Flexible hollow waveguide with two bendings for small values of step angles, and applications

Abstract—This paper presents an improved approach for the propagation of electromagnetic (EM) fields in the case of the flexible 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 along the flexible hollow waveguide, in order to provide a numerical tool for the calculation of the output fields, output power density and output power transmission. The main steps of the method for the two bendings will introduced in the derivation, in detail, for small values of step angles. The derivation for the first section and the second section of the waveguide with the two bendings is based on Maxwell’s equations. The separation of variables is obtained by using the orthogonal-relations. 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. This model can be a useful tool in all the cases of the hollow toroidal waveguides, e.g., in medical and industrial regimes. 1