Application of the generalized eigenvalue method to the theory of the waveguide partially filled with the dissipative dielectric

The problem of wave propagation through a waveguide partially filled with lossy dielectric has been a subject of interest for several years due to its practical importance. However, a good solution to this problem is not achieved in the general case because of the mathematical difficulties caused by the radiation condition which is enforced at an infinite distance from the exciting sources. In the present work we leave out the radiation condition and intend to use the bounded absorption principle together with the generalized eigenvalue method. The latter is adopted in some points in order to apply it to infinite waveguides. The approach we used is based on two ideas which are as follows: a) the original infinite lossy waveguide boundary problem may be replaced by a finite short-circuited waveguide i.e. resonator boundary problem. b) The electromagnetic field excited may be treated as an analytical function of the slab´s dielectric constant and can be computed by means of the analytical expansion