Rigorous analysis of TM modes in arbitrary shaped closed and slotted waveguides

In this thesis, we use Method of Regularization (MoR) to analyse TM modes of closed and slotted waveguides. Cross section of waveguides can be of arbitrary shape assuming that a smooth parametrization is defined. MoR provides us with tools for transforming the corresponding boundary value problems to a functional equation of the second kind. We start with the standard integral representation of the total or scattered field as appropriate in terms of surface quantities. Using Green’s function approach, we obtain a first kind Fredholm integral equation, and convert it into a second kind Fredholm integral equation. The resulting system of infinite linear algebraic equations can be solved effectively using the truncation method, which produces algebraic systems with uniformly bounded condition numbers, when system size tends to infinity. This allows us to predefine truncation number to achieve desired accuracy. Using the connection between cut-off frequencies and normal eigenmodes of a hollow waveguide and the corresponding resonance properties of two-dimensional resonator, we adopt MoR to waveguide problems. We investigate physical features of hollow waveguides of various shapes. Finally, we provide numerical results which show the impact of slot width and wall thickness as well as the qualitative features of the method.