigorous approach is derived for the analysis of electromagnetic (EM) wave propagation in dielectric waveguides with arbitrary profiles, situated inside rectangular metal tubes, and along a curved dielectric waveguide. The first objective is to develop a mode model in order to provide a numerical tool for the calculation of the output fields for radius of curvature 0.1 m ≤ R ≤ ∞. Therefore we take into account all the terms in the calculations, without neglecting the terms of the bending. Another objective is to demonstrate the ability of the model to solve practical problems with inhomogeneous dielectric profiles. The method is based on Fourier coefficients of the transverse dielectric profile and those of the input wave profile. These improvements contribute to the application of the model for inhomogeneous dielectric profiles with single or multiple maxima in the transverse plane. This model is useful for the analysis of dielectric waveguides in the microwave and the millimeter-wave regimes, for diffused optical waveguides in integrated optics, and for IR regimes.

Abstract-This paper presents a rigorous approach for the propagation of electromagnetic (EM) fields along a straight hollow waveguide with a circular cross section. The objectives are to present the technique to calculate the dielectric profiles and their transverse derivatives in the inhomogeneous cross section of the cylindrical hollow waveguide, and to understand the influence of the spot-size and cross section on the output fields and output power density. The derivation is based on Maxwell's equations. The longitudinal components of the fields are developed into the Fourier-Bessel series. The transverse components of the fields are expressed as functions of the longitudinal components in the Laplace plane and are obtained by using the inverse Laplace transform by the residue method. The separation of variables is obtained by using the orthogonal-relations. These objectives contribute to the application of the model for the straight hollow waveguide.

Abstract-This paper presents an improved approach for the propagation of electromagnetic (EM) fields along a helical hollow waveguide that consists of two bendings in the same direction. In this case, the objective is to develop a mode model for infrared (IR) wave propagation, in order to represent the effect of the radius of the cylinder of the helix and the step's angle on the output fields and the output power transmission. This model enables us to understand more precisely the influence of the step's angle and the radius of the cylinder of the helix on the output results of each section (bending). The output transverse components of the field, the output power transmission and the output power density for all bending are improved by increasing the step's angle or the radius of the cylinder of the helix, especially in the cases of space curved waveguides. This mode model can be a useful tool to improve the output results in all the cases of the helical hollow waveguides with two bendings for industrial and medical regimes.