Trapezoidal waveguides: first-order propagation equivalence with rectangular waveguides

In the present paper we present in detail a new and improved version of the method of perturbative equivalence between the propagation characteristics of lossless trapezoidal cross-section waveguides and of rectangular cross-section waveguides. The analysis is carried out within the framework of perturbation theory, and to the first order we develop a very simple geometrical argument that allows one to construct for any given waveguide with trapezoidal cross-section an equivalent waveguide with rectangular cross-section. The numerical investigation of our arguments shows excellent agreement between the propagation characteristics of the two equivalent structures